B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 DATA STEP DATA FROM SAS PAGE 1 Variable # Cases Mean Std Deviation Variance Maximum Minimum X1 1 200 0.5257740339 0.2992056380 0.8952401382E-01 0.9968891912 0.6794007961E-02 X2 2 200 0.5191878884 0.2754967521 0.7589846044E-01 0.9966007485 0.6840690039E-03 X3 3 200 0.5308405059 0.3052396354 0.9317123499E-01 0.9995712438 0.5675205030E-03 X4 4 200 0.5213826903 0.3013271057 0.9079802465E-01 0.9988806187 0.2327912953E-02 Y 5 200 181.1989898 112.4971517 12655.60914 526.0827413 -109.1417754 ERROR 6 200 -0.7677099926E-01 0.9929132743 0.9858767702 2.295684846 -2.928427817 PROBIT 7 200 0.2041411926E-01 1.193899645 1.425396363 3.175865987 -3.267589781 PROBITY 8 200 0.5250000000 0.5006277466 0.2506281407 1.000000000 0.000000000 TOBITY 9 200 0.4757206434 0.6843406651 0.4683221459 3.175865987 0.000000000 YGLS 10 200 181.2593487 112.3273828 12617.44093 525.4371403 -108.7959724 CONSTANT 11 200 1.000000000 0.000000000 0.000000000 1.000000000 1.000000000 Number of observations in data file 200 Current missing variable code 1.000000000000000E+31 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 DATA STEP DATA FROM SAS PAGE 2 SETTING MADE BY BYSET IHEAD = 1 IMAXLN = 57 IPAGE = 2 ILINE= 59 IFILL= 0 IDIREC= 1 ICOL(1-2)= 132 80 IFMT(1-2)= 16 8 RFFMT = (G16.8) IFFMT= (I8) ILINES= 132 OUTPUT (IOUTP) = 2 LISTPR (List parse Table) 0 LISTGE (List generated Code) 0 Printing using byplin_2 string at col 50 integer at 1 10 real*4 at 40 40.0000000 real*8 at 80 80.00000000000000 ISCREEN set as 0 MISSING SET AS 1.000000000000000E+31 READMISS SET AS 0 DROPMISS SET AS 0 SEED SET AS 123457.0000000000 MAXVAR SET AS 99 IBATCH SET AS 4 ISPEAK SET AS 0 USED44 SET AS 0 USED46 SET AS 0 SPACE 1 SET AS 12000000 SPACE 2 SET AS 0 HEADER 1= DATA STEP HEADER 2= DATA FROM SAS DPMPAR(1) = 1.110223024625157E-16 DPMPAR(2) = 2.225073858507201E-308 DPMPAR(3) = 1.797693134862316E+308 ICHECK = 1 TIMELIMIT = 0 NOLABEL = 0 SP = 0 MAXMLENG = 1500 MAXNSENT = 1600 MAXNTOKEN = 9000 MAXLP = 150 MAXTG = 2000 MAXTEMP = 40 FORTMATH = 1 MENULOG = 0 SAVEMENU = 1 FLAG = 1 AUTOEXEC = 0 JULIAN 1 = -999999999 JULIAN 2 = 0 JULIAN 3 = 0 SASDATE = 1 FREQ = 1.000000000000000E+31 DISPLAYM(1) = 0 DISPLAYM(2) = 0 DISPLAYM(3) = 1 DISPLAYM(4) = 0 ALLRUN = 1 MAXLLINES = 255 MAXOLINES = 255 The internal version of B34S is: 8.10R EDITOR = keditw IB34SEDIT = 0 GRAPHSUF = wmf FSAVESUF = fsv PBUNIT = 18 PBNAME = _b34spb.b34 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 DATA STEP DATA FROM SAS PAGE 3 THUNIT = 19 THNAME = _b34sth.hlp SHUNIT = 20 SHUNAME(1) = c:\b34slm\b34sshel.mac SHNAME(2) = c:\b34slm\example.mac SHNAME(3) = c:\b34slm\matrix.mac SHNAME(4) = c:\b34slm\matrix2.mac SHNAME(5) = c:\b34slm\ratspgm.mac SHNAME(6) = c:\b34slm\matlab.mac SHNAME(7) = c:\b34slm\b34stest.mac SHNAME(8) = c:\b34slm\scapgm.mac SHNAME(9) = c:\b34slm\finpgm.mac MENUNAME = c:\b34slm\menu.mac GRAPHNAME = c:\b34slm\graph.mac MATMENU = c:\b34slm\matmenu.mac CITILIST = d:\citibase\citimaxi.lst NEWCITI = c:\b34slm\_newciti.lst MACPATH = B34PATH = FSVPATH = HELPFN = c:\b34slm\b34shelp.dat CLEANTEMP = 0 QUICKFSV = 0 RECVER = 6 RNVER = 6 SAVEASGET(1) = 0 SAVEASGET(2) = 0 DMMODE = 2 GPORT = lpt1 GDRIVER = WINMETAFILE INTERACTER(1)= c:\b34slm\interact.ini INTERACTER(2)= SPEAKEASY(1) = speakez SPEAKEASY(2) = c:\speakez\bin\speakez.exe LOCATION = c:\b34slm\ IGRCHARSET = H SERIALNUM(1) = Dr. Houston H. Stokes PhD SERIALNUM(2) = 1991/1 SERIALNUM(3) = 99.9 SERIALNUM(4) = 31 12 2030 SERIALNUM(5) = Administrator SERIALNUM(6) = UIC-JHY9T9B5W8A GFACTOR = 1.000000000000000 BIOS = 0 IMODE = 0 GMODE 1 = 1280 GMODE 2 = 1024 GMODE 3 = 256 GMODE 4 = 132 GMODE 5 = 25 GMODE 6 = 256 GMODE 7 = 0 GMODE 8 = 132 GMODE 9 = 30 INC = 1 BCOLOR 1 = 1 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 DATA STEP DATA FROM SAS PAGE 4 BCOLOR 2 = 8 BCOLOR 3 = 0 BCOLOR 4 = 0 MOUSE 1 = 1 MOUSE 2 = 1 MOUSE 3 = 0 MOUSE 4 = 3 MOUSE 5 = 3 MOUSE 6 = 3 MOUSE 7 = 3 MOUSE 8 = 3 MOUSE 9 = 3 IWIDTH = 16 NFP = 1 Hardcopy Codes in effect for Version 7 1 -999 2 -999 3 -999 4 -999 5 -999 6 0 7 -999 8 -999 9 -999 10 -999 11 -999 12 -999 13 -999 14 -999 15 -999 16 -999 17 -999 18 -999 19 -999 20 -999 21 -999 22 -999 23 -999 24 -999 25 -999 26 -999 27 -999 D3FILL = 0 STYLE = 0 PRINTERSET = 0 GRAYSCALE 1 = 0 GRAYSCALE 2 = 0 D3AXISFILL 1 = 0 D3AXISFILL 2 = 175 D3AXISFILL 3 = 223 D3AXISFILL 4 = 175 D3AXISFILL 5 = 223 D3AXISFILL 6 = 175 D3AXISFILL 7 = 223 D3INVERT 1 = 0 D3INVERT 2 = 0 D3INVERT 3 = 0 PSPACEON = 0 I GCOLOR GLINE ICHARR ITICK IDASH 1 223 0 1 0 0 2 31 0 2 0 0 3 95 0 3 0 0 4 159 0 4 0 0 5 127 0 5 0 0 6 79 0 6 0 0 7 239 0 7 0 0 8 143 0 8 0 0 9 111 0 9 0 0 WINDOW 1 WBORDER 1 WCOLOR 0 WBCOLOR 7 WTCOLOR 13 WTBCOLOR 7 WBORDERC 0 WBORDERC2 0 WINDOW 2 WBORDER 10 WCOLOR 0 WBCOLOR 15 WTCOLOR 13 WTBCOLOR 7 WBORDERC 10 WBORDERC2 0 WINDOW 3 WBORDER 9 WCOLOR 0 WBCOLOR 15 WTCOLOR 9 WTBCOLOR 7 WBORDERC 1 WBORDERC2 0 WINDOW 4 WBORDER 10 WCOLOR 0 WBCOLOR 15 WTCOLOR 0 WTBCOLOR 15 WBORDERC 5 WBORDERC2 0 CCODE( 1) = 223, TCOLOR( 1) = 223 CCODE( 2) = 175, TCOLOR( 2) = 175 CCODE( 3) = 111, TCOLOR( 3) = 111 CCODE( 4) = 159, TCOLOR( 4) = 159 CCODE( 5) = 47, TCOLOR( 5) = 47 CCODE( 6) = 207, TCOLOR( 6) = 207 CCODE( 7) = 143, TCOLOR( 7) = 143 CCODE( 8) = 239, TCOLOR( 8) = 239 CCODE( 9) = 255, TCOLOR( 9) = 255 CCODE(10) = 79, TCOLOR(10) = 79 CCODE(11) = 95, TCOLOR(11) = 95 CCODE(12) = 127, TCOLOR(12) = 127 CCODE(13) = 31, TCOLOR(13) = 31 CCODE(14) = 191, TCOLOR(14) = 191 CCODE(15) = 63, TCOLOR(15) = 63 CCODE(16) = 0, TCOLOR(16) = 0 Codes for Windows Color number Color Name Size Color Value 1 BLACKCHR 8 0 2 BLACKBKG 8 0 3 BLUEBKG 7 5 4 BLUECHR 7 5 5 GREENBKG 8 3 6 + 1 3 7 GREENCHR 8 3 8 REDBKG 6 3 9 REDCHR 6 1 10 MAGENTABKG 10 1 11 MAGENTACHR 10 6 12 YELLOWBKG 9 6 13 YELLOWCHR 9 2 14 WHITEBKG 8 2 15 WHITECHR 8 7 16 DEFAULT 7 7 17 NORMAL 6 7 18 FLASH 5 7 19 INVERSE 7 112 20 BRIGHT 6 15 21 BRITE 5 8 22 CYANBKG 7 48 23 CYANCHR 7 3 24 NONE 4 0 25 SINGLE 6 1 26 DOUBLE 6 2 27 SINGLE2 7 3 28 DROPSHADOW 10 4 29 FIELD3D1 8 5 30 FIELD3D2 8 6 31 BUTTON3D1 9 7 32 BUTTON3D2 9 8 33 WINDOW3D1 9 9 34 WINDOW3D2 9 10 35 BLACK 5 0 36 RED 3 1 37 YELLOW 6 2 38 GREEN 5 3 39 CYAN 4 4 40 BLUE 4 5 41 MAGENTA 7 6 42 WHITE 5 7 43 GRAY 4 8 44 BRED 4 9 45 BYELLOW 7 10 46 BGREEN 6 11 47 BCYAN 5 12 48 BBLUE 5 13 49 BMAGENTA 8 14 50 BWHITE 6 15 51 NO 2 0 52 YES 3 1 53 DBLUE 5 5 54 PURPLE 6 6 55 BROWN 5 9 56 DWHITE 6 7 57 LAVENDER 8 12 58 GREENBOLD 9 11 59 BLUEBOLD 8 13 60 YELLOWBOLD 10 10 61 BPURPLE 7 14 62 BOLD 4 1 63 FLASH 5 2 64 ITALICS 7 4 65 REVERSE 7 8 66 UNDERLINE 9 16 67 DEFAULT 7 0 MVAR = 11 NOOB = 200 NBTOT = 0 IDBUG = 0 IBATCH = 4 ISAS = 2 IDBUGP = 0 ITRACE = 0 IBBACK = 0 ISPEAK = 0 IFLAG2 = 0 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 REG STEP DATA FROM SAS PAGE 5 REG Command. Version 1 February 1997 Real*8 space available 6000000 Real*8 space used 2099 OLS Estimation Dependent variable Y Adjusted R**2 0.1987082220491153 Standard Error of Estimate 101.6544318325568 Sum of Squared Residuals 1860052.232015989 Model Sum of Squares 654707.8592918504 Total Sum of Squares 2514760.091307839 F(15, 180) 4.223803061157623 F Significance 0.9999988698393326 1/Condition of XPX 2.700050086873703E-03 Number of Observations 196 Durbin-Watson 1.705582328884095 Variable Coefficient Std. Error t X1 { 0} 36.700195 25.356789 1.4473518 X1 { 1} 51.573398 25.441123 2.0271667 X1 { 2} 14.794559 25.705287 0.57554539 X1 { 3} -14.103493 25.699559 -0.54878346 X1 { 4} -23.135432 25.737881 -0.89888642 X2 { 0} 190.27311 28.281279 6.7278820 X2 { 1} -7.4036032 27.985780 -0.26454876 X2 { 2} -21.425668 28.095851 -0.76259188 X2 { 3} 28.621753 28.224150 1.0140873 X2 { 4} 9.2789807 28.160261 0.32950620 X3 { 0} -29.855442 24.548647 -1.2161747 X3 { 1} -16.228915 25.361241 -0.63991015 X3 { 2} -4.7403050 25.281999 -0.18749724 X3 { 3} -9.8471768 24.543097 -0.40121981 X4 { 0} 25.767054 25.239951 1.0208837 CONSTANT { 0} 62.136675 52.754395 1.1778483 Test restriction # 1 Sets to zero Variable Lag X1 0 X1 1 X1 2 X1 3 X1 4 Unrestricted Error SS 1860052.2 Restricted Error SS 1936315.9 F( 5, 180) 1.4760302 Significance 0.80023715 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 REG STEP DATA FROM SAS PAGE 6 REG Command. Version 1 February 1997 Real*8 space available 6000000 Real*8 space used 735 OLS Estimation Dependent variable Y Adjusted R**2 0.2132399381593797 Standard Error of Estimate 99.78440673900759 Sum of Squared Residuals 1941600.926509862 Model Sum of Squares 576865.2920057867 Total Sum of Squares 2518466.218515649 F( 4, 195) 14.48401811171018 F Significance 0.9999999997746845 1/Condition of XPX 1.595289077758794E-02 Number of Observations 200 Durbin-Watson 1.706553837600136 Variable Coefficient Std. Error t X1 { 0} 37.101680 24.293083 1.5272528 X2 { 0} 180.94994 26.652402 6.7892544 X3 { 0} -33.430182 23.239249 -1.4385225 X4 { 0} 17.392541 23.781001 0.73136285 CONSTANT { 0} 76.422798 25.409288 3.0076717 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 ROBUST STEP DATA FROM SAS PAGE 7 ROBUST Command. Version 1 September 1997 Real*8 space available 6000000 Real*8 space used 4627 OLS Estimation Dependent variable Y Adjusted R**2 0.1987082220491153 Standard Error of Estimate 101.6544318325568 Sum of Squared Residuals 1860052.232015989 Model Sum of Squares 654707.8592918504 Total Sum of Squares 2514760.091307839 F(15, 180) 4.223803061157623 F Significance 0.9999988698393326 1/Condition of XPX 2.700050086873703E-03 Number of Observations 196 Durbin-Watson 1.705582328884095 Variable Coefficient Std. Error t X1 { 0} 36.700195 25.356789 1.4473518 X1 { 1} 51.573398 25.441123 2.0271667 X1 { 2} 14.794559 25.705287 0.57554539 X1 { 3} -14.103493 25.699559 -0.54878346 X1 { 4} -23.135432 25.737881 -0.89888642 X2 { 0} 190.27311 28.281279 6.7278820 X2 { 1} -7.4036032 27.985780 -0.26454876 X2 { 2} -21.425668 28.095851 -0.76259188 X2 { 3} 28.621753 28.224150 1.0140873 X2 { 4} 9.2789807 28.160261 0.32950620 X3 { 0} -29.855442 24.548647 -1.2161747 X3 { 1} -16.228915 25.361241 -0.63991015 X3 { 2} -4.7403050 25.281999 -0.18749724 X3 { 3} -9.8471768 24.543097 -0.40121981 X4 { 0} 25.767054 25.239951 1.0208837 CONSTANT { 0} 62.136675 52.754395 1.1778483 Dependent variable Y Adjusted R**2 0.1987082220491153 OLS sum of squared residuals 1860052.232015989 1/Condition of XPX 2.700050086873703E-03 OLS sum of abs(e(t)) 15172.79792007064 Magnitude of largest OLS abs(e(t)) 280.2688216450601 Number of Observations 196 # of iterations to calculate L1 47 L1 output rank 16 L1 sum of squared residuals 1955813.818620441 L1 sum of abs(e(t)) 14837.77923636093 Magnitude of largest L1 abs(e(t)) 327.9089040148737 # of iterations to calculate Minimax 37 Minimax output rank 16 Minimax sum of squared residuals 2514164.930475321 Minimax sum of abs(e(t)) 18246.90704079920 Magnitude of largest Minimax abs(e(t)) 207.3598916674693 Variable OLS Beta L1 Beta Minimax Beta X1 { 0} 36.700195 4.2449324 98.544039 X1 { 1} 51.573398 75.133390 4.3084444 X1 { 2} 14.794559 23.150964 -6.8845024 X1 { 3} -14.103493 -31.863043 34.734083 X1 { 4} -23.135432 -46.926610 30.330075 X2 { 0} 190.27311 221.92652 197.01486 X2 { 1} -7.4036032 31.184038 -52.445273 X2 { 2} -21.425668 -33.264394 14.562257 X2 { 3} 28.621753 23.312520 127.20703 X2 { 4} 9.2789807 0.95685742 -21.391927 X3 { 0} -29.855442 -17.048859 32.670934 X3 { 1} -16.228915 -42.123039 8.7768559 X3 { 2} -4.7403050 -13.802464 -43.090500 X3 { 3} -9.8471768 -13.079985 -71.919918 X4 { 0} 25.767054 37.571180 -6.8654539 CONSTANT { 0} 62.136675 75.965493 -21.207245 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 ROBUST STEP DATA FROM SAS PAGE 8 ROBUST Command. Version 1 September 1997 Real*8 space available 6000000 Real*8 space used 2146 OLS Estimation Dependent variable Y Adjusted R**2 0.2132399381593797 Standard Error of Estimate 99.78440673900759 Sum of Squared Residuals 1941600.926509862 Model Sum of Squares 576865.2920057867 Total Sum of Squares 2518466.218515649 F( 4, 195) 14.48401811171018 F Significance 0.9999999997746845 1/Condition of XPX 1.595289077758794E-02 Number of Observations 200 Durbin-Watson 1.706553837600136 Variable Coefficient Std. Error t X1 { 0} 37.101680 24.293083 1.5272528 X2 { 0} 180.94994 26.652402 6.7892544 X3 { 0} -33.430182 23.239249 -1.4385225 X4 { 0} 17.392541 23.781001 0.73136285 CONSTANT { 0} 76.422798 25.409288 3.0076717 Dependent variable Y Adjusted R**2 0.2132399381593797 OLS sum of squared residuals 1941600.926509862 1/Condition of XPX 1.595289077758794E-02 OLS sum of abs(e(t)) 15718.36129058969 Magnitude of largest OLS abs(e(t)) 293.5289966198676 Number of Observations 200 # of iterations to calculate L1 13 L1 output rank 5 L1 sum of squared residuals 1953950.879518387 L1 sum of abs(e(t)) 15675.92139494121 Magnitude of largest L1 abs(e(t)) 295.7411280167460 # of iterations to calculate Minimax 11 Minimax output rank 5 Minimax sum of squared residuals 2268291.373094921 Minimax sum of abs(e(t)) 17180.67367285009 Magnitude of largest Minimax abs(e(t)) 237.1906336112048 Variable OLS Beta L1 Beta Minimax Beta X1 { 0} 37.101680 18.713195 19.488628 X2 { 0} 180.94994 198.10686 174.62254 X3 { 0} -33.430182 -20.815167 -23.439924 X4 { 0} 17.392541 26.270163 -91.270418 CONSTANT { 0} 76.422798 65.864961 116.84103 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 REGRESSION STEP DATA FROM SAS PAGE 9 Comment TEST OF COMMENT IN NEW SYNTEXT ******************************************************************** Problem Number 1 Subproblem Number 1 F to enter 9.999999776482582E-03 F to remove 4.999999888241291E-03 Tolerance (1.-R**2) for including a variable 1.000000000000000E-05 Maximum Number of Variables Allowed 5 Internal Number of dependent variable 5 Dependent Variable Y Standard Error of Y 112.4971516895854 Degrees of Freedom 199 ............. Step Number 5 Analysis of Variance for reduction in SS due to variable entering Variable Entering 3 Source DF SS MS F F Sig. Multiple R 0.478596 Due Regression 4 0.57687E+06 0.14422E+06 14.484 1.000000 Std Error of Y.X 99.7844 Dev. from Reg. 195 0.19416E+07 9956.9 R Square 0.229054 Total 199 0.25185E+07 12656. Multiple Regression Equation Variable Coefficient Std. Error T Val. T Sig. P. Cor. Elasticity Partial Cor. for Var. not in equation Y = Variable Coefficient F for selection X1 X- 1 37.10168 24.29308 1.527 0.87168 0.1087 0.1077 X2 X- 2 180.9499 26.65240 6.789 1.00000 0.4372 0.5185 X3 X- 3 -33.43018 23.23925 -1.439 0.84811 -0.1025 -0.9794E-01 X4 X- 4 17.39254 23.78100 0.7314 0.53456 0.0523 0.5005E-01 CONSTANT X-11 76.42280 25.40929 3.008 0.99702 Adjusted R Square 0.2132399381593819 -2 * ln(Maximum of Likelihood Function) 2403.716622088913 Akaike Information Criterion (AIC) 2415.716622088913 Scwartz Information Criterion (SIC) 2435.506526288202 Akaike (1970) Finite Prediction Error 10205.85102396207 Generalized Cross Validation 10212.23367000583 Hannan & Quinn (1979) HQ 10552.05080003704 Shibata (1981) 10193.40486417675 Rice (1984) 10218.95224478872 Residual Variance 9956.927828255679 Order of entrance (or deletion) of the variables = 11 4 2 1 3 Estimate of Computational Error in Coefficients 1 2 3 4 5 -0.389026E-13 -0.132313E-12 0.855453E-13 -0.867737E-14 -0.147727E-12 Covariance Matrix of Regression Coefficients Row 1 Variable X- 1 X1 590.15390 Row 2 Variable X- 2 X2 -148.42147 710.35055 Row 3 Variable X- 3 X3 15.431688 -18.914277 540.06268 Row 4 Variable X- 4 X4 -19.951931 92.770449 -38.185490 565.53602 Row 5 Variable X-11 CONSTANT -231.01814 -329.09769 -265.07141 -312.26537 645.63192 Program terminated. All variables put in. Residual Statistics for Original data Von Neumann Ratio 1 ... 1.71513 Durbin-Watson TEST..... 1.70655 Von Neumann Ratio 2 ... 1.71513 For D. F. 195 t(.9999)= 3.9726, t(.999)= 3.3411, t(.99)= 2.6013, t(.95)= 1.9722, t(.90)= 1.6527, t(.80)= 1.2859 Skewness test (Alpha 3) = -.368088 , Peakedness test (Alpha 4)= 3.02977 Normality Test -- Extended grid cell size = 20.00 t Stat Infin 1.653 1.286 1.039 0.843 0.676 0.525 0.386 0.254 0.126 Cell No. 20 15 21 22 19 17 22 32 16 16 Interval 1.000 0.900 0.800 0.700 0.600 0.500 0.400 0.300 0.200 0.100 Act Per 1.000 0.900 0.825 0.720 0.610 0.515 0.430 0.320 0.160 0.080 Normality Test -- Small sample grid cell size = 40.00 Cell No. 35 43 36 54 32 Interval 1.000 0.800 0.600 0.400 0.200 Act Per 1.000 0.825 0.610 0.430 0.160 Extended grid normality test - Prob of rejecting normality assumption Chi= 11.00 Chi Prob= 0.7983 F(8, 195)= 1.37500 F Prob =0.790482 Small sample normality test - Large grid Chi= 7.750 Chi Prob= 0.9485 F(3, 195)= 2.58333 F Prob =0.945430 Autocorrelation function of residuals 1 2 3 4 0.139325 0.648638E-01 0.350550E-01 0.145067 F( 67, 67) = 1.065 1/F = 0.9392 Heteroskedasticity at 0.6009 level Sum of squared residuals 1941600.926509862 Mean squared residual 9708.004632549309 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 REGRESSION STEP DATA FROM SAS PAGE 10 Specification test option selected Graph of residual against X1 Residual 242.42 * . * * * . * . * . * * . * . . . . * . * . . . *. . . . . . . * . . . . . . * . . . . * .. * . . . . . . * . . .. . * . . . . . . . * . . . . . . . . * . . . . . . . * . . . . . . * . . * . . . . . . . . * . . . .. . . . * . . * . . . . . . . *-------------------------.-----------------------------.-----------------.----------------.-.------- * . . . . . * . . . . . . . . . . . . . . *. . . . . . . .. . . * . . . . * . . * . . . . . * . . . . . . . . * . . . .. . *. . . . . * . . . . * . . . * . . . . * . . . * . * . * . . . * . *. * . * . . * * * . * . * . * . * . -293.53 ***************************************************************************************************** 0.67940E-02 0.99689 X1 Residual Sorted against X1 Mod Von Neumann Test 1.984631060975060 Durbin Watson 2.025341441713007 Correlation -9.769161125976622E-16 T statistic for parabola -1.504949022387046 F( 66, 66) = 0.997205 1/F = 1.00280 , Het. at 0.504517641 level Graph of residual against X2 Residual 242.42 * . * * * . * . * . * * . * . . . . * . * . . . * . . . . . . . * . . .. . . * . . * . . . * . . . . .. * . . . . . * . . .. * . *. . . .. . . . * . . .. . . . * . . . . . .. . . . * . . . . . .. . * . . . . . . . . * . . . . . . . . . . . *------------------------------------.------------------------------------.--.----..----------------- * . . . . . * . . . . . . . . . * . . . * . . . . . . . . . . . * . . . . . . . . * . .. . . * .. . . . . . . * . * . . . * . . . . . *. . . . * . . . * . . . . * . .. * . * . * . . . * . * . * . * . . * * * . * . * . * . * . -293.53 ***************************************************************************************************** 0.68407E-03 0.99660 X2 Residual Sorted against X2 Mod Von Neumann Test 2.033895332348161 Durbin Watson 2.075616262242478 Correlation 3.571554978112946E-16 T statistic for parabola 0.1496918623849102 F( 66, 66) = 0.806087 1/F = 1.24056 , Het. at 0.808251722 level B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 REGRESSION STEP DATA FROM SAS PAGE 11 Residual estimates using BLUS transformation option 5 BLUS 1 0.5596 1 2 3 4 5 BLUS 2 0.6168 1 2 3 4 200 BLUS 3 0.6586 1 2 3 199 200 BLUS 4 0.7408 1 2 198 199 200 BLUS 5 0.7157 1 197 198 199 200 BLUS 6 0.6966 196 197 198 199 200 Eigval 1 = 0.29967970 Eigval 2 = 0.22151996 Eigval 3 = 0.11795804 Eigval 4 = 0.99927092E-01 Eigval 5 = 0.17573433E-02 1/ condition of BLUS base X0 MATRIX 0.14936998E-02 BLUS....Sum Eig. = 0.7408 Obs. Deleted = 1 2 198 199 200 Residual Statistics for Original data Von Neumann Ratio 1 ... 1.75588 Durbin-Watson TEST..... 1.74687 Von Neumann Ratio 2 ... 1.75601 Skewness test (Alpha 3) = -.440456 , Peakedness test (Alpha 4)= 3.31441 Normality Test -- Extended grid cell size = 19.50 t Stat Infin 1.653 1.286 1.039 0.843 0.676 0.525 0.386 0.254 0.126 Cell No. 15 21 20 20 18 18 29 19 23 12 Interval 1.000 0.900 0.800 0.700 0.600 0.500 0.400 0.300 0.200 0.100 Act Per 1.000 0.923 0.815 0.713 0.610 0.518 0.426 0.277 0.179 0.062 Normality Test -- Small sample grid cell size = 39.00 Cell No. 36 40 36 48 35 Interval 1.000 0.800 0.600 0.400 0.200 Act Per 1.000 0.815 0.610 0.426 0.179 Extended grid normality test - Prob of rejecting normality assumption Chi= 9.564 Chi Prob= 0.7030 F(8, 195)= 1.19551 F Prob =0.696522 Small sample normality test - Large grid Chi= 2.974 Chi Prob= 0.6044 F(3, 195)= 0.991453 F Prob =0.602080 Autocorrelation function of residuals 1 2 3 4 0.125798 0.413757E-01 0.672477E-01 0.168740 F( 65, 64) = 1.059 1/F = 0.9442 Heteroskedasticity at 0.5905 level Sum of squared residuals 1941600.926510028 Mean squared residual 9956.927828256556 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 REGRESSION STEP DATA FROM SAS PAGE 12 Specification test option selected Graph of residual against X1 Residual 245.88 * . * * * . . * . * * * . * . *. . * . .. . . . . * . . . . . . . * . . . . * . . . . . . . * . . . . . * . . . . . . * . . . . . . . . * . . . . . . . * . . . . . .* .. *. * . . . . . * . . . . . . . . . * . . . . . . . . *-.-----------------------.-----------.----------.-------------.-----------------------------------.- * . . * . . . . *. . . . . . . . . . * . . . . . . . . . . * . * . . .. .. . * . . . . . . * . . * . . * . . *. . . . * . . . . . . * . . * . . . . . . * . . * . .* . * . * . . *. . * . * * . * . . * . * . * . * * . * * . * . -310.56 ***************************************************************************************************** 0.67940E-02 0.99689 X1 Residual Sorted against X1 Mod Von Neumann Test 2.016097014993753 Durbin Watson 2.005758055942327 Correlation -0.1003783163263148 T statistic for parabola -1.227549029996674 F( 65, 65) = 0.943053 1/F = 1.06039 , Het. at 0.593064172 level Graph of residual against X2 Residual 245.88 * . * * * .. * . * * * . * . * . . * . . . . . . . * . . * . . . * .. . . * . * . . . . * .. . . . * . . . . . . *. . . . . . * * . . . . . . . * . . . . . .. . . . .. . . * . . .. . * . . . . . . . . . * . . . . . . . . *---------------.------.-------------------------------------------.------.----.------.-------------- * . . . .. . . . * . . . . . . . . . . * . . . . . . .. . . * . .. . .. . . . . * . . . . . . . . . . * . . . . . . * . . . . *. . . . . . * . . * . . . . . . * . . * . . . . . * . * . . * . . * . * * . * . . * . * . * . * * . * * . * . -310.56 ***************************************************************************************************** 0.68407E-03 0.99660 X2 Residual Sorted against X2 Mod Von Neumann Test 2.105677908584879 Durbin Watson 2.094879560335543 Correlation -1.975227488952105E-02 T statistic for parabola 0.3718480239382690 F( 65, 65) = 0.702122 1/F = 1.42425 , Het. at 0.921680701 level B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 REGRESSION STEP DATA FROM SAS PAGE 13 Residual estimates using BLUS transformation option 2 Eigval 1 = 0.24120784 Eigval 2 = 0.16893620 Eigval 3 = 0.10961214 Eigval 4 = 0.76311824E-01 Eigval 5 = 0.52051824E-01 1/ condition of BLUS base X0 MATRIX 0.31650049E-01 BLUS....Sum Eig. = 0.6481 Obs. Deleted = 98 99 100 101 102 Residual Statistics for Original data Von Neumann Ratio 1 ... 1.70121 Durbin-Watson TEST..... 1.69249 Von Neumann Ratio 2 ... 1.70225 Skewness test (Alpha 3) = -.452173 , Peakedness test (Alpha 4)= 3.19344 Normality Test -- Extended grid cell size = 19.50 t Stat Infin 1.653 1.286 1.039 0.843 0.676 0.525 0.386 0.254 0.126 Cell No. 19 15 21 19 23 19 27 19 19 14 Interval 1.000 0.900 0.800 0.700 0.600 0.500 0.400 0.300 0.200 0.100 Act Per 1.000 0.903 0.826 0.718 0.621 0.503 0.405 0.267 0.169 0.072 Normality Test -- Small sample grid cell size = 39.00 Cell No. 34 40 42 46 33 Interval 1.000 0.800 0.600 0.400 0.200 Act Per 1.000 0.826 0.621 0.405 0.169 Extended grid normality test - Prob of rejecting normality assumption Chi= 6.282 Chi Prob= 0.3843 F(8, 195)= 0.785256 F Prob =0.383816 Small sample normality test - Large grid Chi= 3.077 Chi Prob= 0.6201 F(3, 195)= 1.02564 F Prob =0.617639 Autocorrelation function of residuals 1 2 3 4 0.145759 0.571571E-01 0.578062E-01 0.134562 F( 67, 67) = 1.028 1/F = 0.9728 Heteroskedasticity at 0.5447 level Sum of squared residuals 1941600.926509863 Mean squared residual 9956.927828255706 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 REGRESSION STEP DATA FROM SAS PAGE 14 Specification test option selected Graph of residual against X1 Residual 232.71 * . * . * * * .. * * . * . . . . * * . . * . . . . *. . . . . . . * . . . . .. . .. * . . . . . * . . . . * . . . . . .. . . . * . . . . . * . . . .* . . . . * . . . . . . . .. * . . . . . . . . * . . . . . * . . . . . . . . *----------------------.---.---------------------.--------------------.-------------------.----.---.- * .. . . *. . . . . . . . .. . . * . . . . . . . * .. . .. . .. . . . . * . . . . . . . . * . . . . * *. . . . . . * . . . . . . . . . * . . * . . . . . * . . * . . . . * . . * * . .. * . * . *. . * . * * . * * . * . . * . * * . -300.00 ***************************************************************************************************** 0.67940E-02 0.99689 X1 Residual Sorted against X1 Mod Von Neumann Test 2.083104653054245 Durbin Watson 2.072422065089860 Correlation -4.585703839256972E-02 T statistic for parabola -1.405146109932507 F( 65, 65) = 1.00213 1/F = 0.997878 , Het. at 0.503403291 level Graph of residual against X2 Residual 232.71 * . * . * * * . . * * . * . . . . * * . . * . . . . * . . . . . . . * . * . * . . . * . *. . * . . .. * . . . . . . . . . . *. . . . . * . . . . . . . . . . * . . . . . . . . . * . . . . .. . . * . . . . . * . . . .. . . . *-------------.----------------------------------.---------------.---.---------.------.----.--------- * . . . . * . . . . . . . . . . .. * . . . . . . . * . . . . . .. . . .. . * ... . . . . . * . . . . . . * . . . . . . * . . . . . . . .. * . . *. . . . . * . . * . . . . * . . * * . . . * . * . * . . * . * * . * * . * . . * . * * . -300.00 ***************************************************************************************************** 0.68407E-03 0.99660 X2 Residual Sorted against X2 Mod Von Neumann Test 2.043064692408453 Durbin Watson 2.032587437575585 Correlation -1.486229532231687E-02 T statistic for parabola 0.3947835170475859 F( 65, 65) = 0.834228 1/F = 1.19871 , Het. at 0.766489341 level B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 REGRESSION STEP DATA FROM SAS PAGE 15 ******************************************************************** Problem Number 1 Subproblem Number 2 F to enter 9.999999776482582E-03 F to remove 4.999999888241291E-03 Tolerance (1.-R**2) for including a variable 1.000000000000000E-05 Maximum Number of Variables Allowed 5 Internal Number of dependent variable 5 Dependent Variable Y Standard Error of Y 112.4971516895854 Degrees of Freedom 199 ............. Step Number 5 Analysis of Variance for reduction in SS due to variable entering Variable Entering 4 Source DF SS MS F F Sig. Multiple R 0.478596 Due Regression 4 0.57687E+06 0.14422E+06 14.484 1.000000 Std Error of Y.X 99.7844 Dev. from Reg. 195 0.19416E+07 9956.9 R Square 0.229054 Total 199 0.25185E+07 12656. Multiple Regression Equation Variable Coefficient Std. Error T Val. T Sig. P. Cor. Elasticity Partial Cor. for Var. not in equation Y = Variable Coefficient F for selection X1 X- 1 37.10168 24.29308 1.527 0.87168 0.1087 0.1077 X2 X- 2 180.9499 26.65240 6.789 1.00000 0.4372 0.5185 X3 X- 3 -33.43018 23.23925 -1.439 0.84811 -0.1025 -0.9794E-01 X4 X- 4 17.39254 23.78100 0.7314 0.53456 0.0523 0.5005E-01 CONSTANT X-11 76.42280 25.40929 3.008 0.99702 Adjusted R Square 0.2132399381593820 -2 * ln(Maximum of Likelihood Function) 2403.716622088913 Akaike Information Criterion (AIC) 2415.716622088913 Scwartz Information Criterion (SIC) 2435.506526288202 Akaike (1970) Finite Prediction Error 10205.85102396207 Generalized Cross Validation 10212.23367000582 Hannan & Quinn (1979) HQ 10552.05080003703 Shibata (1981) 10193.40486417675 Rice (1984) 10218.95224478872 Residual Variance 9956.927828255677 Order of entrance (or deletion) of the variables = 2 11 1 3 4 Estimate of Computational Error in Coefficients 1 2 3 4 5 -0.353040E-12 0.568096E-13 -0.433699E-13 -0.762624E-14 0.244765E-12 Covariance Matrix of Regression Coefficients Row 1 Variable X- 1 X1 590.15390 Row 2 Variable X- 2 X2 -148.42147 710.35055 Row 3 Variable X- 3 X3 15.431688 -18.914277 540.06268 Row 4 Variable X- 4 X4 -19.951931 92.770449 -38.185490 565.53602 Row 5 Variable X-11 CONSTANT -231.01814 -329.09769 -265.07141 -312.26537 645.63192 Program terminated. All variables put in. Residual Statistics for Original data Von Neumann Ratio 1 ... 1.71513 Durbin-Watson TEST..... 1.70655 Von Neumann Ratio 2 ... 1.71513 For D. F. 195 t(.9999)= 3.9726, t(.999)= 3.3411, t(.99)= 2.6013, t(.95)= 1.9722, t(.90)= 1.6527, t(.80)= 1.2859 Skewness test (Alpha 3) = -.368088 , Peakedness test (Alpha 4)= 3.02977 Normality Test -- Extended grid cell size = 20.00 t Stat Infin 1.653 1.286 1.039 0.843 0.676 0.525 0.386 0.254 0.126 Cell No. 20 15 21 22 19 17 22 32 16 16 Interval 1.000 0.900 0.800 0.700 0.600 0.500 0.400 0.300 0.200 0.100 Act Per 1.000 0.900 0.825 0.720 0.610 0.515 0.430 0.320 0.160 0.080 Normality Test -- Small sample grid cell size = 40.00 Cell No. 35 43 36 54 32 Interval 1.000 0.800 0.600 0.400 0.200 Act Per 1.000 0.825 0.610 0.430 0.160 Extended grid normality test - Prob of rejecting normality assumption Chi= 11.00 Chi Prob= 0.7983 F(8, 195)= 1.37500 F Prob =0.790482 Small sample normality test - Large grid Chi= 7.750 Chi Prob= 0.9485 F(3, 195)= 2.58333 F Prob =0.945430 Autocorrelation function of residuals 1 2 3 4 0.139325 0.648638E-01 0.350550E-01 0.145067 F( 67, 67) = 1.065 1/F = 0.9392 Heteroskedasticity at 0.6009 level Sum of squared residuals 1941600.926509862 Mean squared residual 9708.004632549308 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 REGRESSION STEP DATA FROM SAS PAGE 16 Specification test option selected Reciprocal of matrix condition for XPX for complete sample 0.15952891E-01 BLUS obs . Del 1 2 3 4 5 BLUS....Sum eigenvalues = 0.76641885 BLUS obs . Del 1 2 3 4 200 BLUS....Sum eigenvalues = 0.74892412 BLUS obs . Del 1 2 3 199 200 BLUS....Sum eigenvalues = 0.75777436 BLUS obs . Del 1 2 198 199 200 BLUS....Sum eigenvalues = 0.77796342 BLUS obs . Del 1 197 198 199 200 BLUS....Sum eigenvalues = 0.68367531 BLUS obs . Del 196 197 198 199 200 BLUS....Sum eigenvalues = 0.59463451 ------------------------------------------- For MVN analysis on data sorted against X1 the optimum base selected from among 6 choices listed above is: BLUS obs . Del 1 2 198 199 200 1 Eigenvalue = 0.4310E-01 2 Eigenvalue = 0.6499E-01 3 Eigenvalue = 0.1576 4 Eigenvalue = 0.2381 5 Eigenvalue = 0.2742 BLUS....Sum eigenvalues = 0.77796342 Sum of squared BLUS residuals = 1941600.9 BLUS efficiency 0.66406743 BLUS implied coefficient vector Name OLS Coef OLS SE BLUS coef OLS - BLUS 1/condition X0 0.25784842E-01 X1 X- 1 37.10168 24.29308 36.66797 0.4337140 X2 X- 2 180.9499 26.65240 185.7688 -4.818849 X3 X- 3 -33.43018 23.23925 -79.49648 46.06630 X4 X- 4 17.39254 23.78100 11.41498 5.977562 CONSTANT X-11 76.42280 25.40929 100.0766 -23.65382 Residual Sorted against X1 Mod Von Neumann Test 2.031613167711146 Durbin Watson 2.021194638645956 Correlation -5.407853895794336E-03 T statistic for parabola -1.639977255126764 F( 65, 65) = 1.05353 1/F = 0.949193 , Het. at 0.582922474 level BLUS obs . Del 98 99 100 101 102 BLUS....Sum eigenvalues = 0.49858765 BLUS obs . Del 99 100 101 102 103 BLUS....Sum eigenvalues = 0.47993144 ------------------------------------------- For data sorted against X1 the optimum base for Heteroskedasticity test is: BLUS obs . Del 98 99 100 101 102 1 Eigenvalue = 0.4893E-03 2 Eigenvalue = 0.2924E-01 3 Eigenvalue = 0.8159E-01 4 Eigenvalue = 0.1409 5 Eigenvalue = 0.2464 BLUS....Sum eigenvalues = 0.49858765 Sum of squared BLUS residuals = 1941600.9 BLUS efficiency 0.61178270 BLUS implied coefficient vector Name OLS Coef OLS SE BLUS coef OLS - BLUS 1/condition X0 0.47852074E-03 X1 X- 1 37.10168 24.29308 45.03257 -7.930888 X2 X- 2 180.9499 26.65240 171.7492 9.200706 X3 X- 3 -33.43018 23.23925 -64.58755 31.15736 X4 X- 4 17.39254 23.78100 19.94511 -2.552572 CONSTANT X-11 76.42280 25.40929 91.14406 -14.72126 Residual Sorted against X1 Mod Von Neumann Test 2.046828413155442 Durbin Watson 2.036331857190525 Correlation -2.023783730381042E-02 T statistic for parabola -1.552070738860072 F( 97, 98) = 0.964295 1/F = 1.03703 , Het. at 0.570906735 level BLUS obs . Del 50 51 149 150 151 BLUS....Sum eigenvalues = 0.63733357 BLUS obs . Del 50 51 52 150 151 BLUS....Sum eigenvalues = 0.59566742 ------------------------------------------- For data sorted against X1 the optimum base for convexity test using a parabola is: BLUS obs . Del 50 51 149 150 151 1 Eigenvalue = 0.2049E-01 2 Eigenvalue = 0.6697E-01 3 Eigenvalue = 0.1508 4 Eigenvalue = 0.1656 5 Eigenvalue = 0.2335 BLUS....Sum eigenvalues = 0.63733357 Sum of squared BLUS residuals = 1941600.9 BLUS efficiency 0.64866780 BLUS implied coefficient vector Name OLS Coef OLS SE BLUS coef OLS - BLUS 1/condition X0 0.14966350E-01 X1 X- 1 37.10168 24.29308 18.67477 18.42691 X2 X- 2 180.9499 26.65240 174.0250 6.924967 X3 X- 3 -33.43018 23.23925 -40.00458 6.574397 X4 X- 4 17.39254 23.78100 16.97621 0.4163291 CONSTANT X-11 76.42280 25.40929 90.37078 -13.94798 Residual Sorted against X1 Mod Von Neumann Test 2.050582143859339 Durbin Watson 2.040066337993389 Correlation 6.965713894547480E-02 T statistic for parabola -1.534252879660240 F( 65, 65) = 1.04083 1/F = 0.960775 , Het. at 0.563826996 level BLUS obs . Del 1 2 3 4 5 BLUS....Sum eigenvalues = 0.63812478 BLUS obs . Del 1 2 3 4 200 BLUS....Sum eigenvalues = 0.65955957 BLUS obs . Del 1 2 3 199 200 BLUS....Sum eigenvalues = 0.70708425 BLUS obs . Del 1 2 198 199 200 BLUS....Sum eigenvalues = 0.74769785 BLUS obs . Del 1 197 198 199 200 BLUS....Sum eigenvalues = 0.71200434 BLUS obs . Del 196 197 198 199 200 BLUS....Sum eigenvalues = 0.73896097 ------------------------------------------- For MVN analysis on data sorted against X2 the optimum base selected from among 6 choices listed above is: BLUS obs . Del 1 2 198 199 200 1 Eigenvalue = 0.4310E-01 2 Eigenvalue = 0.6964E-01 3 Eigenvalue = 0.1446 4 Eigenvalue = 0.1598 5 Eigenvalue = 0.3306 BLUS....Sum eigenvalues = 0.74769785 Sum of squared BLUS residuals = 1941600.9 BLUS efficiency 0.66048495 BLUS implied coefficient vector Name OLS Coef OLS SE BLUS coef OLS - BLUS 1/condition X0 0.34175649E-01 X1 X- 1 37.10168 24.29308 11.60265 25.49903 X2 X- 2 180.9499 26.65240 214.0608 -33.11090 X3 X- 3 -33.43018 23.23925 -56.25838 22.82819 X4 X- 4 17.39254 23.78100 -25.03357 42.42611 CONSTANT X-11 76.42280 25.40929 109.1158 -32.69303 Residual Sorted against X2 Mod Von Neumann Test 2.015179186713154 Durbin Watson 2.004844934473595 Correlation -0.1123449241694724 T statistic for parabola 4.083494889319034E-04 F( 65, 65) = 0.916136 1/F = 1.09154 , Het. at 0.637459175 level BLUS obs . Del 98 99 100 101 102 BLUS....Sum eigenvalues = 0.57912359 BLUS obs . Del 99 100 101 102 103 BLUS....Sum eigenvalues = 0.51286126 ------------------------------------------- For data sorted against X2 the optimum base for Heteroskedasticity test is: BLUS obs . Del 98 99 100 101 102 1 Eigenvalue = 0.2679E-02 2 Eigenvalue = 0.6304E-01 3 Eigenvalue = 0.9623E-01 4 Eigenvalue = 0.1619 5 Eigenvalue = 0.2552 BLUS....Sum eigenvalues = 0.57912359 Sum of squared BLUS residuals = 1941600.9 BLUS efficiency 0.62879631 BLUS implied coefficient vector Name OLS Coef OLS SE BLUS coef OLS - BLUS 1/condition X0 0.21402885E-02 X1 X- 1 37.10168 24.29308 35.77540 1.326277 X2 X- 2 180.9499 26.65240 196.3926 -15.44261 X3 X- 3 -33.43018 23.23925 -10.79800 -22.63218 X4 X- 4 17.39254 23.78100 -6.245113 23.63765 CONSTANT X-11 76.42280 25.40929 59.45592 16.96688 Residual Sorted against X2 Mod Von Neumann Test 2.063077549821929 Durbin Watson 2.052497664951038 Correlation -5.371751126950044E-02 T statistic for parabola -4.857854167924352E-02 F( 97, 98) = 0.833297 1/F = 1.20005 , Het. at 0.815122626 level BLUS obs . Del 50 51 149 150 151 BLUS....Sum eigenvalues = 0.54521463 BLUS obs . Del 50 51 52 150 151 BLUS....Sum eigenvalues = 0.53374496 ------------------------------------------- For data sorted against X2 the optimum base for convexity test using a parabola is: BLUS obs . Del 50 51 149 150 151 1 Eigenvalue = 0.6443E-02 2 Eigenvalue = 0.7369E-01 3 Eigenvalue = 0.9187E-01 4 Eigenvalue = 0.1685 5 Eigenvalue = 0.2047 BLUS....Sum eigenvalues = 0.54521463 Sum of squared BLUS residuals = 1941600.9 BLUS efficiency 0.63293131 BLUS implied coefficient vector Name OLS Coef OLS SE BLUS coef OLS - BLUS 1/condition X0 0.52998782E-02 X1 X- 1 37.10168 24.29308 -14.13395 51.23563 X2 X- 2 180.9499 26.65240 188.8497 -7.899808 X3 X- 3 -33.43018 23.23925 -45.36150 11.93132 X4 X- 4 17.39254 23.78100 -1.158222 18.55076 CONSTANT X-11 76.42280 25.40929 122.4077 -45.98491 Residual Sorted against X2 Mod Von Neumann Test 2.066797431831964 Durbin Watson 2.056198470643078 Correlation 1.931137455326071E-03 T statistic for parabola -3.204230812248495E-02 F( 65, 65) = 0.900829 1/F = 1.11009 , Het. at 0.662501699 level B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 REGRESSION STEP DATA FROM SAS PAGE 17 ******************************************************************** Problem Number 1 Subproblem Number 3 F to enter 9.999999776482582E-03 F to remove 4.999999888241291E-03 Tolerance (1.-R**2) for including a variable 1.000000000000000E-05 Maximum Number of Variables Allowed 5 Internal Number of dependent variable 10 Dependent Variable YGLS Standard Error of Y 112.3273828117338 Degrees of Freedom 199 ............. Step Number 5 Analysis of Variance for reduction in SS due to variable entering Variable Entering 4 Source DF SS MS F F Sig. Multiple R 0.478524 Due Regression 4 0.57495E+06 0.14374E+06 14.478 1.000000 Std Error of Y.X 99.6383 Dev. from Reg. 195 0.19359E+07 9927.8 R Square 0.228985 Total 199 0.25109E+07 12617. Multiple Regression Equation Variable Coefficient Std. Error T Val. T Sig. P. Cor. Elasticity Partial Cor. for Var. not in equation YGLS = Variable Coefficient F for selection X1 X- 1 36.97290 24.25751 1.524 0.87092 0.1085 0.1072 X2 X- 2 180.5791 26.61337 6.785 1.00000 0.4370 0.5172 X3 X- 3 -33.88166 23.20522 -1.460 0.85412 -0.1040 -0.9923E-01 X4 X- 4 17.36442 23.74618 0.7313 0.53450 0.0523 0.4995E-01 CONSTANT X-11 76.99775 25.37208 3.035 0.99726 Adjusted R Square 0.2131694351905976 -2 * ln(Maximum of Likelihood Function) 2403.130449749594 Akaike Information Criterion (AIC) 2415.130449749594 Scwartz Information Criterion (SIC) 2434.920353948883 Akaike (1970) Finite Prediction Error 10175.98287719891 Generalized Cross Validation 10182.34684397639 Hannan & Quinn (1979) HQ 10521.16947507865 Shibata (1981) 10163.57314198281 Rice (1984) 10189.04575637375 Residual Variance 9927.788172876983 Order of entrance (or deletion) of the variables = 2 11 1 3 4 Estimate of Computational Error in Coefficients 1 2 3 4 5 -0.352389E-12 0.567126E-13 -0.434240E-13 -0.732862E-14 0.245408E-12 Covariance Matrix of Regression Coefficients Row 1 Variable X- 1 X1 588.42677 Row 2 Variable X- 2 X2 -147.98710 708.27166 Row 3 Variable X- 3 X3 15.386526 -18.858923 538.48215 Row 4 Variable X- 4 X4 -19.893540 92.498950 -38.073737 563.88094 Row 5 Variable X-11 CONSTANT -230.34205 -328.13456 -264.29566 -311.35151 643.74243 Program terminated. All variables put in. Residual Statistics for Original data Von Neumann Ratio 1 ... 1.73475 Durbin-Watson TEST..... 1.72608 Von Neumann Ratio 2 ... 1.73475 For D. F. 195 t(.9999)= 3.9726, t(.999)= 3.3411, t(.99)= 2.6013, t(.95)= 1.9722, t(.90)= 1.6527, t(.80)= 1.2859 Skewness test (Alpha 3) = -.362689 , Peakedness test (Alpha 4)= 3.02070 Normality Test -- Extended grid cell size = 20.00 t Stat Infin 1.653 1.286 1.039 0.843 0.676 0.525 0.386 0.254 0.126 Cell No. 19 17 21 21 18 19 22 30 17 16 Interval 1.000 0.900 0.800 0.700 0.600 0.500 0.400 0.300 0.200 0.100 Act Per 1.000 0.905 0.820 0.715 0.610 0.520 0.425 0.315 0.165 0.080 Normality Test -- Small sample grid cell size = 40.00 Cell No. 36 42 37 52 33 Interval 1.000 0.800 0.600 0.400 0.200 Act Per 1.000 0.820 0.610 0.425 0.165 Extended grid normality test - Prob of rejecting normality assumption Chi= 7.300 Chi Prob= 0.4954 F(8, 195)= 0.912500 F Prob =0.492846 Small sample normality test - Large grid Chi= 5.550 Chi Prob= 0.8643 F(3, 195)= 1.85000 F Prob =0.860549 Autocorrelation function of residuals 1 2 3 4 0.129482 0.634141E-01 0.334666E-01 0.146625 F( 67, 67) = 1.058 1/F = 0.9447 Heteroskedasticity at 0.5916 level Sum of squared residuals 1935918.693711016 Mean squared residual 9679.593468555080 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 REGRESSION STEP DATA FROM SAS PAGE 18 Doing Gen. Least Squares using residual Dif. Eq. of order 1 Lag Coefficients 1 0.130802 Standard Error of Y 127.7705255310685 Degrees of Freedom 198 ............. Step Number 5 Analysis of Variance for reduction in SS due to variable entering Variable Entering 4 Source DF SS MS F F Sig. Multiple R 0.471720 Due Regression 4 0.71927E+06 0.17982E+06 13.881 1.000000 Std Error of Y.X 113.817 Dev. from Reg. 194 0.25131E+07 12954. R Square 0.222519 Total 198 0.32324E+07 16325. Multiple Regression Equation Variable Coefficient Std. Error T Val. T Sig. P. Cor. Elasticity Partial Cor. for Var. not in equation YGLS = Variable Coefficient F for selection X1 X- 1 28.01962 23.87897 1.173 0.75793 0.0839 0.8128E-01 X2 X- 2 177.6227 26.53948 6.693 1.00000 0.4331 0.5088 X3 X- 3 -38.25370 22.58822 -1.694 0.90804 -0.1207 -0.1120 X4 X- 4 19.64566 23.27903 0.8439 0.60025 0.0605 0.5651E-01 CONSTANT X-11 83.94545 25.46559 3.296 0.99884 Adjusted R Square 0.2064889203070728 -2 * ln(Maximum of Likelihood Function) 2444.041264822915 Akaike Information Criterion (AIC) 2456.041264822915 Scwartz Information Criterion (SIC) 2475.801093771262 Akaike (1970) Finite Prediction Error 13279.79736781824 Generalized Cross Validation 13288.18616239565 Hannan & Quinn (1979) HQ 13731.91786082520 Shibata (1981) 13263.44132612963 Rice (1984) 13297.01880853800 Residual Variance 12954.31213821485 Order of entrance (or deletion) of the variables = 2 11 3 1 4 Covariance Matrix of Regression Coefficients Row 1 Variable X- 1 X1 570.20526 Row 2 Variable X- 2 X2 -148.53666 704.34381 Row 3 Variable X- 3 X3 10.106222 -7.3459240 510.22779 Row 4 Variable X- 4 X4 -24.737127 89.645131 -21.007478 541.91303 Row 5 Variable X-11 CONSTANT -213.75994 -331.58097 -261.60129 -305.90872 648.49652 Program terminated. All variables put in. Residual Statistics for Smoothed Original data For GLS Y and Y estimate scaled by 0.8691984013524984 Von Neumann Ratio 1 ... 1.98583 Durbin-Watson TEST..... 1.97585 Von Neumann Ratio 2 ... 1.98583 For D. F. 194 t(.9999)= 3.9730, t(.999)= 3.3414, t(.99)= 2.6014, t(.95)= 1.9723, t(.90)= 1.6527, t(.80)= 1.2859 Skewness test (Alpha 3) = -.293127 , Peakedness test (Alpha 4)= 2.93323 Normality Test -- Extended grid cell size = 19.90 t Stat Infin 1.653 1.286 1.039 0.843 0.676 0.525 0.386 0.254 0.126 Cell No. 18 21 19 15 25 18 22 23 18 20 Interval 1.000 0.900 0.800 0.700 0.600 0.500 0.400 0.300 0.200 0.100 Act Per 1.000 0.910 0.804 0.709 0.633 0.508 0.417 0.307 0.191 0.101 Normality Test -- Small sample grid cell size = 39.80 Cell No. 39 34 43 45 38 Interval 1.000 0.800 0.600 0.400 0.200 Act Per 1.000 0.804 0.633 0.417 0.191 Extended grid normality test - Prob of rejecting normality assumption Chi= 3.864 Chi Prob= 0.1308 F(8, 194)= 0.483040 F Prob =0.132667 Small sample normality test - Large grid Chi= 1.879 Chi Prob= 0.4022 F(3, 194)= 0.626466 F Prob =0.401282 Autocorrelation function of residuals 1 2 3 4 0.345094E-02 0.410309E-01 0.921176E-02 0.163523 F( 66, 66) = 1.012 1/F = 0.9884 Heteroskedasticity at 0.5189 level Sum of squared residuals 2513136.554813672 Mean squared residual 12628.82690861142 Gen. Least Squares ended by satisfying tolerance. B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 LIST STEP DATA FROM SAS PAGE 19 Listing for observation 1 to observation 50. Obs X1 X2 X3 X4 Y PROBITY TOBITY YGLS 1 0.8400 0.3141 0.3875 0.2927 206.6 1.000 0.3398 205.1 2 0.7478 0.8673 0.5845 0.5654E-01 224.5 0.000 0.000 224.0 3 0.2145 0.7982 0.2076 0.3773 195.3 0.000 0.000 195.6 4 0.5241 0.8776 0.5673 0.2823 211.6 0.000 0.000 212.2 5 0.5250 0.8467 0.3747 0.3709 324.9 1.000 0.7628 325.4 6 0.9279 0.9947 0.2888 0.1420 526.1 1.000 2.649 525.4 7 0.1019 0.2376 0.9633 0.8230 216.6 1.000 1.180 214.3 8 0.3717 0.6957 0.5932 0.6969 156.3 0.000 0.000 155.2 9 0.8146 0.7722 0.9620 0.9314 149.4 1.000 0.7156 150.1 10 0.5571 0.7312 0.9886 0.9065 336.0 1.000 2.405 336.8 11 0.5719 0.7755 0.7737 0.4260E-01 61.73 0.000 0.000 60.51 12 0.9747 0.6252 0.1472 0.1289 64.65 0.000 0.000 66.31 13 0.8212 0.5956 0.7149 0.1512 113.3 0.000 0.000 115.0 14 0.4041 0.1753 0.4054 0.6205 32.71 0.000 0.000 33.55 15 0.4939E-01 0.1043 0.5167 0.4005 30.06 0.000 0.000 30.98 16 0.4140 0.9524 0.2635 0.3619E-01 360.8 1.000 0.4397 361.5 17 0.2821 0.1968 0.8239 0.5820 173.0 1.000 0.5183 172.2 18 0.8622 0.8007 0.8860 0.9294 405.1 1.000 3.176 404.4 19 0.5842 0.2915 0.6953 0.6358 172.7 1.000 0.5601 171.0 20 0.3957 0.3382 0.6013 0.2519 180.4 0.000 0.000 180.0 21 0.5595 0.8305 0.1042 0.1504 239.6 0.000 0.000 239.3 22 0.9502 0.4561 0.4020 0.8539 309.3 1.000 1.879 309.6 23 0.8511 0.7793 0.4375 0.8628 344.0 1.000 1.872 342.8 24 0.2508 0.8190 0.4448 0.9840 256.5 1.000 0.5428 255.6 25 0.6408 0.1267 0.9964 0.1583 157.8 1.000 0.6032 157.7 26 0.3116 0.3650 0.5502 0.7893 221.6 1.000 0.6681 220.9 27 0.1498 0.3852 0.4961 0.5708 149.6 0.000 0.000 149.0 28 0.9355 0.8057 0.7030 0.8154 375.5 1.000 2.571 375.6 29 0.1383 0.9035E-01 0.5659 0.2825 131.9 0.000 0.000 130.6 30 0.2148 0.1261 0.5521 0.5063 3.913 0.000 0.000 3.559 31 0.4053 0.3015 0.2490 0.6241 113.5 0.000 0.000 114.5 32 0.3071E-01 0.8460E-01 0.9103 0.7043 9.734 0.000 0.000 10.17 33 0.2892 0.1012 0.5030 0.5747 38.38 0.000 0.000 39.10 34 0.5535 0.7131 0.2545 0.1503 86.03 0.000 0.000 86.69 35 0.1673 0.9566E-01 0.6993 0.2618 115.7 0.000 0.000 117.2 36 0.7425 0.8168 0.2258 0.9836 258.9 1.000 0.6980 258.7 37 0.9560 0.9143 0.1234 0.4616 301.7 1.000 0.5779 301.8 38 0.8462 0.4745 0.1291 0.2418 236.2 1.000 0.6395E-01 236.1 39 0.6106 0.7100 0.4748 0.9835E-01 329.8 1.000 0.9098 329.4 40 0.9020 0.5383 0.4337 0.3613 323.1 1.000 1.468 322.1 41 0.6258 0.6593 0.3673 0.7450 310.5 1.000 1.242 309.3 42 0.2365 0.1339 0.2725 0.6764 116.3 0.000 0.000 115.4 43 0.5350 0.4620 0.8285 0.1229 118.2 0.000 0.000 118.3 44 0.9653 0.1604 0.9431 0.9204 206.0 1.000 1.991 206.4 45 0.4110 0.8413 0.8002 0.6017 230.3 1.000 0.5473 229.3 46 0.4929 0.7902 0.4065 0.7245 239.8 1.000 0.3212 239.9 47 0.3654 0.4395E-01 0.6382 0.6996 122.9 1.000 0.9147E-01 123.0 48 0.1327E-01 0.9692 0.7882 0.1189 192.2 0.000 0.000 191.9 49 0.4893E-01 0.3401 0.6125 0.5834 25.13 0.000 0.000 25.81 50 0.9039E-02 0.9168 0.8776 0.3172E-01 120.9 0.000 0.000 122.1 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 PLOT STEP DATA FROM SAS PAGE 20 Y 526.1 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ** * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * * * * * * * * ** * * ** * * * * * * ** * * * * * * * * * * ** * * * * * * * * * * * * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ** * * * * * * * * * * * * -109.1 ***************************************************************************************************** 0.6794E-02 0.9969 X1 TEST OF THE NEW GRAPH OPTION B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 PLOT STEP DATA FROM SAS PAGE 21 PLOT FOR T = 10 TO 30 Individual scale for all variables plotted Variable Code Max Min 1 Y X- 5 Y 405.07 3.9131 2 X1 X- 1 X 0.97469 0.49390E-01 3 X2 X- 2 Z 0.95236 0.90353E-01 ***************************************************************************************************** 10 * * * * 11 * * * * 12 * * * * 13 * * * * 14 * * * * 15 *** * 16 * * * * 17 * * * * 18 * * * * 19 * * * * 20 * * * * 21 * * * * 22 * * * * 23 * * * * 24 * * * * 25 * * * * 26 * * * * 27 * * * * 28 * * * * 29 ** * * 30 ** * * B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 PROBIT STEP DATA FROM SAS PAGE 22 Multivariate Probit Analysis (June 1995). Equation # 1 Dependent variable is X- 8 PROBITY The iteration has converged. 1/ Cond of variance covariance of coef 9.267575665617762E-03 # of Iterations 4 Log of likelihood function -108.2917334994993 Convergence tolerance 1.000000000000000E-05 **Summary of results** Partial Derivatives Variable Max Likelihood Est. Std. Error t score At Max Den. At X Mean X-11 CONSTANT -2.6895391 0.42825579 -6.2802166 -1.0729647 -1.0697039 X- 1 X1 1.6357691 0.34843599 4.6946043 0.65257372 0.65059051 X- 2 X2 0.93448991 0.38073679 2.4544250 0.37280540 0.37167243 X- 3 X3 1.3697772 0.34203925 4.0047370 0.54645893 0.54479821 X- 4 X4 1.3335310 0.34455043 3.8703505 0.53199884 0.53038207 Variance Covariance Matrix 1 2 3 4 5 1 0.183403 -0.766710E-01 -0.883034E-01 -0.815342E-01 -0.872582E-01 2 -0.766710E-01 0.121408 -0.106886E-01 0.205627E-01 0.144841E-01 3 -0.883034E-01 -0.106886E-01 0.144961 0.788580E-02 0.279290E-01 4 -0.815342E-01 0.205627E-01 0.788580E-02 0.116991 0.950113E-02 5 -0.872582E-01 0.144841E-01 0.279290E-01 0.950113E-02 0.118715 At point of means, E(dependent variable) 0.5311236988676484 # of observations 200 # limits 95 # nonlimits 105 (-2.0) times the log likelihood ratio 60.17519668303342 Distributed as Chi squared with DF 4 Significance of Chi squared statistic 0.9999999999973349 Calculated probabilities for selected obs. 1 - 5 Obs. # Y value Yhat Error Density 1 1.0000000 0.45985283 0.54014717 0.3969205 2 0.0000000 0.58710418 -0.58710418 0.3893950 3 0.0000000 0.21034350 -0.21034350 0.2884781 4 0.0000000 0.55620259 -0.55620259 0.3949768 5 1.0000000 0.48734172 0.51265828 0.3987414 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 PROBIT STEP DATA FROM SAS PAGE 23 Multivariate Probit Analysis (June 1995). Equation # 1 Dependent variable is X- 8 PROBITY The iteration has converged. 1/ Cond of variance covariance of coef 9.267575665617762E-03 # of Iterations 4 Log of likelihood function -108.2917334994993 Convergence tolerance 1.000000000000000E-05 **Summary of results** Partial Derivatives Variable Max Likelihood Est. Std. Error t score At Max Den. At X Mean X-11 CONSTANT -2.6895391 0.42825579 -6.2802166 -1.0729647 -1.0697039 X- 1 X1 1.6357691 0.34843599 4.6946043 0.65257372 0.65059051 X- 2 X2 0.93448991 0.38073679 2.4544250 0.37280540 0.37167243 X- 3 X3 1.3697772 0.34203925 4.0047370 0.54645893 0.54479821 X- 4 X4 1.3335310 0.34455043 3.8703505 0.53199884 0.53038207 Variance Covariance Matrix 1 2 3 4 5 1 0.183403 -0.766710E-01 -0.883034E-01 -0.815342E-01 -0.872582E-01 2 -0.766710E-01 0.121408 -0.106886E-01 0.205627E-01 0.144841E-01 3 -0.883034E-01 -0.106886E-01 0.144961 0.788580E-02 0.279290E-01 4 -0.815342E-01 0.205627E-01 0.788580E-02 0.116991 0.950113E-02 5 -0.872582E-01 0.144841E-01 0.279290E-01 0.950113E-02 0.118715 At point of means, E(dependent variable) 0.5311236988676484 # of observations 200 # limits 95 # nonlimits 105 (-2.0) times the log likelihood ratio 60.17519668303342 Distributed as Chi squared with DF 4 Significance of Chi squared statistic 0.9999999999973349 Evaluation at specified points - specification 1 Variable Max likelihood est Specified point Partial derivative CONSTANT -2.6895391 1.0000000 -1.0728311 X1 1.6357691 0.30100000 0.65249245 X2 0.93448991 0.81180000 0.37275898 X3 1.3697772 0.53084051 0.54639088 X4 1.3335310 0.52138269 0.53193259 At specified point calculated point for depandent variable -2075521457 Evaluation at specified points - specification 2 Variable Max likelihood est Specified point Partial derivative CONSTANT -2.6895391 1.0000000 -1.0546943 X1 1.6357691 0.44400000 0.64146170 X2 0.93448991 0.77712000 0.36645728 X3 1.3697772 0.53084051 0.53715383 X4 1.3335310 0.52138269 0.52293997 At specified point calculated point for depandent variable -767850553 Calculated probabilities for selected obs. 1 - 5 Obs. # Y value Yhat Error Density 1 1.0000000 0.45985283 0.54014717 0.3969205 2 0.0000000 0.58710418 -0.58710418 0.3893950 3 0.0000000 0.21034350 -0.21034350 0.2884781 4 0.0000000 0.55620259 -0.55620259 0.3949768 5 1.0000000 0.48734172 0.51265828 0.3987414 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 TOBIT STEP DATA FROM SAS PAGE 24 Multiple TOBIT Analysis. Version June 1995. Weight selected 1.000 Value imputed as limit 0.000000000000000E+00 The number of iterations is 4 Summary of Results for TOBIT Model Dependent variable is TOBITY Variable B(I) B(I)*F(Z) B(I)/SIGMA SE T-Statistic Partial1 Partial2 CONSTANT -2.2760540 -1.1871042 -2.5202630 0.33728327 -7.4722442 -1.0039705 -0.85428731 X1 1.2751446 0.66506750 1.4119611 0.28841243 4.8956320 0.56246801 0.47860896 X2 0.80675780 0.42077456 0.89331881 0.31043190 2.8776643 0.35586197 0.30280607 X3 1.1266554 0.58762115 1.2475399 0.27330081 4.5647134 0.49696926 0.42287550 X4 1.2227456 0.63773814 1.3539399 0.27719872 4.8843659 0.53935474 0.45894167 Note: Partial1 = DENSITY * (B(I) / SIGMA) Partial2 = B(I)*(1.0 -(Z * DENSITY / F(Z)) -((DENSITY**2)/(F(Z)**2))) At point of means DENSITY 0.3983594246120059 F(Z) 0.5215624296681960 Z 5.407533831722617E-02 E(Y) 0.3852298800843668 E(YSTAR) 0.7386074191146009 Ref: McDonald-Moffitt Uses of TOBIT Analysis RES May 1980 Number of observations 200 Number of Limits 95 Number of Nonlimits 105 Standard error of regression (SIGMA) 0.9031017676217414 Log of Maximum of Likelihood function -191.8356427209481 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 LOGLIN STEP DATA FROM SAS PAGE 25 LOGLIN Option - For information see Univariate and Multivariate Loglinear and Logistic Models by Nerlove and Press. Code modified July 1996. Data set contained 200 positively weighted observations. Data set summary statistics after weighting Variable Name Maximum Minimum Mean Variance X1 0.996889 0.679401E-02 0.525774 0.890764E-01 X2 0.996601 0.684069E-03 0.519188 0.755190E-01 X3 0.999571 0.567521E-03 0.530841 0.927054E-01 X4 0.998881 0.232791E-02 0.521383 0.903440E-01 Data set OK. Least squares coefficients and starting values for PROBITY -1/ Condition 0.1371E-01 Explanatory Variable OLS Coefficient Inverse Taylor Series Start Value X1 0.51982985 2.0845307 X2 0.27123997 1.0876791 X3 0.41739917 1.6737811 X4 0.40531204 1.6253115 CONSTANT -0.32203261 -3.2965386 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 LOGLIN STEP DATA FROM SAS PAGE 26 At iteration 1 Log Likelihood is - 0.109981678991663E+03 Old coefficient change in coef. Gradiant New coefficient 1 -3.2965 -0.83815 -0.96295 -4.1347 Loop 6 2 2.0845 0.45062 -2.0596 2.5352 Loop 6 3 1.0877 0.33842 -1.4886 1.4261 Loop 6 4 1.6738 0.44076 -1.9605 2.1145 Loop 6 5 1.6253 0.42108 -1.7507 2.0464 Loop 6 At iteration 1 Log Likelihood is - 0.108632652443386E+03 Old coefficient change in coef. Gradiant New coefficient 1 -4.1347 -0.83815 -0.21393 -4.9728 Loop 6 2 2.5352 0.45062 -0.48370 2.9858 Loop 6 3 1.4261 0.33842 -0.35439 1.7645 Loop 6 4 2.1145 0.44076 -0.46550 2.5553 Loop 6 5 2.0464 0.42108 -0.40788 2.4675 Loop 6 At iteration 1 Log Likelihood is - 0.108795922520195E+03 Old coefficient change in coef. Gradiant New coefficient 1 -4.9728 0.52711 0.42464 -4.4457 LOOP 9 2 2.9858 -0.28340 0.79639 2.7024 LOOP 9 3 1.7645 -0.21283 0.56071 1.5517 LOOP 9 4 2.5553 -0.27720 0.74061 2.2781 LOOP 9 5 2.4675 -0.26482 0.69253 2.2027 LOOP 9 At iteration 2 Log Likelihood is - 0.108534759574147E+03 Old coefficient change in coef. Gradiant New coefficient 1 -4.4457 -0.21753E-01 0.34193E-01 -4.4675 Loop 6 2 2.7024 -0.25142E-01 0.22385E-01 2.6772 Loop 6 3 1.5517 0.48177E-01 0.79548E-02 1.5999 Loop 6 4 2.2781 0.21168E-01 0.12282E-01 2.2993 Loop 6 5 2.2027 -0.26446E-01 0.25694E-01 2.1762 Loop 6 At iteration 2 Log Likelihood is - 0.108542403427998E+03 Old coefficient change in coef. Gradiant New coefficient 1 -4.4675 0.20126E-01 -0.41522 -4.4473 LOOP 9 2 2.6772 0.23262E-01 -0.27823 2.7005 LOOP 9 3 1.5999 -0.44575E-01 -0.95555E-01 1.5553 LOOP 9 4 2.2993 -0.19586E-01 -0.14540 2.2797 LOOP 9 5 2.1762 0.24469E-01 -0.31358 2.2007 LOOP 9 At iteration 3 Log Likelihood is - 0.108534709365310E+03 Old coefficient change in coef. Gradiant New coefficient 1 -4.4473 -0.47231E-02 0.61433E-03 -4.4521 Loop 6 2 2.7005 0.88186E-02 -0.31331E-04 2.7093 Loop 6 3 1.5553 0.13413E-02 0.23199E-03 1.5566 Loop 6 4 2.2797 -0.36346E-02 0.52647E-03 2.2761 Loop 6 5 2.2007 -0.27223E-03 0.36946E-03 2.2004 Loop 6 At iteration 3 Log Likelihood is - 0.108534910488403E+03 Old coefficient change in coef. Gradiant New coefficient 1 -4.4521 0.46671E-02 -0.50811E-01 -4.4474 LOOP 9 2 2.7093 -0.87142E-02 0.27802E-02 2.7006 LOOP 9 3 1.5566 -0.13254E-02 -0.19189E-01 1.5553 LOOP 9 4 2.2761 0.35915E-02 -0.43980E-01 2.2796 LOOP 9 5 2.2004 0.26901E-03 -0.31081E-01 2.2007 LOOP 9 Conditional Estimation of Equation for PROBITY Log of Likelihood Function -108.534709 after 3 iterations Explanatory Asymptotic Asymptotic Asymptotic Variable Coefficient Gradient Standard Error t-ratio Significance -------------- -------------- -------------- -------------- -------------- -------------- Constant -2.22370265 -0.253828278E-05 0.378908953 -5.86869917 0.439227565E-08 X1 1.35030054 -0.101981133E-05 0.298993925 4.51614709 0.629749310E-05 X2 0.777653251 -0.994215090E-06 0.322298904 2.41283244 0.158290948E-01 X3 1.13982361 0.344737301E-06 0.292406786 3.89807509 0.969603516E-04 X4 1.10033494 0.149651040E-05 0.294477368 3.73656879 0.186548434E-03 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 ECOMP STEP DATA FROM SAS PAGE 27 Error Component Analysis The number of individuals or regions in the cross section is 25 The number of periods in the time series is 8 The number of independent variables (excluding the constant) is 4 Data read using Region-First convention. 1199 words of 12000000 available were used. OLS regression of Y on levels: Coefficient of determination, R**2 = 0.22905421 Sum of squared residuals = 1941600.9 Standard error of estimate = 99.784407 1/cond of matrix XPX = 0.15952891E-01 Variable Coefficient Standard Error T-Ratio __________________________________________________________________ X1 37.101680 24.293083 1.527 X2 180.94994 26.652402 6.789 X3 -33.430182 23.239249 -1.439 X4 17.392541 23.781001 0.7314 CONSTANT 76.422798 25.409288 3.008 Rhohat from OLS equation 0.1763200888426077 OLS equation Rhohat not used in third stage. OLS regression of Y on deviations from regional means: Coefficient of determination, R**2 = 0.23331242 Sum of squared residuals = 1594445.6 Standard error of estimate = 90.193828 1/cond of matrix XPX = 0.62270161 Variable Coefficient Standard Error T-Ratio __________________________________________________________________ X1 53.567051 23.256377 2.303 X2 171.63973 26.093380 6.578 X3 -37.797874 22.148476 -1.707 X4 17.022193 22.557079 0.7546 Rhohat from second stage equation 0.1810846251075177 OLS regression of Y on transformed variables: Coefficient of determination, R**2 = 0.23104773 Sum of squared residuals = 2101575.7 Standard error of estimate = 103.81383 1/cond of matrix XPX = 0.35601388E-01 Variable Coefficient Standard Error T-Ratio __________________________________________________________________ X1 47.189028 23.703447 1.991 X2 175.24195 26.351300 6.650 X3 -35.995712 22.613964 -1.592 X4 17.166229 23.070777 0.7441 CONSTANT 50.179234 17.474280 2.872 Autocorrelations of YGLS Order of differencing = 0 N= 200 Sqrt(1/N) = 0.70710678E-01 Mean= 181.25935 SD= 112.32738 LAG 1-12 0.169593 0.057931 0.023141 0.118560 -.121671 -.110716 0.028594 -.019396 -.126094 0.045041 0.061657 0.058804 13-24 -.083326 -.113996 -.010324 0.026093 0.089848 0.263556 0.168413 0.081832 -.026360 0.075016 0.020494 -.170524 25-36 -.048656 -.028933 0.033779 -.051474 -.052035 0.108239 -.055192 -.104772 -.044436 0.057692 -.077830 -.097952 37-48 0.007484 0.105448 -.128913 0.009074 -.007380 0.005513 -.089535 0.011172 0.079111 -.136440 -.044218 0.107153 49-50 0.108443 -.044144 Autocorrelations of X1 Order of differencing = 0 N= 200 Sqrt(1/N) = 0.70710678E-01 Mean= 0.52577403 SD= 0.29920564 LAG 1-12 -.032518 0.047960 -.003815 0.011957 -.153939 0.033757 -.029533 -.127278 -.082648 0.025210 0.014221 -.086529 13-24 0.018122 0.075782 -.078560 0.052080 0.037174 0.061824 -.047853 0.056701 0.009298 0.027636 -.050874 0.143368 25-36 0.057115 -.126623 0.079981 0.050282 -.001172 0.008225 0.042853 -.065559 -.099720 0.115885 -.067731 0.144330 37-48 -.180399 0.189811 -.187462 0.069272 -.099613 0.039231 0.045663 -.006197 0.013792 -.008236 -.127347 0.171435 49-50 0.018292 -.044302 Cross correlations of X1 on lags of YGLS Order of differencing = 0 N = 200 Lag 1-12 0.080536 -.034304 -.101329 -.014964 -.133271 0.018174 -.128245 -.091902 -.133171 -.116420 -.048851 0.046590 13-24 0.061007 -.029256 0.151304 0.108664 0.110689 0.085808 0.090712 0.022582 -.047205 0.039423 -.085208 -.045612 25-36 -.084660 0.025710 -.266034 -.090758 -.139443 -.065270 -.010432 -.091088 0.122310 0.000483 0.061032 0.092382 37-48 0.041485 -.007240 0.075271 0.002605 -.205506 -.065732 0.064894 -.013068 -.208373 -.112287 -.090665 -.091010 49-50 0.049574 -.019330 Cross correlations of YGLS on lags of X1 Order of differencing = 0 N = 200 Lag 1-12 0.099191 0.023754 -.000439 -.078129 0.133520 0.044702 -.124666 -.003618 -.001809 0.096616 -.022278 0.251492 13-24 -.061382 0.025199 -.123145 0.055286 0.013273 0.105120 0.008783 -.013237 -.036951 0.034462 0.028174 -.018427 25-36 -.007095 0.056257 0.033950 0.086848 0.060600 0.092268 -.048955 0.032151 -.037085 0.017190 0.012024 0.089931 37-48 0.018085 -.034328 0.065458 -.071867 -.027091 0.092033 -.018079 0.034347 0.104299 0.061970 -.150402 0.111539 49-50 -.045975 -.037114 At zero lag cross correlation equals 0.200642 Autocorrelations of YGLS Order of differencing = 1 N= 199 Sqrt(1/N) = 0.70888121E-01 Mean= -1.1839687 SD= 144.46396 LAG 1-12 -.430754 -.057673 -.068733 0.201983 -.142394 -.084736 0.109053 0.033767 -.155577 0.091939 0.012099 0.079603 13-24 -.066158 -.089807 0.039881 -.006501 -.071637 0.152945 0.010281 0.006691 -.125757 0.100601 0.083643 -.188461 25-36 0.049891 -.022586 0.093465 -.052510 -.091219 0.192266 -.059187 -.067688 -.033878 0.140383 -.059701 -.089120 37-48 0.003570 0.203889 -.215374 0.081501 -.006449 0.063982 -.117666 0.015936 0.158664 -.168617 -.036913 0.080319 49-50 0.099066 -.106051 Autocorrelations of X1 Order of differencing = 1 N= 199 Sqrt(1/N) = 0.70888121E-01 Mean= -0.35717496E-02 SD= 0.42949083 LAG 1-12 -.542792 0.069286 -.035513 0.092482 -.168625 0.122548 0.016791 -.077501 -.029212 0.066909 0.037369 -.103140 13-24 0.026338 0.102877 -.134236 0.068769 -.019193 0.058377 -.093973 0.064819 -.026101 0.043586 -.124360 0.128703 25-36 0.046649 -.188188 0.112230 0.013989 -.030152 -.012541 0.076897 -.041844 -.118446 0.198003 -.197068 0.244677 37-48 -.325900 0.354231 -.298930 0.209670 -.140525 0.052508 0.030124 -.027734 0.015065 0.041378 -.183261 0.209592 49-50 -.040031 -.088339 Cross correlations of X1 on lags of YGLS Order of differencing = 1 N = 199 Lag 1-12 0.001946 -.033001 -.076593 0.110590 -.138551 0.157208 -.102317 0.040423 -.022932 -.029957 -.015467 0.042256 13-24 0.057767 -.151578 0.120307 -.018627 0.010084 -.022987 0.050364 -.003164 -.084581 0.118174 -.086514 0.040656 25-36 -.087147 0.218223 -.251387 0.122239 -.063736 0.009301 0.079862 -.159048 0.172951 -.096499 0.021325 0.034456 37-48 -.002467 -.064300 0.084780 0.066378 -.179746 0.005471 0.108807 0.061543 -.160108 0.047488 0.010998 -.080646 49-50 0.117476 -.084942 Cross correlations of YGLS on lags of X1 Order of differencing = 1 N = 199 Lag 1-12 -.016818 -.025933 0.027300 -.148264 0.163780 0.038571 -.147684 0.055717 -.057950 0.138692 -.211414 0.300543 13-24 -.210062 0.121638 -.174747 0.119810 -.069426 0.093766 -.029078 -.011698 -.038115 0.035208 0.024709 -.031428 25-36 -.034293 0.042877 -.037619 0.043089 -.027052 0.089335 -.105480 0.071786 -.062844 0.038481 -.053657 0.066083 37-48 -.011060 -.074106 0.117642 -.078615 -.034413 0.106646 -.074132 -.008809 0.050875 0.082203 -.233153 0.221054 49-50 -.084793 0.046061 At zero lag cross correlation equals 0.113899 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 RR STEP DATA FROM SAS PAGE 28 Recursive Residual Option. Version 1 July 1994 Real*8 space available 6000000 Real*8 space used 5362 All tests will be performed using original data order. OLS results for complete data set ( 200 obs ) OLS Estimation Dependent variable Y Adjusted R**2 0.2132399381593797 Standard Error of Estimate 99.78440673900759 Sum of Squared Residuals 1941600.926509862 Model Sum of Squares 576865.2920057867 Total Sum of Squares 2518466.218515649 F( 4, 195) 14.48401811171018 F Significance 0.9999999997746845 1/Condition of XPX 1.595289077758794E-02 Number of Observations 200 Durbin-Watson 1.706553837600136 Variable Coefficient Std. Error t X1 X- 1 37.101680 24.293083 1.5272528 X2 X- 2 180.94994 26.652402 6.7892544 X3 X- 3 -33.430182 23.239249 -1.4385225 X4 X- 4 17.392541 23.781001 0.73136285 CONSTANT X-11 76.422798 25.409288 3.0076717 Problem # 1 B coefficient vector for first 5 observations X1 591.10970 X2 491.81218 X3 -447.24363 X4 472.08587 CONSTANT -409.35910 Reciprocal matrix condition 0.47718011E-03 Plot of 1th step ahead recursive residual REC RES 216.51 * . * * . * . * * . . . . * * . . . . * . . . . . . * . . . . . *. .. . . . . * . . . . . . . . * . .. . . . * . . . . . . * . . . . . . . . . * . . .. . . * . . . .. .. . . * . . . * . . . . * . . . . . . . . *----.---.----------.------------.----------.---.-----------------------------------.---------------- *. . . . . . . . * . * .. . . . * .. . . . . . ... . * . . . .. . . * . . . * . . . .. . . . . . . . * . . . . . . . * . . . * . . . . . * . . . . . * . . * . . * . . . * . . . * . . . * * * . * * . . * . . * . * . * * . . * . . * * * * * * . -343.74 ***************************************************************************************************** 1.0000 195.00 TIME Tests on 1th step ahead recursive residual Wilcoxon Median Test 9651. Z 0.1217 Prob 0.5484 DW 1.800 MOD VN 1.803 Siegal Sign (# +) 95 Harvey-Collier Psi =( -3.530 / 7.160 )= t of -0.4930 Wilcoxon test on E(X(T)*X(T+ 1)) # positive (S) 98 Signed Rank 9727. Z 0.3442 Prob 0.634640 DF 194 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 RR STEP DATA FROM SAS PAGE 29 Listing of B coefficients OBS # X1 X2 X3 X4 CONSTANT 6. 538.4 450.0 -382.0 466.0 -374.7 7. 619.6 481.2 -85.17 950.1 -687.9 8. 317.2 207.9 -47.65 252.1 -129.5 9. 94.81 71.32 -107.9 -63.34 228.6 10. 109.5 119.8 -51.87 -10.75 143.6 11. 159.8 109.8 -220.0 161.5 129.8 12. 39.37 217.1 -98.30 137.0 43.19 13. 31.72 228.8 -115.4 153.9 39.63 14. 36.68 288.7 -81.28 137.8 -23.65 15. 33.55 285.6 -81.02 135.6 -18.56 16. -1.486 318.1 -94.56 115.3 1.987 17. -11.20 285.8 -66.84 99.46 25.07 18. 21.24 300.0 -66.00 145.1 -15.04 19. 27.71 289.5 -66.25 147.9 -11.10 20. 22.77 274.3 -53.40 127.8 6.195 21. 23.95 272.1 -46.36 126.1 2.622 22. 44.99 261.6 -70.30 150.9 2.679 23. 44.96 261.6 -70.25 150.8 2.699 24. 67.14 241.7 -50.46 123.9 0.8164 25. 79.63 217.3 -18.35 99.06 6.324 26. 75.71 213.4 -22.82 104.4 12.46 27. 76.54 213.7 -22.46 104.3 11.56 28. 84.96 216.9 -20.16 110.3 2.467 29. 76.62 203.8 -21.54 104.0 21.11 30. 82.46 219.2 -15.23 102.7 3.067 31. 81.39 226.1 -3.321 97.57 -5.821 32. 91.39 230.2 -12.92 96.76 -9.580 33. 91.18 238.1 -8.243 95.01 -16.92 34. 93.74 233.1 4.286 104.9 -31.18 35. 88.59 226.1 10.27 96.39 -22.01 36. 85.02 224.7 23.52 83.46 -22.18 37. 84.52 224.7 24.19 83.33 -22.33 38. 93.25 216.4 15.03 81.68 -15.34 39. 92.39 223.1 19.79 68.08 -11.40 40. 107.6 214.1 17.77 65.96 -10.26 41. 108.2 214.7 12.98 71.25 -9.535 42. 107.4 212.4 9.759 72.76 -6.492 43. 106.6 212.4 2.752 78.53 -6.293 44. 106.7 212.3 2.792 78.57 -6.334 45. 110.2 206.8 -1.387 78.18 -3.649 46. 112.0 204.2 -0.3113E-01 76.04 -3.543 47. 112.3 201.4 -0.4753 76.99 -2.004 48. 114.5 199.3 -1.840 77.95 -1.979 49. 124.9 198.8 -1.259 75.95 -8.272 50. 132.3 191.3 -8.066 80.99 -7.811 51. 146.8 187.7 1.951 75.57 -18.77 52. 129.2 182.0 -7.351 54.26 1.964 53. 103.0 196.0 -14.51 52.96 7.683 54. 106.4 193.7 -13.10 53.17 7.067 55. 106.1 197.3 -4.378 47.00 2.200 56. 109.0 191.2 -0.3869 40.52 6.081 57. 111.3 190.7 -1.571 38.13 7.449 58. 110.5 186.0 -12.76 48.88 13.45 59. 85.20 201.2 -42.07 73.44 19.13 60. 88.69 211.2 -27.16 69.61 4.356 61. 77.96 223.1 -28.69 72.98 1.074 62. 80.96 224.0 -16.94 70.61 -8.007 63. 104.1 204.0 -37.62 48.30 7.773 64. 105.0 201.4 -34.08 47.18 6.748 65. 112.2 193.0 -41.11 56.12 8.547 66. 113.2 189.9 -45.39 53.12 12.69 67. 113.5 191.8 -48.84 55.43 12.71 68. 110.9 195.4 -53.60 51.90 15.74 69. 110.9 195.4 -53.61 51.88 15.76 70. 124.3 196.5 -42.58 56.03 -1.971 71. 117.8 186.8 -55.55 58.22 10.50 72. 117.5 185.7 -55.67 58.32 11.50 73. 115.9 186.1 -57.55 59.71 12.02 74. 113.3 184.9 -49.60 62.18 9.990 75. 113.2 188.1 -43.84 61.93 4.539 76. 109.7 188.2 -41.36 60.86 4.860 77. 109.0 190.6 -38.04 64.79 -0.5891 78. 103.1 193.0 -29.73 62.27 -0.3623 79. 99.96 195.1 -25.91 60.95 -1.872 80. 92.44 201.0 -34.01 63.66 0.6536 81. 94.82 195.6 -30.49 67.48 -0.7181 82. 103.1 191.8 -27.94 58.96 1.243 83. 97.12 193.4 -26.51 58.26 4.235 84. 96.84 193.8 -27.16 61.89 3.535 85. 94.83 196.5 -25.92 62.85 2.490 86. 95.00 199.0 -24.18 63.27 0.3498 87. 94.18 197.5 -25.65 64.67 1.296 88. 90.41 194.5 -34.76 58.14 14.95 89. 88.73 194.4 -37.69 61.74 16.79 90. 85.29 196.5 -35.55 61.89 15.62 91. 85.18 196.6 -35.65 61.64 15.88 92. 81.66 196.0 -34.59 68.26 15.81 93. 74.43 189.7 -38.27 60.40 26.84 94. 65.19 185.3 -47.73 59.97 40.95 95. 64.00 184.8 -48.57 62.12 40.62 96. 60.53 184.3 -47.98 64.98 41.57 97. 57.48 188.1 -46.03 62.22 40.75 98. 62.17 185.8 -51.95 65.77 41.97 99. 61.99 186.0 -51.88 65.92 41.90 100. 61.92 186.1 -51.81 65.85 41.84 101. 61.10 186.4 -52.54 66.38 42.08 102. 60.39 186.7 -53.15 66.03 42.70 103. 61.00 186.4 -48.92 67.74 38.63 104. 59.59 186.6 -49.03 69.30 38.26 105. 55.98 182.5 -53.74 64.47 46.44 106. 57.47 180.0 -53.59 64.25 46.39 107. 57.35 180.0 -53.38 64.11 46.41 108. 57.55 179.4 -53.05 62.94 46.63 109. 59.01 179.5 -54.13 59.91 48.51 110. 62.90 176.7 -54.99 61.80 46.78 111. 58.17 174.7 -54.65 58.68 50.88 112. 56.09 171.4 -57.37 57.93 56.76 113. 53.38 175.1 -61.04 54.64 60.80 114. 49.54 179.8 -59.65 54.24 60.70 115. 44.12 174.9 -46.88 45.14 62.20 116. 39.51 173.3 -43.10 37.98 68.50 117. 39.14 172.9 -42.56 37.41 68.78 118. 39.97 173.5 -42.40 36.95 68.39 119. 40.60 174.3 -42.67 37.81 67.08 120. 41.12 176.3 -40.57 37.86 64.32 121. 40.43 178.8 -38.53 35.41 64.10 122. 35.03 174.6 -44.04 40.25 68.46 123. 30.34 178.1 -47.22 38.24 72.69 124. 30.72 178.0 -46.34 38.43 72.16 125. 30.34 178.3 -45.58 37.33 72.09 126. 30.69 177.6 -46.26 36.79 72.73 127. 33.00 183.7 -39.16 41.19 63.52 128. 29.15 184.2 -36.42 42.78 62.30 129. 29.33 184.2 -36.94 43.16 62.42 130. 28.76 183.0 -37.48 42.25 64.44 131. 28.69 184.1 -38.66 41.84 64.93 132. 30.90 182.7 -41.01 39.16 66.42 133. 30.97 180.8 -40.06 40.39 66.56 134. 23.08 186.5 -35.17 37.88 67.81 135. 24.67 188.9 -38.33 36.01 68.93 136. 25.29 186.2 -40.68 39.72 68.59 137. 25.64 188.7 -38.94 40.89 65.11 138. 25.33 189.1 -38.93 40.92 64.99 139. 21.76 184.4 -45.69 39.52 75.22 140. 18.80 185.1 -47.63 41.59 76.91 141. 20.76 181.4 -44.87 46.05 75.22 142. 20.71 181.8 -45.38 46.19 75.09 143. 18.56 181.8 -47.76 46.63 78.06 144. 18.00 182.0 -47.94 46.97 78.23 145. 15.86 183.8 -49.32 47.64 78.45 146. 10.93 189.5 -50.65 51.18 78.27 147. 13.04 189.5 -48.56 49.57 77.29 148. 22.15 176.9 -55.38 44.29 83.44 149. 21.19 175.4 -46.77 38.50 81.44 150. 19.63 174.5 -49.45 35.75 86.27 151. 21.86 173.1 -50.59 35.43 86.96 152. 19.72 173.4 -53.44 33.98 89.63 153. 20.02 173.4 -54.10 33.43 90.25 154. 17.61 173.8 -53.58 31.58 92.71 155. 17.31 174.3 -54.99 30.60 93.53 156. 16.61 173.7 -54.98 30.22 94.22 157. 18.65 172.9 -52.33 28.77 93.41 158. 16.28 175.1 -49.58 30.94 91.63 159. 16.91 175.8 -49.61 30.40 91.51 160. 15.21 176.8 -48.13 31.93 89.93 161. 13.18 177.7 -49.81 31.45 92.14 162. 13.97 176.5 -48.54 29.97 92.18 163. 14.46 176.9 -48.89 30.60 91.47 164. 17.93 173.5 -51.65 28.64 93.24 165. 18.43 175.0 -54.08 29.64 93.65 166. 20.60 172.5 -53.77 28.00 94.82 167. 20.63 172.1 -53.81 27.92 94.86 168. 19.76 166.5 -49.59 21.29 100.8 169. 21.04 170.3 -45.88 24.93 95.06 170. 21.02 170.3 -45.89 24.93 95.07 171. 19.01 170.2 -43.82 26.82 94.70 172. 19.97 169.3 -44.91 27.29 94.75 173. 19.93 169.4 -44.03 27.02 94.57 174. 21.69 169.9 -42.67 25.51 93.11 175. 22.00 171.0 -43.47 25.84 92.41 176. 21.97 171.5 -43.31 26.65 91.91 177. 22.28 172.2 -43.48 27.28 91.31 178. 22.81 172.1 -43.45 26.69 91.74 179. 19.97 168.9 -45.93 22.97 97.57 180. 21.59 168.7 -45.09 23.28 95.76 181. 21.31 168.3 -44.58 22.78 95.97 182. 26.91 171.6 -39.32 19.55 88.66 183. 26.15 172.6 -38.54 19.47 87.99 184. 25.92 172.0 -38.78 18.93 89.13 185. 25.59 173.2 -39.25 18.63 88.92 186. 28.89 171.0 -42.41 19.54 88.84 187. 29.08 170.8 -42.22 19.39 88.77 188. 28.82 171.0 -41.97 19.17 88.84 189. 29.35 171.4 -42.90 19.22 89.04 190. 32.70 169.5 -40.38 16.76 88.77 191. 28.92 172.8 -39.70 15.20 90.14 192. 29.80 173.7 -38.14 16.90 87.22 193. 30.01 173.2 -37.88 17.16 87.13 194. 29.88 172.8 -37.01 16.36 87.57 195. 32.81 176.6 -38.04 16.68 85.10 196. 32.68 176.9 -37.40 15.89 84.92 197. 31.50 175.1 -37.58 15.81 86.92 198. 34.07 179.8 -36.85 20.00 79.82 199. 33.42 179.5 -37.53 20.62 80.49 200. 37.10 180.9 -33.43 17.39 76.42 Plot of B coefficient for X1 B COEF 619.59 *. * * * * * * *. * * * * * * * * * * * * * * * * * . * * * * * * * * * * * * . * . * . * . . .. * . ****. .** .**..**. * . . * . . .****. * . .**.* *. .** * .*. . . * .****.***** * * * .* * ** . *. ****** .******.. * .* ****** **.**** .**********. * * *. *-----*---------------------------------------------------------------------------------------------- -11.198 ***************************************************************************************************** 1.0000 195.00 TIME Plot of B coefficient for X2 B COEF 481.23 *. * * * *. * * * * * * * * * * * * * * * * . * * . * . * *. * . * . * * * * . * .. * . ...*. * * . .... .* * . . ** . * . ** . . * . .. * ..... *** *.**..**. ... * * .. . *** .****.* .***...*** . * ***.******. **.*******. * *. ****. * . .**** ** .** * * * * * * . * . * * * * . 71.323 ***************************************************************************************************** 1.0000 195.00 TIME Plot of B coefficient for X3 B COEF 24.193 * . * ... * . ... *--------------.---..*-.--.-------------------------------------------------------------------------- * .. . *.. .. * .. .. . . * .** . * .. ..**.. . * . *. ... .**. * .*****. .*...****. * . . ... .. .*. .. .** **. .***... .**. .******. ... * . . . ..*. .** .***. ....**. .*. * .* .. * * * * *. * . . * . * . * * * * * * * * * * * * * . * * * * * * * * * * * * * * * * * * *. -382.04 ***************************************************************************************************** 1.0000 195.00 TIME Plot of B coefficient for X4 B COEF 950.13 *. * * * * * * * * * * * * * * * * * * * * * * * *. * * * * * * * * * * . * * * * * .. * * * .* * . * . **. . * . . .*.*. * .****** ** .***..*.** ****.**.. * *.*. *****. .. . * ..** . .**. ..****. * . ***.*. .*.. .*.***************.. .. *------------------------------------------------------------------------------------------..*****.-. * . * * . -63.339 ***************************************************************************************************** 1.0000 195.00 TIME Plot of B coefficient for CONSTANT B COEF 228.61 * . * * * * * . * . * . * **.*******.***************. * .***************** . * . ..** .***. * . . *.. .. * . .*. ...** ***.*** . .** *-----...*.-.*.--.*****..-.--*---.---***.*.---------------------------------------------------------- * * . .**. . * * * * * * . * * * * * * * * * * * * *. * * * * * * * * * * * * * * * *. -687.87 ***************************************************************************************************** 1.0000 195.00 TIME Plot of CUSUM of 1th step ahead recursive residual CUSUM 0.96872 *. * . * .. *.----------..----...-------------------------------------------------------------------------------- * * . .*. * .. *. * * . . . * . . . * . . . . * . . . * .* *. . * . . .. . * * . * . .. * * . . . * . * * . .. * . .. * .. * . . * . .. . . . . . * . . . .... . * . . . . * .. . * ... . . . .. * . . . * . . . . * . .. * . * . . . * * . . .* . * .. * . * . . * . .. .. . . . . * .. . * . . . ... . . * . .. .. . . * . *. . .. * .. . ... * .. ... . . * . *- . . . *-- . * -- . . * - .. * -- * * -- .. .. * -- . * - . -19.023 ***************************************************************************************************** 1.0000 195.00 TIME If value within relevant range, 1% confidence bounds are shown. Harvey-Collier Psi =( -8.540 / 0.3902 )= t of -21.89 Plot of CUSUMSQ of 1th step ahead recursive residual C0(.95) = 0.13081 DF = 96 CUSUMSQ 1.0000 * -------------* * -- ** * -- **** * -- ***. * -- ***. * -- *. * --- ***** * --- ** .. --- * --- **.. --- * --- ****.. --- * --- ***** .. --- * --- * .. --- * --- * .. --- * --- ... --- * --- .*. --- * --- .** --- * --- .*** --- * --- ..** --- * --- ...** --- * -- .**** --- * -- .*** -- * -- **** -- * -- ... -- * -- ..** -- * -- ***** -- * -- *****.. -- * --- * .. --- * --- **.. --- * --- ****. --- * --- ***.. --- * --- ****.. --- * --- *** .. --- * -- **** .. -- * -- .. -- * -- * .. -- * -- *.. -- * -- *. -- * -- **** -- * -- ..* -- * -- ... -- * -- ... -- * -- ... * -- * -- ... ****** -- *- ...*** -- * ***** --- * ****. --- * **... --- * *... --- * *.. --- **.------------- 0.0000 ***************************************************************************************************** 1.0000 195.00 TIME Tests on CUSUMSQ of 1th step ahead recursive residual Maximum distance CUSUMSQ from diagonal 0.7532E-01 DF 96 Probability from Durbin Table 0.8638 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 RR STEP DATA FROM SAS PAGE 30 Chow test option selected For equation 1 ( 50) obs go from 1 to 50 OLS Estimation Dependent variable Y Adjusted R**2 0.4875993162528404 Standard Error of Estimate 81.89764293586019 Sum of Squared Residuals 301825.0763302342 Model Sum of Squares 339575.2621716651 Total Sum of Squares 641400.3385018994 F( 4, 45) 12.65707192351186 F Significance 0.9999994439858170 1/Condition of XPX 1.221177931804238E-02 Number of Observations 50 Durbin-Watson 1.215251567035409 Variable Coefficient Std. Error t X1 X- 1 132.34130 42.644429 3.1033667 X2 X- 2 191.34408 41.851872 4.5719359 X3 X- 3 -8.0661892 48.038003 -0.16791267 X4 X- 4 80.986836 40.164463 2.0163804 CONSTANT X-11 -7.8111839 45.236772 -0.17267333 ------------------------------------------------------------------------------------------------------------------------ For equation 2 ( 50) obs go from 51 to 100 OLS Estimation Dependent variable Y Adjusted R**2 4.328068640101901E-02 Standard Error of Estimate 115.3677616054629 Sum of Squared Residuals 598937.4188034717 Model Sum of Squares 82742.45449347096 Total Sum of Squares 681679.8732969427 F( 4, 45) 1.554173414162639 F Significance 0.7970665730313373 1/Condition of XPX 1.208383606008493E-02 Number of Observations 50 Durbin-Watson 1.575481959858247 Variable Coefficient Std. Error t X1 X- 1 6.0334486 60.214738 0.10019887 X2 X- 2 145.68049 65.630675 2.2197013 X3 X- 3 -67.555558 53.621106 -1.2598688 X4 X- 4 45.810957 57.510971 0.79656032 CONSTANT X-11 91.730432 65.164695 1.4076707 ------------------------------------------------------------------------------------------------------------------------ For equation 3 ( 50) obs go from 101 to 150 OLS Estimation Dependent variable Y Adjusted R**2 5.666176509892729E-02 Standard Error of Estimate 104.8180973174360 Sum of Squared Residuals 494407.5086361367 Model Sum of Squares 76283.70562762476 Total Sum of Squares 570691.2142637614 F( 4, 45) 1.735798250067379 F Significance 0.8412308049261890 1/Condition of XPX 1.494116526384110E-02 Number of Observations 50 Durbin-Watson 2.003540087771578 Variable Coefficient Std. Error t X1 X- 1 -49.334464 49.904743 -0.98857265 X2 X- 2 133.21192 57.579456 2.3135320 X3 X- 3 -35.814315 45.757626 -0.78269608 X4 X- 4 -11.560854 49.194889 -0.23500111 CONSTANT X-11 167.24444 53.002731 3.1553928 ------------------------------------------------------------------------------------------------------------------------ For equation 4 ( 50) obs go from 151 to 200 OLS Estimation Dependent variable Y Adjusted R**2 0.3614876762677517 Standard Error of Estimate 85.93801431277339 Sum of Squared Residuals 332340.4036810100 Model Sum of Squares 234417.2914278633 Total Sum of Squares 566757.6951088733 F( 4, 45) 7.935220934180239 F Significance 0.9999372982967387 1/Condition of XPX 1.772124167728302E-02 Number of Observations 50 Durbin-Watson 2.205945446830746 Variable Coefficient Std. Error t X1 X- 1 85.813001 41.009789 2.0925004 X2 X- 2 224.39867 49.480694 4.5350752 X3 X- 3 -0.65657917 37.827732 -0.17357085E-01 X4 X- 4 -51.128535 42.574483 -1.2009197 CONSTANT X-11 55.510665 41.373791 1.3416867 F( 15, 180) = 1.48716 1/F = 0.672422 F Probability 0.88618447 Plot of the Quandt Likelihood Ratio .. Minimum is an indication of a shift in structure Lambda -0.70902 * . * .*. . . * .* . .... . * * ** . .*.**. . * . . . . . ... * .* ***. ** . . *. * . . .. . *.*.**... * .. * ** . .. * . * .. . * .** * . * . . . *. * * *. *.. .** . *. * .. . * . . . . .. . ....** . . . * * .... .*.*. . . . * . ... . * . *. * .. . * . * * *. * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *. -20.228 ***************************************************************************************************** 1.0000 189.00 Time Moving regression option selected. Moving regressions from 20 obs to 24 obs with increment 2 will be calculated if possible. Begin obs # M1, M2, M, M3 then Res. Sum of squares for each regression OBS # M1 M2 M M3 Res Sum SQ Moving regression with 20 observations will be attempted 1 429.59579 0.0000000 0.0000000 0.0000000 191389.79 2 11001.753 12879.920 23881.673 0.0000000 182718.32 3 11010.357 12885.298 23895.655 0.0000000 188853.33 4 31810.604 25746.243 57556.847 0.0000000 180200.12 5 50859.671 29486.349 80346.021 0.0000000 188752.11 6 52942.340 32602.538 85544.878 0.0000000 197677.54 7 53246.634 116482.73 169729.37 0.0000000 135533.15 8 59639.820 119686.79 179326.61 0.0000000 133377.41 9 64956.703 129609.98 194566.69 5316.8833 129940.79 10 75102.213 175642.61 250744.82 15462.394 98584.804 11 75704.834 175858.43 251563.26 16065.014 107135.84 12 93479.990 230009.45 323489.44 33840.170 71568.530 13 94568.064 263913.76 358481.82 34928.245 63790.658 14 129295.05 308158.05 437453.09 69655.226 33450.616 15 132267.06 312233.82 444500.88 72627.243 57153.743 16 134998.71 312313.23 447311.94 75358.892 59621.349 17 135027.70 332789.41 467817.10 75387.877 50198.587 18 137694.76 333958.17 471652.93 78054.940 49193.132 19 148410.60 335200.16 483610.76 88770.776 50265.786 20 151241.73 335851.83 487093.57 91601.915 57521.393 21 154569.57 336512.73 491082.30 94929.747 59306.984 22 157769.94 336615.98 494385.93 98130.125 62282.603 23 168199.79 337389.22 505589.01 108559.97 64124.729 24 172699.62 337596.31 510295.93 113059.80 71525.136 25 173514.30 338280.63 511794.94 113874.48 73007.624 26 173574.39 338320.31 511894.70 113934.57 73449.667 27 174324.60 345160.75 519485.35 114684.78 67482.817 28 175153.03 347460.55 522613.58 115513.21 66160.727 29 178657.93 351177.00 529834.93 119018.11 63882.503 30 179858.58 360207.81 540066.39 120218.76 59420.634 31 191635.11 364509.99 556145.10 131995.29 56456.416 32 308661.33 364574.98 673236.31 249021.51 66441.013 33 366348.75 364580.47 730929.23 306708.94 163243.83 34 371612.54 366514.20 738126.74 311972.72 209683.15 35 374875.43 395472.51 770347.94 315235.61 191048.65 36 375837.78 397979.15 773816.92 316197.96 191960.14 37 378944.30 402590.38 781534.67 319304.48 189409.06 38 413974.33 402809.52 816783.85 354334.51 191383.28 39 478886.40 404121.03 883007.43 419246.58 219875.56 40 503762.70 423424.55 927187.25 444122.88 245973.67 41 513013.55 448904.06 961917.62 453373.73 240692.69 42 519098.54 469481.88 988580.42 459458.72 231536.82 43 575464.73 472101.90 1047566.6 515824.91 234396.63 44 577125.57 472928.84 1050054.4 517485.75 271455.81 45 631355.52 532332.97 1163688.5 571715.70 235305.10 46 650821.07 555890.13 1206711.2 591181.25 261537.81 47 663937.35 563830.96 1227768.3 604297.53 268069.18 48 673777.54 581126.49 1254904.0 614137.72 262709.98 49 687253.40 598202.50 1285455.9 627613.58 257835.88 50 700889.44 598288.16 1299177.6 641249.62 268864.73 51 701385.99 645939.14 1347325.1 641746.17 254735.43 52 709354.48 646687.61 1356042.1 649714.66 254448.25 53 712895.74 720955.28 1433851.0 653255.92 194244.47 54 762291.83 776769.60 1539061.4 702652.01 148664.78 55 765398.55 780170.74 1545569.3 705758.73 186922.31 56 772596.49 789330.29 1561926.8 712956.67 181541.36 57 773771.89 833740.19 1607512.1 714132.07 152740.81 58 851011.19 853987.62 1704998.8 791371.37 138935.46 59 852681.32 877029.52 1729710.8 793041.50 175457.36 60 863131.33 903561.74 1766693.1 803491.51 160403.46 61 872975.77 907999.27 1780975.0 813335.95 165215.22 62 898994.20 924688.67 1823682.9 839354.38 159489.00 63 923420.94 930519.29 1853940.2 863781.12 171957.80 64 928008.31 1011426.3 1939434.6 868368.49 131878.58 65 929220.24 1011427.8 1940648.1 869580.42 135998.50 66 931072.40 1033727.6 1964800.0 871432.58 119167.68 67 931153.53 1042832.6 1973986.2 871513.71 113090.38 68 965209.18 1054405.4 2019614.6 905569.36 106220.90 69 975055.01 1067094.5 2042149.6 915415.19 123671.05 70 976072.85 1068389.0 2044461.9 916433.03 131114.35 71 977495.17 1132723.8 2110218.9 917855.35 88220.188 72 990519.40 1146543.7 2137063.1 930879.58 79369.015 73 1029071.7 1153108.6 2182180.2 969431.87 85605.495 74 1030099.2 1153664.7 2183763.9 970459.37 114690.46 75 1031964.1 1154167.8 2186131.9 972324.29 114980.92 76 1036691.2 1168928.8 2205620.0 977051.40 104305.09 77 1043751.5 1170599.1 2214350.6 984111.64 106605.03 78 1070132.5 1186148.7 2256281.3 1010492.7 100193.90 79 1070784.6 1187131.1 2257915.7 1011144.8 119614.31 80 1072458.5 1193609.9 2266068.4 1012818.7 115283.79 81 1073204.6 1214877.4 2288082.0 1013564.8 104051.07 82 1073860.8 1219104.5 2292965.3 1014221.0 102285.29 83 1091084.8 1248912.1 2339996.9 1031445.0 82446.766 84 1091556.1 1250028.9 2341585.0 1031916.3 93672.826 85 1093122.3 1252414.4 2345536.8 1033482.5 91914.574 86 1099780.0 1253034.2 2352814.2 1040140.2 92624.403 87 1108048.8 1269186.7 2377235.5 1048409.0 86064.026 88 1109868.2 1279509.6 2389377.9 1050228.4 83222.519 89 1122168.1 1286020.9 2408189.0 1062528.3 79754.209 90 1127846.1 1291407.4 2419253.4 1068206.3 84561.247 91 1129289.4 1295870.0 2425159.4 1069649.6 84264.714 92 1134193.8 1295949.1 2430142.9 1074554.0 85389.658 93 1145318.3 1321268.2 2466586.5 1085678.5 67839.374 94 1160514.1 1334281.2 2494795.4 1100874.3 64647.615 95 1206136.0 1335345.2 2541481.2 1146496.2 75614.880 96 1208198.2 1338016.4 2546214.6 1148558.4 105296.10 97 1214933.3 1338220.6 2553153.9 1155293.5 106569.55 98 1220809.5 1352399.7 2573209.2 1161169.6 101011.11 99 1239825.4 1375660.2 2615485.6 1180185.6 86459.576 100 1244101.1 1376829.0 2620930.1 1184461.3 97876.518 101 1244938.5 1378406.5 2623345.0 1185298.7 99251.109 102 1274945.6 1379784.2 2654729.8 1215305.8 98842.734 103 1279218.2 1384526.2 2663744.4 1219578.4 117803.69 104 1286562.4 1395788.9 2682351.3 1226922.6 111750.18 105 1286933.5 1397389.1 2684322.6 1227293.7 115968.06 106 1287155.7 1397475.3 2684630.9 1227515.9 116214.80 107 1340896.9 1400906.5 2741803.4 1281257.1 113357.91 108 1344476.8 1408079.4 2752556.2 1284837.0 146524.75 109 1347589.9 1409414.9 2757004.8 1287950.0 148121.75 110 1348201.1 1421065.7 2769266.8 1288561.3 142164.00 111 1350300.1 1471224.3 2821524.5 1290660.3 105753.28 112 1384033.5 1472774.1 2856807.6 1324393.7 106048.68 113 1390334.8 1490400.5 2880735.3 1330695.0 114418.76 114 1395297.1 1493145.4 2888442.5 1335657.3 116608.05 115 1412067.6 1493343.8 2905411.3 1352427.7 120202.20 116 1435739.7 1535467.7 2971207.3 1376099.9 99568.913 117 1436670.5 1550591.1 2987261.6 1377030.7 107971.24 118 1443609.7 1552093.3 2995703.0 1383969.8 107647.50 119 1483328.8 1555177.2 3038506.0 1423688.9 109995.37 120 1484297.2 1557102.8 3041400.0 1424657.4 142650.55 121 1511881.5 1564556.9 3076438.4 1452241.7 137628.69 122 1512392.1 1569030.6 3081422.7 1452752.3 157063.33 123 1515715.2 1583761.1 3099476.3 1456075.4 147726.77 124 1521638.0 1584169.8 3105807.8 1461998.2 150397.93 125 1523448.9 1584211.8 3107660.8 1463809.1 154813.08 126 1537258.8 1591753.9 3129012.7 1477619.0 150227.47 127 1546475.8 1603204.8 3149680.6 1486836.0 152342.12 128 1668257.9 1624864.2 3293122.1 1608618.0 144967.40 129 1771540.1 1644476.3 3416016.4 1711900.2 216636.59 130 1772082.0 1645284.8 3417366.8 1712442.2 297655.61 131 1776472.4 1649139.3 3425611.7 1716832.6 294974.48 132 1777665.3 1649624.4 3427289.7 1718025.5 298064.88 133 1777690.2 1654361.4 3432051.6 1718050.4 295067.07 134 1779407.9 1655182.9 3434590.9 1719768.1 294495.43 135 1779486.1 1685284.4 3464770.5 1719846.3 275311.02 136 1781816.1 1706094.4 3487910.4 1722176.2 264180.29 137 1791369.6 1719437.5 3510807.0 1731729.8 257385.37 138 1811721.1 1782519.4 3594240.6 1752081.3 219609.02 139 1818355.5 1791546.1 3609901.6 1758715.7 229047.20 140 1832038.4 1797057.1 3629095.6 1772398.6 230488.13 141 1832217.9 1798676.3 3630894.2 1772578.1 239818.83 142 1835869.5 1854602.8 3690472.3 1776229.7 201251.53 143 1901556.0 1862535.8 3764091.7 1841916.2 198054.78 144 1909857.9 1874163.5 3784021.4 1850218.0 216987.48 145 1927586.9 1877508.8 3805095.7 1867947.1 220587.54 146 1927986.5 1880742.3 3808728.8 1868346.7 233693.40 147 1928282.8 1940632.1 3868914.9 1868643.0 181418.59 148 1954268.3 1941026.6 3895294.9 1894628.5 181451.22 149 1985890.9 2019067.8 4004958.7 1926251.0 146854.05 150 1987208.2 2081386.8 4068595.0 1927568.4 124582.32 151 1996693.9 2084104.9 4080798.8 1937054.1 123523.80 152 2007899.4 2087120.1 4095019.5 1948259.6 127837.13 153 2008087.2 2108134.7 4116221.9 1948447.4 118434.19 154 2014095.7 2108139.6 4122235.3 1954455.9 118593.58 155 2020628.9 2114247.7 4134876.6 1960989.1 116360.74 156 2020753.4 2128351.7 4149105.2 1961113.6 111508.37 157 2020770.8 2137947.7 4158718.5 1961131.0 103677.77 158 2021057.3 2137958.8 4159016.0 1961417.5 103683.76 159 2061242.2 2143945.9 4205188.1 2001602.4 98886.582 160 2067645.4 2144604.0 4212249.4 2008005.6 124024.40 161 2071151.0 2171118.0 4242269.0 2011511.2 111404.07 162 2135484.0 2178673.2 4314157.2 2075844.2 108710.54 163 2138246.6 2181942.6 4320189.1 2078606.8 155006.11 164 2140166.6 2185893.9 4326060.5 2080526.8 154148.09 165 2141512.1 2195873.5 4337385.6 2081872.3 148402.76 166 2174458.6 2217180.0 4391638.6 2114818.8 131748.26 167 2181128.7 2220013.1 4401141.8 2121488.9 155866.58 168 2181445.9 2222084.7 4403530.6 2121806.1 159004.27 169 2183329.8 2270096.2 4453426.0 2123689.9 125126.63 170 2187040.4 2292388.2 4479428.6 2127400.6 109971.86 171 2210983.7 2293601.2 4504584.9 2151343.9 111223.33 172 2228519.0 2342556.1 4571075.1 2168879.2 95185.836 173 2236195.8 2344985.3 4581181.1 2176556.0 103416.08 174 2236545.1 2345072.9 4581617.9 2176905.2 108558.40 175 2239404.1 2361359.4 4600763.5 2179764.3 98513.510 176 2243707.0 2361545.6 4605252.5 2184067.1 100371.29 177 2272627.7 2369366.9 4641994.6 2212987.9 96752.105 178 2299519.7 2372217.6 4671737.4 2239879.9 115480.70 179 2330830.8 2373028.6 4703859.4 2271191.0 134157.05 180 2341219.8 2420378.3 4761598.0 2281580.0 125280.26 181 2341219.8 2421000.3 4762220.1 2281580.0 133236.62 Moving reg. with 20 OBS ..M1, M2, M, M3 = resp 13006.777 13450.002 26456.778 12963.522 -------------------------------------------------------------------------------- Moving regression with 22 observations will be attempted 1 0.58950403E-01 0.0000000 0.0000000 0.0000000 194851.11 2 10924.543 7983.1530 18907.696 0.0000000 188863.59 3 26561.669 8166.4160 34728.085 0.0000000 195727.38 4 28409.708 10487.754 38897.462 0.0000000 203816.47 5 28559.050 14369.290 42928.339 0.0000000 202071.00 6 31490.047 17375.946 48865.993 0.0000000 199543.95 7 36207.257 96145.457 132352.71 4717.2098 141300.34 8 47291.007 98493.488 145784.50 15800.960 143343.67 9 48872.716 108185.95 157058.67 17382.668 144317.81 10 62581.995 156750.91 219332.90 31091.947 107840.34 11 64311.018 156758.54 221069.56 32820.971 118344.23 12 79318.025 208092.51 287410.53 47827.977 85250.616 13 84236.344 229428.68 313665.03 52746.297 83935.239 14 86227.921 263558.05 349785.97 54737.874 63250.667 15 86974.154 267152.46 354126.61 55484.106 61725.077 16 89952.586 267259.96 357212.55 58462.539 62189.899 17 99732.702 288108.70 387841.40 68242.655 52239.662 18 102680.80 289333.35 392014.15 71190.748 58399.818 19 106129.98 289666.46 395796.43 74639.929 60695.234 20 109363.53 290709.86 400073.39 77873.479 62938.762 21 119406.69 291389.75 410796.44 87916.640 64705.008 22 125700.08 291754.56 417454.65 94210.037 71873.087 23 127336.58 293251.84 420588.43 95846.535 73946.950 24 127539.03 294062.61 421601.64 96048.978 74346.170 25 127934.90 295505.81 423440.71 96444.855 73515.578 26 128107.45 295515.23 423622.68 96617.405 73848.261 27 132162.66 301895.34 434058.00 100672.62 68271.226 28 133950.30 304584.23 438534.53 102460.25 69372.245 29 145779.97 308221.15 454001.12 114289.92 67915.414 30 263965.61 318797.63 582763.24 232475.56 69343.050 31 321682.53 323138.44 644820.97 290192.48 163401.03 32 327180.84 323380.73 650561.56 295690.79 211280.17 33 329309.29 323380.78 652690.07 297819.24 216093.43 34 330331.12 325057.37 655388.50 298841.08 216493.27 35 333300.66 353856.00 687156.66 301810.61 194024.66 36 364790.04 355736.82 720526.85 333299.99 194622.11 37 428818.65 357093.03 785911.68 397328.60 220797.76 38 453905.71 357510.90 811416.62 422415.67 262301.74 39 467877.50 357515.74 825393.24 436387.45 278466.27 40 480667.75 379659.47 860327.22 449177.71 272216.93 41 542070.88 411749.67 953820.55 510580.83 256217.47 42 543866.09 438982.53 982848.62 512376.04 274518.42 43 583831.15 441882.04 1025713.2 552341.11 273375.95 44 587239.26 443330.67 1030569.9 555749.21 306336.89 45 594153.85 474407.57 1068561.4 562663.80 287825.90 46 599519.62 488312.67 1087832.3 568029.57 280713.03 47 612240.21 492977.39 1105217.6 580750.16 280302.86 48 631626.47 506249.16 1137875.6 600136.42 279760.77 49 631984.77 527828.56 1159813.3 600494.73 278935.90 50 638949.37 528837.35 1167786.7 607459.32 278348.98 51 644237.27 571387.40 1215624.7 612747.22 261941.36 52 696892.16 572884.10 1269776.3 665402.11 265200.44 53 699456.62 651775.68 1351232.3 667966.57 238369.54 54 705832.49 706606.71 1412439.2 674342.45 192808.94 55 705833.72 711143.97 1416977.7 674343.67 193757.32 56 766214.82 718620.34 1484835.2 734724.77 187104.04 57 771004.95 745806.49 1516811.4 739514.90 210501.07 58 775262.81 767666.35 1542929.2 743772.76 198524.13 59 787261.26 792115.90 1579377.2 755771.21 180123.75 60 820294.86 810374.97 1630669.8 788804.82 177602.29 61 844995.29 814284.34 1659279.6 813505.24 198176.09 62 855382.02 837662.63 1693044.6 823891.97 198207.44 63 866423.65 846447.51 1712871.2 834933.61 199889.57 64 869237.08 937115.04 1806352.1 837747.03 136897.20 65 869380.87 937300.00 1806680.9 837890.83 138989.62 66 898880.20 960199.84 1859080.0 867390.16 120635.11 67 907192.17 966928.07 1874120.2 875702.12 138067.11 68 907807.79 972221.75 1880029.5 876317.74 142219.42 69 908019.30 986104.22 1894123.5 876529.26 132934.30 70 923531.00 987205.71 1910736.7 892040.95 132206.59 71 957044.00 1049788.2 2006832.2 925553.95 100505.60 72 959507.84 1055809.4 2015317.3 928017.79 122926.65 73 961167.97 1067166.0 2028334.0 929677.92 115733.31 74 965280.94 1067393.0 2032673.9 933790.89 117002.31 75 971119.66 1068458.3 2039578.0 939629.61 119282.18 76 996133.06 1079990.2 2076123.3 964643.01 114337.50 77 997053.31 1080175.4 2077228.7 965563.26 134432.25 78 997987.64 1098467.9 2096455.6 966497.60 121016.55 79 998117.29 1099513.9 2097631.2 966627.24 121037.15 80 999333.07 1105096.2 2104429.3 967843.03 116835.44 81 1013340.9 1124050.4 2137391.3 981850.85 104611.86 82 1013692.0 1124572.0 2138264.1 982201.99 114635.03 83 1016031.6 1152265.2 2168296.8 984541.59 94858.340 84 1022399.0 1153598.9 2175997.9 990908.92 95583.316 85 1028248.8 1156911.5 2185160.2 996758.72 98013.054 86 1031373.3 1156933.2 2188306.5 999883.28 101069.17 87 1038278.3 1172466.4 2210744.6 1006788.2 92268.713 88 1045999.9 1179801.1 2225801.0 1014509.8 92748.096 89 1047344.5 1184943.1 2232287.6 1015854.4 93349.276 90 1053023.1 1191009.7 2244032.8 1021533.1 88968.676 91 1066829.9 1195837.5 2262667.5 1035339.9 89800.983 92 1081657.1 1197022.8 2278679.9 1050167.0 98656.943 93 1120102.9 1220937.3 2341040.2 1088612.9 89471.196 94 1122449.1 1231139.0 2353588.1 1090959.1 108098.93 95 1129109.9 1231511.2 2360621.1 1097619.8 109517.19 96 1133718.5 1234640.9 2368359.4 1102228.4 112003.56 97 1150520.3 1235805.6 2386325.9 1119030.2 114976.36 98 1161416.5 1243224.2 2404640.8 1129926.5 120483.69 99 1162439.9 1273409.9 2435849.8 1130949.8 101508.47 100 1188790.2 1274493.6 2463283.8 1157300.1 101377.63 101 1194878.6 1275395.2 2470273.8 1163388.5 120802.54 102 1197355.4 1275410.3 2472765.7 1165865.4 125664.32 103 1197803.5 1279190.3 2476993.8 1166313.5 124938.63 104 1197868.5 1288704.9 2486573.5 1166378.5 117348.54 105 1253968.6 1290123.7 2544092.3 1222478.5 116395.94 106 1259580.3 1294095.7 2553675.9 1228090.2 157811.24 107 1261797.5 1300917.2 2562714.7 1230307.5 156176.40 108 1262080.2 1307947.1 2570027.3 1230590.2 152370.02 109 1264553.1 1309731.3 2574284.5 1233063.1 151011.90 110 1285709.2 1319075.1 2604784.3 1254219.2 145835.14 111 1289527.0 1359042.2 2648569.2 1258037.0 130846.67 112 1293289.3 1360391.2 2653680.5 1261799.3 132334.77 113 1308126.5 1375306.3 2683432.7 1276636.4 121841.52 114 1334347.9 1375733.0 2710080.9 1302857.8 133102.42 115 1336247.9 1375746.6 2711994.4 1304757.8 155642.60 116 1342164.1 1420700.2 2762864.3 1310674.1 121496.36 117 1383124.2 1435909.2 2819033.3 1351634.1 113570.81 118 1383782.9 1438062.1 2821845.0 1352292.9 147183.17 119 1413028.4 1441590.1 2854618.5 1381538.3 144718.94 120 1413593.0 1444013.8 2857606.8 1382103.0 167402.45 121 1416028.4 1452635.7 2868664.1 1384538.4 161223.04 122 1425366.6 1457445.6 2882812.2 1393876.6 159670.60 123 1426996.9 1474112.6 2901109.5 1395506.9 155714.54 124 1442411.4 1474964.8 2917376.2 1410921.4 156306.25 125 1451997.2 1475166.8 2927164.0 1420507.1 169322.62 126 1582806.1 1483208.2 3066014.3 1551316.1 169752.44 127 1685537.8 1485635.4 3171173.1 1654047.7 270280.38 128 1686303.4 1556394.9 3242698.3 1654813.4 305346.85 129 1690055.2 1565389.8 3255445.0 1658565.1 298755.67 130 1691699.3 1565723.5 3257422.8 1660209.3 301520.59 131 1691879.6 1569962.6 3261842.1 1660389.5 299362.55 132 1693704.8 1570545.8 3264250.6 1662214.7 299071.64 133 1694149.1 1575476.6 3269625.7 1662659.1 296508.59 134 1694643.6 1576454.9 3271098.5 1663153.5 296135.17 135 1707998.9 1606971.9 3314970.8 1676508.8 275503.00 136 1726203.5 1622761.5 3348964.9 1694713.4 277466.85 137 1730517.6 1644386.7 3374904.3 1699027.6 277608.45 138 1743942.8 1700138.3 3444081.1 1712452.7 240645.26 139 1743956.9 1705993.7 3449950.7 1712466.9 246908.84 140 1744828.1 1713724.0 3458552.2 1713338.1 241070.90 141 1794525.6 1714743.9 3509269.5 1763035.5 240866.64 142 1802658.3 1769136.7 3571795.0 1771168.2 227437.46 143 1818081.5 1769529.3 3587610.8 1786591.5 233280.05 144 1819377.0 1779641.8 3599018.8 1787887.0 238126.46 145 1820362.4 1782204.3 3602566.8 1788872.4 237031.34 146 1848227.8 1785922.9 3634150.7 1816737.7 234967.45 147 1903252.8 1848266.1 3751518.8 1871762.7 201805.71 148 1903313.8 1849521.1 3752835.0 1871823.8 244438.04 149 1921221.7 1949289.6 3870511.2 1889731.6 170291.86 150 1929783.6 2017187.7 3946971.4 1898293.6 132070.04 151 1929784.2 2019752.5 3949536.7 1898294.1 135770.98 152 1935585.0 2020752.3 3956337.3 1904095.0 135008.26 153 1942597.2 2041269.9 3983867.0 1911107.1 121679.37 154 1943308.7 2041345.2 3984653.9 1911818.7 126955.32 155 1943560.7 2047899.0 3991459.7 1912070.7 121898.39 156 1944160.5 2062551.3 4006711.8 1912670.4 111719.03 157 1988989.1 2072294.0 4061283.0 1957499.0 103965.68 158 1995796.1 2073076.3 4068872.4 1964306.1 133420.36 159 1997282.6 2083629.6 4080912.2 1965792.5 130282.83 160 2064204.6 2084613.7 4148818.3 2032714.6 130736.38 161 2067000.8 2107218.5 4174219.2 2035510.7 165786.70 162 2069359.5 2118116.1 4187475.6 2037869.5 159441.27 163 2070922.3 2121456.8 4192379.1 2039432.2 159124.14 164 2096725.3 2126252.9 4222978.2 2065235.2 156883.30 165 2099380.2 2130510.7 4229891.0 2067890.2 174554.90 166 2099554.5 2148140.6 4247695.1 2068064.4 161813.63 167 2101038.7 2149621.2 4250659.9 2069548.6 161053.07 168 2101079.5 2151881.4 4252960.9 2069589.4 160038.17 169 2123833.4 2193071.4 4316904.8 2092343.4 128441.23 170 2130617.8 2215565.2 4346183.0 2099127.7 129519.12 171 2132507.7 2216049.2 4348556.9 2101017.7 133303.71 172 2133037.1 2247726.4 4380763.6 2101547.1 110353.43 173 2138413.5 2250167.5 4388581.1 2106923.5 108887.31 174 2139781.0 2250188.6 4389969.6 2108290.9 112742.44 175 2166735.6 2264797.2 4431532.8 2135245.5 103811.49 176 2189865.9 2265185.2 4455051.0 2158375.8 124105.62 177 2221420.3 2270621.6 4492041.9 2189930.3 136197.14 178 2231783.0 2271690.2 4503473.2 2200293.0 156190.27 179 2231783.0 2273009.9 4504792.9 2200293.0 163491.22 Moving reg. with 22 OBS ..M1, M2, M, M3 = resp 12538.107 12769.719 25307.825 12501.665 -------------------------------------------------------------------------------- Moving regression with 24 observations will be attempted 1 12989.777 0.0000000 0.0000000 0.0000000 200051.88 2 15026.259 2976.8697 18003.128 0.0000000 206299.45 3 15039.004 3617.2392 18656.243 0.0000000 207548.15 4 17984.267 6194.5686 24178.836 0.0000000 205505.76 5 24301.936 10194.528 34496.464 6317.6692 204523.94 6 33598.246 12954.447 46552.693 15613.979 207246.13 7 34978.810 89990.584 124969.39 16994.543 155726.28 8 44097.723 93635.953 137733.68 26113.456 154035.46 9 46485.231 101869.78 148355.01 28500.964 153781.57 10 55850.332 147919.45 203769.78 37866.065 119865.25 11 63066.888 147940.87 211007.76 45082.621 127804.85 12 65064.323 194719.48 259783.81 47080.056 101744.25 13 65065.958 214019.23 279085.19 47081.691 90643.960 14 69150.066 248308.98 317459.05 51165.799 65145.618 15 72845.064 252556.21 325401.28 54860.797 64369.939 16 75851.113 252687.06 328538.17 57866.846 67261.547 17 79138.172 265076.07 344214.24 61153.905 61978.190 18 82743.770 266253.54 348997.31 64759.503 63967.900 19 93104.586 266884.77 359989.36 75120.319 66304.346 20 98367.482 267616.97 365984.45 80383.215 73498.162 21 99600.553 269110.16 368710.72 81616.286 75111.177 22 99882.775 269110.55 368993.33 81898.508 75943.375 23 100258.42 270269.41 370527.83 82274.148 75278.493 24 100269.24 271127.13 371396.38 82284.977 74870.412 25 105427.94 272407.28 377835.22 87443.676 73938.581 26 107540.02 272407.76 379947.77 89555.749 78443.240 27 120325.28 279829.46 400154.74 102341.01 73166.919 28 240678.90 284218.41 524897.31 222694.64 80353.986 29 297962.25 301614.15 599576.40 279977.98 172106.18 30 303659.86 307344.65 611004.51 285675.59 215061.92 31 305599.92 311632.25 617232.17 287615.65 216294.54 32 306909.69 311715.52 618625.21 288925.42 217893.38 33 307194.51 311715.61 618910.12 289210.25 218915.75 34 338602.23 313703.14 652305.38 320617.97 217447.91 35 401028.43 339589.12 740617.55 383044.16 222696.66 36 426330.59 342955.73 769286.32 408346.32 262619.29 37 440460.95 343012.05 783473.01 422476.69 278899.37 38 457185.47 343792.77 800978.23 439201.20 290636.27 39 499670.12 344916.33 844586.45 481685.85 304297.26 40 500032.88 364316.12 864349.00 482048.61 317211.19 41 533295.40 387463.72 920759.12 515311.13 297507.48 42 537007.02 407290.00 944297.02 519022.75 308771.42 43 546040.14 409057.41 955097.55 528055.87 310150.60 44 546197.24 411096.51 957293.74 528212.97 314636.21 45 554586.43 437310.97 991897.40 536602.17 295347.13 46 577842.16 447254.93 1025097.1 559857.89 293780.27 47 578567.00 450840.31 1029407.3 560582.73 307637.46 48 584858.77 466354.65 1051213.4 566874.50 294998.42 49 587726.52 488881.82 1076608.3 569742.25 284296.55 50 632947.86 489265.84 1122213.7 614963.59 286439.99 51 635186.86 513581.83 1148768.7 617202.59 312295.83 52 635509.03 516880.10 1152389.1 617524.76 311490.96 53 635511.61 593308.23 1228819.8 617527.34 242394.10 54 694078.62 643553.01 1337631.6 676094.36 197859.88 55 697542.29 648842.61 1346384.9 679558.02 237446.92 56 706166.82 653248.53 1359415.4 688182.56 236444.81 57 718092.34 682993.94 1401086.3 700108.07 219070.71 58 769761.21 709356.85 1479118.1 751776.95 209231.39 59 796958.38 733433.53 1530391.9 778974.11 227717.89 60 808493.60 771343.87 1579837.5 790509.34 221800.91 61 816986.43 777809.46 1594795.9 799002.17 227617.26 62 823347.37 798274.89 1621622.3 805363.11 216812.93 63 823351.69 807416.01 1630767.7 805367.42 213786.04 64 853072.67 900895.32 1753968.0 835088.40 139258.39 65 859968.10 901904.69 1761872.8 841983.84 161904.85 66 861334.18 921694.78 1783029.0 843349.91 152062.22 67 861334.27 929827.70 1791162.0 843350.00 146409.97 68 881406.79 935655.91 1817062.7 863422.53 142733.91 69 920336.67 953339.10 1873675.8 902352.40 147644.65 70 930875.15 953661.32 1884536.5 912890.88 179739.67 71 932219.26 1030633.9 1962853.1 914234.99 128351.10 72 934473.37 1034678.8 1969152.2 916489.11 126395.78 73 940563.37 1044266.8 1984830.2 922579.11 120425.32 74 970634.86 1044512.8 2015147.6 952650.60 125268.16 75 971493.03 1046538.0 2018031.0 953508.76 148335.52 76 972158.68 1062430.9 2034589.6 954174.41 135442.74 77 972382.28 1062715.3 2035097.6 954398.02 135798.93 78 973596.71 1080744.5 2054341.2 955612.44 121878.42 79 989441.57 1081609.4 2071051.0 971457.30 122183.05 80 989459.10 1084393.5 2073852.6 971474.84 132310.90 81 991210.05 1108147.2 2099357.2 973225.79 115255.91 82 995656.67 1108713.6 2104370.3 977672.40 116170.86 83 999108.00 1133665.2 2132773.2 981123.74 101777.64 84 1002605.4 1134000.7 2136606.1 984621.18 103459.63 85 1009209.9 1137023.9 2146233.8 991225.62 103953.67 86 1026711.6 1137052.6 2163764.1 1008727.3 109399.95 87 1028313.6 1157149.9 2185463.5 1010329.4 105547.55 88 1032227.7 1168410.6 2200638.4 1014243.5 98418.990 89 1045277.7 1172141.0 2217418.6 1027293.4 98799.113 90 1059049.0 1176959.8 2236008.8 1041064.7 103748.06 91 1097698.3 1180239.2 2277937.5 1079714.0 111813.25 92 1098676.0 1182851.5 2281527.4 1080691.7 137116.32 93 1107485.9 1205576.9 2313062.7 1089501.6 118049.16 94 1113716.6 1217043.9 2330760.5 1095732.4 115043.41 95 1131067.0 1218237.7 2349304.7 1113082.8 119445.69 96 1139792.7 1221517.9 2361310.6 1121808.4 128892.12 97 1141554.4 1227138.3 2368692.7 1123570.2 131056.54 98 1165944.2 1230957.7 2396901.9 1147959.9 129245.57 99 1171917.1 1260562.6 2432479.8 1153932.9 122283.10 100 1174000.0 1261159.3 2435159.2 1156015.7 126583.98 101 1174172.2 1261961.3 2436133.6 1156188.0 127662.02 102 1174210.2 1261970.6 2436180.8 1156226.0 127798.16 103 1225150.4 1265376.5 2490526.9 1207166.1 125305.10 104 1230101.3 1270780.6 2500881.9 1212117.0 161510.25 105 1232800.9 1270950.6 2503751.5 1214816.6 165507.20 106 1233075.4 1275479.6 2508555.0 1215091.1 164454.94 107 1234585.8 1282528.8 2517114.6 1216601.5 158399.21 108 1249405.7 1288602.7 2538008.4 1231421.5 154539.09 109 1252622.1 1289255.9 2541877.9 1234637.8 165279.50 110 1263221.5 1294884.4 2558105.9 1245237.2 163074.44 111 1278394.0 1339146.0 2617540.0 1260409.7 136165.63 112 1305153.7 1340854.2 2646008.0 1287169.5 146613.64 113 1307237.9 1355559.6 2662797.5 1289253.6 156589.40 114 1312945.0 1356900.8 2669845.8 1294960.7 157161.20 115 1355581.4 1356939.5 2712520.9 1337597.1 161283.01 116 1355871.9 1407175.0 2763046.9 1337887.6 158163.33 117 1385627.4 1419001.8 2804629.2 1367643.2 148924.09 118 1385891.1 1422102.5 2807993.6 1367906.8 171609.01 119 1389545.7 1425220.7 2814766.4 1371561.4 169236.53 120 1397791.9 1427386.0 2825177.9 1379807.7 171047.43 121 1398242.6 1436249.5 2834492.1 1380258.3 170666.49 122 1412514.4 1441010.3 2853524.8 1394530.1 167303.95 123 1421650.3 1455149.2 2876799.5 1403666.0 169663.79 124 1552792.9 1455418.6 3008211.5 1534808.6 176124.08 125 1644136.9 1455857.0 3099993.9 1626152.6 279066.41 126 1648709.4 1456952.5 3105661.9 1630725.1 355076.21 127 1653109.4 1458146.5 3111255.9 1635125.1 357759.90 128 1654317.8 1529392.8 3183710.6 1636333.6 311084.84 129 1654434.0 1540037.8 3194471.8 1636449.7 303197.10 130 1657070.5 1540542.9 3197613.4 1639086.2 302887.37 131 1657162.1 1545473.4 3202635.5 1639177.8 301058.97 132 1657928.5 1546015.3 3203943.8 1639944.2 300720.09 133 1667862.1 1550736.6 3218598.6 1649877.8 297308.32 134 1682808.2 1551515.5 3234323.7 1664823.9 305151.94 135 1686629.9 1570537.6 3257167.5 1668645.7 303963.22 136 1693504.1 1584610.1 3278114.2 1675519.8 298619.54 137 1693687.1 1607639.1 3301326.2 1675702.8 288271.16 138 1694496.4 1657658.3 3352154.7 1676512.1 251329.75 139 1756429.5 1663385.2 3419814.7 1738445.2 247592.88 140 1764466.7 1679380.4 3443847.0 1746482.4 267168.75 141 1779211.7 1681888.3 3461100.0 1761227.4 271273.95 142 1780152.9 1735245.1 3515398.1 1762168.7 247029.99 143 1781350.8 1735555.6 3516906.4 1763366.6 247498.41 144 1810877.0 1745336.3 3556213.3 1792892.7 240111.68 145 1860301.0 1747315.0 3607616.0 1842316.7 261973.12 146 1860542.1 1755754.2 3616296.3 1842557.8 294366.61 147 1877871.8 1810930.1 3688801.9 1859887.5 245290.74 148 1882164.7 1811024.0 3693188.6 1864180.4 257744.26 149 1882624.4 1891251.7 3773876.1 1864640.1 197535.37 150 1890860.7 1968171.4 3859032.0 1872876.4 137860.89 151 1896324.2 1971744.4 3868068.6 1878339.9 139290.15 152 1897894.9 1973822.6 3871717.5 1879910.6 141866.84 153 1898182.2 1993168.5 3891350.6 1880197.9 127664.49 154 1898681.9 1993272.6 3891954.5 1880697.7 127832.19 155 1927499.3 1999651.2 3927150.5 1909515.0 122735.68 156 1934161.9 2007265.9 3941427.8 1916177.7 137806.44 157 1935678.1 2011574.7 3947252.8 1917693.8 139850.56 158 2002205.1 2012183.3 4014388.4 1984220.9 140649.92 159 2002611.9 2023790.7 4026402.6 1984627.7 181763.97 160 2005340.6 2023862.4 4029203.0 1987356.3 181977.22 161 2005509.0 2044669.5 4050178.5 1987524.7 169085.15 162 2027956.2 2053399.8 4081355.9 2009971.9 162359.55 163 2031137.3 2056467.8 4087605.1 2013153.0 178897.29 164 2031238.5 2057849.1 4089087.6 2013254.3 180473.80 165 2031566.1 2062445.9 4094012.0 2013581.9 176903.20 166 2031708.9 2078135.2 4109844.1 2013724.6 163454.28 167 2051413.1 2080141.4 4131554.5 2033428.8 162155.40 168 2057835.3 2083206.0 4141041.3 2039851.0 174793.44 169 2058859.2 2123018.7 4181877.9 2040874.9 147485.21 170 2059185.6 2139427.1 4198612.7 2041201.3 135218.24 171 2068360.8 2140041.4 4208402.2 2050376.5 134945.10 172 2069427.7 2174624.1 4244051.8 2051443.4 114716.84 173 2089346.9 2176766.0 4266112.9 2071362.6 113892.00 174 2112096.9 2176777.6 4288874.4 2094112.6 129750.70 175 2140998.6 2184774.2 4325772.9 2123014.4 141046.19 176 2152335.7 2184782.9 4337118.6 2134351.4 160380.38 177 2152335.7 2189093.3 4341428.9 2134351.4 165841.14 Moving reg. with 24 OBS ..M1, M2, M, M3 = resp 12229.180 12438.030 24667.210 12126.997 Problem # 2 Depending on parameters set no output may result B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 RR STEP DATA FROM SAS PAGE 31 Recursive Residual Option. Version 1 July 1994 Real*8 space available 6000000 Real*8 space used 5387 All tests will be performed using original data order. OLS results for complete data set ( 200 obs ) OLS Estimation Dependent variable Y Adjusted R**2 0.2132399381593797 Standard Error of Estimate 99.78440673900759 Sum of Squared Residuals 1941600.926509862 Model Sum of Squares 576865.2920057867 Total Sum of Squares 2518466.218515649 F( 4, 195) 14.48401811171018 F Significance 0.9999999997746845 1/Condition of XPX 1.595289077758794E-02 Number of Observations 200 Durbin-Watson 1.706553837600136 Variable Coefficient White Std. Error t X1 X- 1 37.101680 25.560231 1.4515393 X2 X- 2 180.94994 25.234510 7.1707332 X3 X- 3 -33.430182 23.221449 -1.4396252 X4 X- 4 17.392541 24.555506 0.70829495 CONSTANT X-11 76.422798 26.367677 2.8983515 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 RR STEP DATA FROM SAS PAGE 32 Recursive Residual Option. Version 1 July 1994 Real*8 space available 6000000 Real*8 space used 5362 All tests will be performed using original data order. OLS results for complete data set ( 200 obs ) OLS Estimation Dependent variable Y Adjusted R**2 0.2132399381593797 Standard Error of Estimate 99.78440673900759 Sum of Squared Residuals 1941600.926509862 Model Sum of Squares 576865.2920057867 Total Sum of Squares 2518466.218515649 F( 4, 195) 14.48401811171018 F Significance 0.9999999997746845 1/Condition of XPX 1.595289077758794E-02 Number of Observations 200 Durbin-Watson 1.706553837600136 Variable Coefficient Std. Error t X1 X- 1 37.101680 24.293083 1.5272528 X2 X- 2 180.94994 26.652402 6.7892544 X3 X- 3 -33.430182 23.239249 -1.4385225 X4 X- 4 17.392541 23.781001 0.73136285 CONSTANT X-11 76.422798 25.409288 3.0076717 Summary Table for RESIDUALS FOR COMPLETE SAMPLE Mean= 0.64943606E-13 Variance= 9708.0046 Standard Deviation= 98.529207 Skewness= -0.38233578 Kurtosis= 0.18713222 # of observations 200 Hinich bispectrum summary table. M G L BICOH Lamda 8 -0.52668557 -0.93806390 1.3612862 0.10000000E-15 9 -0.26058593 -1.5464127 1.3839300 0.10000000E-15 10 -0.33516372 0.29146825 1.3704657 0.10000000E-15 11 0.20879343 1.2108599 1.4345472 0.10000000E-15 12 1.1687423 0.55417197 1.5666967 0.10000000E-15 13 1.0914921 2.1656838 1.5643719 0.10000000E-15 14 1.1450724 1.5369125 1.5824589 0.10000000E-15 15 0.47698239 3.1717771 1.4822555 0.10000000E-15 Mean for G = 0.37108092 Mean for L = 0.80579963 For the above table NWD = 45 WT = 0.56243921 M = # of terms averaged to estimate bispectrum. G = (Z) statistic to test for Gaussianity. L = (Z) statistic to test for linearity. BICOH = average skewness (measure of nonlinear predictability). LAMDA = estimate of non-centrality. WT = whiteness statistic. Smoothing has not been done. RESIDUALS FOR COMPLETE SAMPLE Engle (1982) LM test. Lag 10 Lamda 11.169955 Sig. 0.65556875 Dickey-Fuller Unit Root Test (I) Lag 0 t test -12.127403 Prob of I(1) 0.0000 Aug. Dickey-Fuller Test (II) Lag 0 t test -12.095902 Prob of I(1) 0.0000 Aug. Dickey-Fuller Test (II) Lag 10 t test -3.9696167 Prob of I(1) 0.0000 Aug. Dickey-Fuller Test with Trend (IV) Lag 0 t test -12.069112 Prob of I(1) 0.0000 Aug. Dickey-Fuller Test with Trend (IV) Lag 10 t test -3.9868584 Prob of I(1) 0.0100 Phillips-Perron Unit Root Test (I) Lag 0 t test -12.127403 Prob of I(1) 0.0100 Aug. Phillips-Perron Test (II) Lag 0 t test -12.095902 Prob of I(1) 0.0100 Aug. Phillips-Perron Test (II) Lag 10 t test -12.123613 Prob of I(1) 0.0100 Aug. Phillips-Perron Test w. Trend (IV) Lag 0 t test -12.069112 Prob of I(1) 0.0100 Aug. Phillips-Perron Test w. Trend (IV) Lag 10 t test -12.090901 Prob of I(1) 0.0100 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 QR STEP DATA FROM SAS PAGE 33 QR option version 1 July 1996 Comments THIS IS A TEST OF THE COMMENT FOR QR Of 6000000 Real*8 space, 1400 is being used. OLS using QR decomposition for Y = Y X- 5 Number of observations = 200 Adjusted R square = 0.2132399381593799 Standard Error of Estimate = 99.78440673900758 Sum of Squared Residuals = 1941600.926509862 Variable Coefficient Standard Error t value CONSTANT X-11 76.4227977367839200 25.4092880214552600 3.00767174870281900 X3 X- 3 -33.4301824638569600 23.2392487732219700 -1.43852250948738700 X4 X- 4 17.3925408853981500 23.7810012822083300 0.731362850495715600 X1 X- 1 37.1016800502428800 24.2930833422734900 1.52725282038120600 X2 X- 2 180.949940058078100 26.6524023984587300 6.78925439263749900 Plot of residual against time RESIDUAL 242.42 * . * * * . * . * . * * . * . . . . * . * . . . * . . . . . . . * . . . . . . * . . * . . . . * . . . . . . * . . . . . * . . . .. . . * . . . . . . . . *. . . . . . . * . . . . . . * . . * . . . . .. . . * . . . . .. . . * . ... . .. . . . . *---------.-------.--------------------------------.------.----------------------------------.------- *. . . . . * . . . . . .. . . . ... . *. . . . . . .. . .. * . . . . . .. . * . . . . . * . . . .. . . . * . . . .. . * . . . * * . . . . * . . . * .. . . * . . . * . * . * . . . * . * . * . * . . * * * . * . * . * . * . -293.53 ***************************************************************************************************** 1.0000 200.00 TIME Singular values of X 20.73386408571959 4.601312023515604 4.183617041044921 3.545436798869441 2.883778644067273 PC Regression Coef. -2592.922176940513 -500.7684599592112 -81.22298916413878 -386.0627936275023 -117.5753024727914 t val. PC Reg. Coef. -25.98524420476302 -5.018504156355840 -0.8139847879897973 -3.868969173082063 -1.178293345776130 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 STAT. PROC. STEP DATA FROM SAS PAGE 34 MPROBIT Option (Version June 1995) Written by Richard McKelvey based on model for chotomous multivariate probit developed by William Zavoina and R. McKelvey Routines heavily modified by H. H. Stokes January 1985 for B34S. For 0-1 case, MPROBIT routines produce same results as B34S PROBIT option. References by McKelvey and Zavoina - An IBM FORTRAN IV Program to perform N-Chotomous Multivariate PROBIT Analysis (Behavioral Science v 16, 1971 pp. 186-7) - A Statistical Model for the Analysis of Ordinal Dependent variables (Journal of Math. Sociology v 4, 1975 pp. 103-120) N-Chotomous PROBIT Analysis: SAMPLE DATA FROM SAS TESTING TO SEE IF LIKE PROBIT COMMAND Description of variables included in analysis. Variable Sample Sample Name Number B34S # Mean Variance PROBITY 1 8 0.52500000 0.25062814 X1 2 1 0.52577403 0.89524014E-01 X2 3 2 0.51918789 0.75898460E-01 X3 4 3 0.53084051 0.93171235E-01 X4 5 4 0.52138269 0.90798025E-01 Breakdown of Dependent Variable PROBITY Code value of response Frequency R( 1)= 0.0 95 R( 2)= 1.0 105 Number of valid responses 200 Number of missing data cases 0 Number of total cases 200 Number of Allowable iterations = 50 Tolerence assumed = 0.10000000E-05 N-Chotomous PROBIT Analysis: SAMPLE DATA FROM SAS TESTING TO SEE IF LIKE PROBIT COMMAND History of computation Change in Log Likelihood Iteration Estimate 1 / cond function 0 0.85328D+01 0.17014D-01 -0.13863D+03 1 0.64616D+00 0.14518D-01 -0.10958D+03 2 0.59096D-02 0.12191D-01 -0.10830D+03 3 0.41918D-06 0.11977D-01 -0.10829D+03 N-Chotomous PROBIT Analysis: SAMPLE DATA FROM SAS TESTING TO SEE IF LIKE PROBIT COMMAND Iteration has converged on 3th iteration ---------------------------- Betas------------------------------ ------------------------- MU'S ------------------------- Maximum Maximum Represents Likelihood Standard Likelihood Standard Coefficient Effect of Estimate Error MLE/SE Coefficient Estimate Error MLE/SE Beta( 0) Constant -2.6895649 0.4282 -6.281 MU( 1) 0.00000 Beta( 1) X1 1.6357857 0.3484 4.695 Beta( 2) X2 0.93449787 0.3807 2.455 Beta( 3) X3 1.3697909 0.3420 4.005 Beta( 4) X4 1.3335445 0.3445 3.870 Log of the Likelihood Function = -108.2917020753128 -2.0 Times Log likelihood ratio = 60.17525953140640 (This is Chi squared with DF = 4 Chi Square Significance = 0.9999999999973350 Estimated Analysis of Variance Explained sum of squares = 136.6317080755604 Residual sum of squares = 200.0000000000000 Total sum of squares = 336.6317080755604 Estimated R Squared = 0.4058789020697124 Percent predicted correctly = 0.6800000000000000 Rank order correlation Y vs. Yhat = 0.3569803295360041 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 STAT. PROC. STEP DATA FROM SAS PAGE 35 MLOGLIN option (XLOGLIN Program) Maximum Likelihood Estimation of Multivariate Log-Linear Probability Model developed by M. Nerlove and S. J. Press Written by S. Kawasaki in 1977, Evanston Revised by S. Kawasaki in 1982, Berlin Revised and extended by H. H. Stokes (with assistance from E. Lehrer) April 1983 Extended by T. S. Klein and R. Klein November 1987 Revised and improved September 1988 by H. H. Stokes Name of level for each endogenous variable (except the last category) Endogenous variable 1 has 2 levels Level 1 = TEST Endogenous variables loaded from B34S XLOGLIN # Name B34S # 1 PROBITY X-( 8) Exogenous variables loaded from B34S XLOGLIN # Name B34S # 1 CONSTANT 2 X1 X-( 1) 3 X2 X-( 2) 4 X3 X-( 3) 5 X4 X-( 4) Basis Matrix used 1 1. -1. Interpretation of Basis Matrix Indicator Indexes for Generalized Parameter 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 1 TEST 1. If indicator=0, that basis vector is not used. This indicator corresponds to both the index of the basis vector above and also to the indicator of end. var. in the final parameter-estimates table. Initial values of parameters are all set to zero. Required REAL*4 space: 2456, space available: 12000000 Initial value of Log Likelihood Function -138.62944 Gradient = 10.000000 25.472040 15.573124 21.501671 19.589418 Initial H Matrix as the inverse of the Hessian Matrix when the values of parameters are all zeros. 1/condition = 0.13705048E-01 1 0.6484E-01 2 -0.2320E-01 0.5927E-01 3 -0.3305E-01 -0.1491E-01 0.7134E-01 4 -0.2662E-01 0.1550E-02 -0.1900E-02 0.5424E-01 5 -0.3136E-01 -0.2004E-02 0.9317E-02 -0.3835E-02 0.5680E-01 XLOGLIN converged at iteration 5 Final value of Log-Likelihood Function = -108.5347 Asymptotic Covariance Matrix of Estimated Parameters Asymptotic Covariance Matrix as the H-Matrix of D-P-F methodd 1 0.1398 2 -0.6119E-01 0.8885E-01 3 -0.6265E-01 -0.5662E-02 0.9416E-01 4 -0.6775E-01 0.1936E-01 0.1272E-01 0.7905E-01 5 -0.6858E-01 0.1494E-01 0.2541E-01 0.1699E-01 0.7566E-01 Asymptotic Covariance Matrix as the negative inverse of the analytically expressed Hessian Matrix 1/condition = 0.83230754E-02 1 0.1436 2 -0.6175E-01 0.8940E-01 3 -0.6845E-01 -0.4811E-02 0.1039 4 -0.6499E-01 0.2011E-01 0.9412E-02 0.8550E-01 5 -0.6859E-01 0.1342E-01 0.2340E-01 0.1017E-01 0.8672E-01 Parameter Estimates Indicator Estimated Standard t ratio Gradiant Correction Exo. Var. End. Var. Parameter Error Effect 1 1 1 2.2237 0.37891 5.8687 -0.64736E-04 -0.47822E-04 CONSTANT TEST 2 2 1 -1.3503 0.29899 -4.5161 -0.30185E-04 -0.98089E-06 X1 TEST 3 3 1 -0.77765 0.32230 -2.4128 -0.15545E-04 0.62181E-04 X2 TEST 4 4 1 -1.1398 0.29241 -3.8981 -0.36810E-04 0.21094E-04 X3 TEST 5 5 1 -1.1003 0.29448 -3.7366 -0.47918E-04 0.28851E-04 X4 TEST Correction is the change in the value of a parameter from previous point to present point. For interpretation of interactions of end. Var. see corresponding indicators in interpretation of basis-matrix table above. Contingency Table Observed Estimated Observed Estimated Indexes of Frequencies Frequencies Proportions Proportions Endogenous Variables 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 95 93.13 0.4750 0.4657 1 2 105 106.87 0.5250 0.5343 2 Estimated values are evaluated at the means of exogenous variables. Mean Values of Exogenious Variables Index of Name Mean Exo. Var. 1 CONSTANT 1.0000000 2 X1 0.52577403 3 X2 0.51918789 4 X3 0.53084051 5 X4 0.52138269 Likelihood Ratio Statistic -2(LOG(L(0))-LOG(L(*)))= 60.189454 D.F.= 5 L(*)= value of Likelihood Function optimized here. L(0)= value of Likelihood Function whose parameters are all zeros. B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 STAT. PROC. STEP DATA FROM SAS PAGE 36 MLOGLIN option (XLOGLIN Program) Maximum Likelihood Estimation of Multivariate Log-Linear Probability Model developed by M. Nerlove and S. J. Press Written by S. Kawasaki in 1977, Evanston Revised by S. Kawasaki in 1982, Berlin Revised and extended by H. H. Stokes (with assistance from E. Lehrer) April 1983 Extended by T. S. Klein and R. Klein November 1987 Revised and improved September 1988 by H. H. Stokes Name of level for each endogenous variable (except the last category) Endogenous variable 1 has 2 levels Level 1 = TEST Endogenous variables loaded from B34S XLOGLIN # Name B34S # 1 PROBITY X-( 8) Exogenous variables loaded from B34S XLOGLIN # Name B34S # 1 CONSTANT 2 X1 X-( 1) 3 X2 X-( 2) 4 X3 X-( 3) 5 X4 X-( 4) Basis Matrix used 1 1. -1. Interpretation of Basis Matrix Indicator Indexes for Generalized Parameter 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 1 TEST 1. If indicator=0, that basis vector is not used. This indicator corresponds to both the index of the basis vector above and also to the indicator of end. var. in the final parameter-estimates table. Initial values of parameters are all set to zero. Required REAL*4 space: 2476, space available: 12000000 Initial value of Log Likelihood Function -138.62944 Gradient = 10.000000 25.472040 15.573124 21.501671 19.589418 Initial H Matrix as the inverse of the Hessian Matrix when the values of parameters are all zeros. 1/condition = 0.13705048E-01 1 0.6484E-01 2 -0.2320E-01 0.5927E-01 3 -0.3305E-01 -0.1491E-01 0.7134E-01 4 -0.2662E-01 0.1550E-02 -0.1900E-02 0.5424E-01 5 -0.3136E-01 -0.2004E-02 0.9317E-02 -0.3835E-02 0.5680E-01 XLOGLIN converged at iteration 5 Final value of Log-Likelihood Function = -108.5347 Asymptotic Covariance Matrix of Estimated Parameters Asymptotic Covariance Matrix as the H-Matrix of D-P-F methodd 1 0.1398 2 -0.6119E-01 0.8885E-01 3 -0.6265E-01 -0.5662E-02 0.9416E-01 4 -0.6775E-01 0.1936E-01 0.1272E-01 0.7905E-01 5 -0.6858E-01 0.1494E-01 0.2541E-01 0.1699E-01 0.7566E-01 Asymptotic Covariance Matrix as the negative inverse of the analytically expressed Hessian Matrix 1/condition = 0.83230754E-02 1 0.1436 2 -0.6175E-01 0.8940E-01 3 -0.6845E-01 -0.4811E-02 0.1039 4 -0.6499E-01 0.2011E-01 0.9412E-02 0.8550E-01 5 -0.6859E-01 0.1342E-01 0.2340E-01 0.1017E-01 0.8672E-01 Parameter Estimates Indicator Estimated Standard t ratio Gradiant Correction Exo. Var. End. Var. Parameter Error Effect 1 1 1 2.2237 0.37891 5.8687 -0.64736E-04 -0.47822E-04 CONSTANT TEST 2 2 1 -1.3503 0.29899 -4.5161 -0.30185E-04 -0.98089E-06 X1 TEST 3 3 1 -0.77765 0.32230 -2.4128 -0.15545E-04 0.62181E-04 X2 TEST 4 4 1 -1.1398 0.29241 -3.8981 -0.36810E-04 0.21094E-04 X3 TEST 5 5 1 -1.1003 0.29448 -3.7366 -0.47918E-04 0.28851E-04 X4 TEST Correction is the change in the value of a parameter from previous point to present point. For interpretation of interactions of end. Var. see corresponding indicators in interpretation of basis-matrix table above. Contingency Table Observed Estimated Observed Estimated Indexes of Frequencies Frequencies Proportions Proportions Endogenous Variables 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 95 93.13 0.4750 0.4657 1 2 105 106.87 0.5250 0.5343 2 Estimated values are evaluated at the means of exogenous variables. Mean Values of Exogenious Variables Index of Name Mean Exo. Var. 1 CONSTANT 1.0000000 2 X1 0.52577403 3 X2 0.51918789 4 X3 0.53084051 5 X4 0.52138269 Probability evaluated at specified point Index of Name of Specified Value Exo. Var. Specified Var. 2 X1 0.30100000 3 X2 0.81180000 When some variables are not specified, their mean values are used. Specified Probability Index of Factors Probability at means 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 0.5036 0.4657 1 2 0.4964 0.5343 2 Elasticity of probability with respect to variable X3 Elasticity Partial Derivative Indexes of End. Var.s dP/dX 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 -0.6007 -0.5699 1 2 0.6094 0.5699 2 Likelihood Ratio Statistic -2(LOG(L(0))-LOG(L(*)))= 60.189454 D.F.= 5 L(*)= value of Likelihood Function optimized here. L(0)= value of Likelihood Function whose parameters are all zeros. B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 STAT. PROC. STEP DATA FROM SAS PAGE 37 MLOGLIN option (XLOGLIN Program) Maximum Likelihood Estimation of Multivariate Log-Linear Probability Model developed by M. Nerlove and S. J. Press Written by S. Kawasaki in 1977, Evanston Revised by S. Kawasaki in 1982, Berlin Revised and extended by H. H. Stokes (with assistance from E. Lehrer) April 1983 Extended by T. S. Klein and R. Klein November 1987 Revised and improved September 1988 by H. H. Stokes Name of level for each endogenous variable (except the last category) Endogenous variable 1 has 2 levels Level 1 = TEST Endogenous variables loaded from B34S XLOGLIN # Name B34S # 1 PROBITY X-( 8) Exogenous variables loaded from B34S XLOGLIN # Name B34S # 1 CONSTANT 2 X1 X-( 1) 3 X2 X-( 2) 4 X3 X-( 3) 5 X4 X-( 4) Basis Matrix used 1 1. -1. Interpretation of Basis Matrix Indicator Indexes for Generalized Parameter 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 1 TEST 1. If indicator=0, that basis vector is not used. This indicator corresponds to both the index of the basis vector above and also to the indicator of end. var. in the final parameter-estimates table. Initial values of parameters are all set to zero. Required REAL*4 space: 2484, space available: 12000000 Initial value of Log Likelihood Function -138.62944 Gradient = 10.000000 25.472040 15.573124 21.501671 19.589418 Initial H Matrix as the inverse of the Hessian Matrix when the values of parameters are all zeros. 1/condition = 0.13705048E-01 1 0.6484E-01 2 -0.2320E-01 0.5927E-01 3 -0.3305E-01 -0.1491E-01 0.7134E-01 4 -0.2662E-01 0.1550E-02 -0.1900E-02 0.5424E-01 5 -0.3136E-01 -0.2004E-02 0.9317E-02 -0.3835E-02 0.5680E-01 XLOGLIN converged at iteration 5 Final value of Log-Likelihood Function = -108.5347 Asymptotic Covariance Matrix of Estimated Parameters Asymptotic Covariance Matrix as the H-Matrix of D-P-F methodd 1 0.1398 2 -0.6119E-01 0.8885E-01 3 -0.6265E-01 -0.5662E-02 0.9416E-01 4 -0.6775E-01 0.1936E-01 0.1272E-01 0.7905E-01 5 -0.6858E-01 0.1494E-01 0.2541E-01 0.1699E-01 0.7566E-01 Asymptotic Covariance Matrix as the negative inverse of the analytically expressed Hessian Matrix 1/condition = 0.83230754E-02 1 0.1436 2 -0.6175E-01 0.8940E-01 3 -0.6845E-01 -0.4811E-02 0.1039 4 -0.6499E-01 0.2011E-01 0.9412E-02 0.8550E-01 5 -0.6859E-01 0.1342E-01 0.2340E-01 0.1017E-01 0.8672E-01 Parameter Estimates Indicator Estimated Standard t ratio Gradiant Correction Exo. Var. End. Var. Parameter Error Effect 1 1 1 2.2237 0.37891 5.8687 -0.64736E-04 -0.47822E-04 CONSTANT TEST 2 2 1 -1.3503 0.29899 -4.5161 -0.30185E-04 -0.98089E-06 X1 TEST 3 3 1 -0.77765 0.32230 -2.4128 -0.15545E-04 0.62181E-04 X2 TEST 4 4 1 -1.1398 0.29241 -3.8981 -0.36810E-04 0.21094E-04 X3 TEST 5 5 1 -1.1003 0.29448 -3.7366 -0.47918E-04 0.28851E-04 X4 TEST Correction is the change in the value of a parameter from previous point to present point. For interpretation of interactions of end. Var. see corresponding indicators in interpretation of basis-matrix table above. Contingency Table Observed Estimated Observed Estimated Indexes of Frequencies Frequencies Proportions Proportions Endogenous Variables 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 95 93.13 0.4750 0.4657 1 2 105 106.87 0.5250 0.5343 2 Estimated values are evaluated at the means of exogenous variables. Mean Values of Exogenious Variables Index of Name Mean Exo. Var. 1 CONSTANT 1.0000000 2 X1 0.52577403 3 X2 0.51918789 4 X3 0.53084051 5 X4 0.52138269 Probability evaluated at specified point Index of Name of Specified Value Exo. Var. Specified Var. 2 X1 0.30100000 3 X2 0.81180000 When some variables are not specified, their mean values are used. Specified Probability Index of Factors Probability at means 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 0.5036 0.4657 1 2 0.4964 0.5343 2 Elasticity of probability with respect to variable X3 Elasticity Partial Derivative Indexes of End. Var.s dP/dX 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 -0.6007 -0.5699 1 2 0.6094 0.5699 2 Likelihood Ratio Statistic -2(LOG(L(0))-LOG(L(*)))= 60.189454 D.F.= 5 L(*)= value of Likelihood Function optimized here. L(0)= value of Likelihood Function whose parameters are all zeros. B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 DATA STEP KMENTA TEST DATA PAGE 38 Variable # Cases Mean Std Deviation Variance Maximum Minimum Q 1 20 100.8982000 3.756498224 14.11127891 106.2320000 92.42400000 P 2 20 100.0190500 5.926086394 35.11849994 113.4900000 86.49800000 D 3 20 97.53500000 11.83048137 139.9602895 127.1000000 75.10000000 F 4 20 96.62500000 12.70879824 161.5135526 110.8000000 68.60000000 A 5 20 10.50000000 5.916079783 35.00000000 20.00000000 1.000000000 CONSTANT 6 20 1.000000000 0.000000000 0.000000000 1.000000000 1.000000000 Number of observations in data file 20 Current missing variable code 1.000000000000000E+31 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 LIST STEP KMENTA TEST DATA PAGE 39 Listing for observation 1 to observation 20. Obs Q P D F A 1 98.485000 100.32300 87.400000 98.000000 1.0000000 2 99.187000 104.26400 97.600000 99.100000 2.0000000 3 102.16300 103.43500 96.700000 99.100000 3.0000000 4 101.50400 104.50600 98.200000 98.100000 4.0000000 5 104.24000 98.001000 99.800000 110.80000 5.0000000 6 103.24300 99.456000 100.50000 108.20000 6.0000000 7 103.99300 101.06600 103.20000 105.60000 7.0000000 8 99.900000 104.76300 107.80000 109.80000 8.0000000 9 100.35000 96.446000 96.600000 108.70000 9.0000000 10 102.82000 91.228000 88.900000 100.60000 10.000000 11 95.435000 93.085000 75.100000 81.000000 11.000000 12 92.424000 98.801000 76.900000 68.600000 12.000000 13 94.535000 102.90800 84.600000 70.900000 13.000000 14 98.757000 98.756000 90.600000 81.400000 14.000000 15 105.79700 95.119000 103.10000 102.30000 15.000000 16 100.22500 98.451000 105.10000 105.00000 16.000000 17 103.52200 86.498000 96.400000 110.50000 17.000000 18 99.929000 104.01600 104.40000 92.500000 18.000000 19 105.22300 105.76900 110.70000 89.300000 19.000000 20 106.23200 113.49000 127.10000 93.000000 20.000000 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 SIMEQ STEP KMENTA TEST DATA PAGE 40 TEST CASE FROM KMENTA 1971 PAGE 565 - 582 Summary of Input Parameters and Model Number of systems to be estimated - - - 2 Number of identities - - - - - - - - - 0 Number of exogenous variables - - - - 4 Number of endogenous variables - - - - 2 Number of data points in time - - - - - 20 Maximum number of unknowns per system - 4 Print Parameter - - - - - - - - - - - - 2 Solutions wanted 0 => no, 1 => yes - - Reduced form coefficients - - - - - - - 1 Ordinary Least Squares - - - - - - - - 1 LIMLE Solution - - - - - - - - - - - - 1 Two Stage Least Squares - - - - - - - - 1 Three Stage Least Squares - - - - - - - 1 Three Stage Covariance Matrix - - - - - 1 Iterated Three Stage Least Squares - - 0 Covariance Matrix for I3SLSQ - - - - - 0 Maximum number of iterations - - - - - 25 Functional Minimization 3SLSQ - - - - - 0 Covariance Matrix for Functional Min. - 0 Systems described by the following columns of data (Variables) Name of the System LHS No. X NO. Y DEMAND EQ. 2 Q 2 1 1 CONSTANT 1 P 2 D * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * SUPPLY EQ. 2 Q 3 1 1 CONSTANT 1 P 3 F 4 A * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 SIMEQ STEP KMENTA TEST DATA PAGE 41 TEST CASE FROM KMENTA 1971 PAGE 565 - 582 Least Squares Solution for System Number 1 DEMAND EQ. Condition Number of Matrix is greater than 21.04911571706159 Relative Numerical Error in the Solution 1.301987681166638E-11 LHS Endogenous Variable No. 2 Q Exogenous Variables (Predetermined) Std. Error t 1 CONSTANT 99.89542 7.519362 13.28509 2 D 0.3346356 0.4542183E-01 7.367285 Endogenous Variables (Jointly Dependent) Std. Error t 3 P -0.3162988 0.9067741E-01 -3.488177 Residual Variance for Structural Disturbances 3.725391173733892 Ratio of Norm Residual to Norm LHS 1.762488253954560E-02 Covariance Matrix of Estimated Parameters CONSTANT D P 1 2 3 CONSTANT 1 56.54 D 2 0.3216E-01 0.2063E-02 P 3 -0.5948 -0.2333E-02 0.8222E-02 Correlation Matrix of Estimated Parameters CONSTANT D P 1 2 3 CONSTANT 1 1.000 D 2 0.9417E-01 1.000 P 3 -0.8724 -0.5665 1.000 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 SIMEQ STEP KMENTA TEST DATA PAGE 42 TEST CASE FROM KMENTA 1971 PAGE 565 - 582 Least Squares Solution for System Number 2 SUPPLY EQ. Condition Number of Matrix is greater than 17.67594711864223 Relative Numerical Error in the Solution 1.318741471618151E-11 LHS Endogenous Variable No. 2 Q Exogenous Variables (Predetermined) Std. Error t 1 CONSTANT 58.27543 11.46291 5.083825 2 F 0.2481333 0.4618785E-01 5.372263 3 A 0.2483023 0.9751777E-01 2.546227 Endogenous Variables (Jointly Dependent) Std. Error t 4 P 0.1603666 0.9488394E-01 1.690134 Residual Variance for Structural Disturbances 5.784441135907554 Ratio of Norm Residual to Norm LHS 2.130622575072544E-02 Covariance Matrix of Estimated Parameters CONSTANT F A P 1 2 3 4 CONSTANT 1 131.4 F 2 -0.3044 0.2133E-02 A 3 -0.2792 0.1316E-02 0.9510E-02 P 4 -0.9875 0.8440E-03 0.5220E-03 0.9003E-02 Correlation Matrix of Estimated Parameters CONSTANT F A P 1 2 3 4 CONSTANT 1 1.000 F 2 -0.5749 1.000 A 3 -0.2498 0.2921 1.000 P 4 -0.9079 0.1926 0.5642E-01 1.000 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 SIMEQ STEP KMENTA TEST DATA PAGE 43 TEST CASE FROM KMENTA 1971 PAGE 565 - 582 Contemporaneous Covariance of Residuals (Structural Disturbances) For Least Squares Solution. Condition Number of residual columns, 2.664758 DEMAND E SUPPLY E 1 2 DEMAND E 1 3.167 SUPPLY E 2 3.411 4.628 Correlation Matrix of Residuals DEMAND E SUPPLY E 1 2 DEMAND E 1 1.000 SUPPLY E 2 0.8912 1.000 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 SIMEQ STEP KMENTA TEST DATA PAGE 44 TEST CASE FROM KMENTA 1971 PAGE 565 - 582 Coefficients of the Reduced Form Equations. Least Squares Solution. Condition number of matrix used to find the reduced form coefficients is no smaller than 4.195815340351579 P Q 1 2 CONSTANT 1 87.31 72.28 D 2 0.7020 0.1126 F 3 -0.5206 0.1647 A 4 -0.5209 0.1648 Mean sum of squares of residuals for the reduced form equations. 1 P 0.42748D+01 2 Q 0.39192D+01 Condition Number of columns of exogenous variables, 11.845 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 SIMEQ STEP KMENTA TEST DATA PAGE 45 TEST CASE FROM KMENTA 1971 PAGE 565 - 582 Limited Information - Maximum Likelihood Solution f 1 DEMAND EQ. Rank and Condition Number of Exogenous Columns 2 8.5174634 Rank and Condition Number of Endogenous Variables orthogonal to X(K) 2 6.5593694 Rank and Condition Number of Endogenous Variables orthogonal to X 2 2.3005812 Value of LIML Parameter is 1.173867141559841 Condition Number of Matrix is greater than 8.517463415017575 Relative Numerical Error in the Solution 4.487883690647531E-12 LHS Endogenous Variable No. 2 Q Standard Deviation Equals 2SLSQ Standard Deviation. Exogenous Variables (Predetermined) 1 CONSTANT 93.61922 2 D 0.3100134 Endogenous Variables (Jointly Dependent) 3 P -0.2295381 Residual Variance for Structural Disturbances 3.926009688207962 Ratio of Norm Residual to Norm LHS 1.809322459330604E-02 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 SIMEQ STEP KMENTA TEST DATA PAGE 46 TEST CASE FROM KMENTA 1971 PAGE 565 - 582 Limited Information - Maximum Likelihood Solution f 2 SUPPLY EQ. Rank and Condition Number of Exogenous Columns 3 8.2098363 Rank and Condition Number of Endogenous Variables orthogonal to X(K) 1 1.0000000 Rank and Condition Number of Endogenous Variables orthogonal to X 2 1.0000000 Value of LIML Parameter is 1.000000000000000 Condition Number of Matrix is greater than 8.209836250820180 Relative Numerical Error in the Solution 4.943047984855735E-12 LHS Endogenous Variable No. 2 Q Standard Deviation Equals 2SLSQ Standard Deviation. Exogenous Variables (Predetermined) 1 CONSTANT 49.53244 2 F 0.2556057 3 A 0.2529242 Endogenous Variables (Jointly Dependent) 4 P 0.2400758 Residual Variance for Structural Disturbances 6.039577731391617 Ratio of Norm Residual to Norm LHS 2.177103664979223E-02 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 SIMEQ STEP KMENTA TEST DATA PAGE 47 TEST CASE FROM KMENTA 1971 PAGE 565 - 582 Contemporaneous Covariance of Residuals (Structural Disturbances) For LIMLE Solution. Condition Number of residual columns, 2.811594 DEMAND E SUPPLY E 1 2 DEMAND E 1 3.337 SUPPLY E 2 3.629 4.832 Correlation Matrix of Residuals DEMAND E SUPPLY E 1 2 DEMAND E 1 1.000 SUPPLY E 2 0.9038 1.000 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 SIMEQ STEP KMENTA TEST DATA PAGE 48 TEST CASE FROM KMENTA 1971 PAGE 565 - 582 Coefficients of the Reduced Form Equations. LIMLE Solution. Condition number of matrix used to find the reduced form coefficients is no smaller than 4.258817996669486 P Q 1 2 CONSTANT 1 93.88 72.07 D 2 0.6601 0.1585 F 3 -0.5443 0.1249 A 4 -0.5386 0.1236 Mean sum of squares of residuals for the reduced form equations. 1 P 0.41286D+01 2 Q 0.38401D+01 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 SIMEQ STEP KMENTA TEST DATA PAGE 49 TEST CASE FROM KMENTA 1971 PAGE 565 - 582 Two Stage Least Squares Solution for System Number 1 DEMAND EQ. Condition Number of Matrix is greater than 21.98482284147018 Relative Numerical Error in the Solution 1.411421448020441E-11 LHS Endogenous Variable No. 2 Q Exogenous Variables (Predetermined) Std. Error t Theil SE Theil t 1 CONSTANT 94.63330 7.920838 11.94738 7.302652 12.95876 2 D 0.3139918 0.4694366E-01 6.688695 0.4327991E-01 7.254908 Endogenous Variables (Jointly Dependent) Std. Error t Theil SE Theil t 3 P -0.2435565 0.9648429E-01 -2.524313 0.8895412E-01 -2.738002 Residual Variance for Structural Disturbances 3.866416929101937 Ratio of Norm Residual to Norm LHS 1.795538131264630E-02 Covariance Matrix of Estimated Parameters CONSTANT D P 1 2 3 CONSTANT 1 62.74 D 2 0.4930E-01 0.2204E-02 P 3 -0.6734 -0.2642E-02 0.9309E-02 Correlation Matrix of Estimated Parameters CONSTANT D P 1 2 3 CONSTANT 1 1.000 D 2 0.1326 1.000 P 3 -0.8812 -0.5833 1.000 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 SIMEQ STEP KMENTA TEST DATA PAGE 50 TEST CASE FROM KMENTA 1971 PAGE 565 - 582 Two Stage Least Squares Solution for System Number 2 SUPPLY EQ. Condition Number of Matrix is greater than 18.21923089332271 Relative Numerical Error in the Solution 1.431397195953368E-11 LHS Endogenous Variable No. 2 Q Exogenous Variables (Predetermined) Std. Error t Theil SE Theil t 1 CONSTANT 49.53244 12.01053 4.124086 10.74254 4.610868 2 F 0.2556057 0.4725007E-01 5.409637 0.4226175E-01 6.048158 3 A 0.2529242 0.9965509E-01 2.537996 0.8913422E-01 2.837565 Endogenous Variables (Jointly Dependent) Std. Error t Theil SE Theil t 4 P 0.2400758 0.9993385E-01 2.402347 0.8938355E-01 2.685905 Residual Variance for Structural Disturbances 6.039577731391617 Ratio of Norm Residual to Norm LHS 2.177103664979223E-02 Covariance Matrix of Estimated Parameters CONSTANT F A P 1 2 3 4 CONSTANT 1 144.3 F 2 -0.3238 0.2233E-02 A 3 -0.2952 0.1377E-02 0.9931E-02 P 4 -1.095 0.9362E-03 0.5791E-03 0.9987E-02 Correlation Matrix of Estimated Parameters CONSTANT F A P 1 2 3 4 CONSTANT 1 1.000 F 2 -0.5706 1.000 A 3 -0.2467 0.2924 1.000 P 4 -0.9126 0.1983 0.5815E-01 1.000 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 SIMEQ STEP KMENTA TEST DATA PAGE 51 TEST CASE FROM KMENTA 1971 PAGE 565 - 582 Contemporaneous Covariance of Residuals (Structural Disturbances) For Two Stage Least Squares Solution. Condition Number of residual columns, 2.804709 DEMAND E SUPPLY E 1 2 DEMAND E 1 3.286 SUPPLY E 2 3.593 4.832 Correlation Matrix of Residuals DEMAND E SUPPLY E 1 2 DEMAND E 1 1.000 SUPPLY E 2 0.9017 1.000 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 SIMEQ STEP KMENTA TEST DATA PAGE 52 TEST CASE FROM KMENTA 1971 PAGE 565 - 582 Coefficients of the Reduced Form Equations. Two Stage Least Squares Solution Condition number of matrix used to find the reduced form coefficients is no smaller than 4.135372945327849 P Q 1 2 CONSTANT 1 93.25 71.92 D 2 0.6492 0.1559 F 3 -0.5285 0.1287 A 4 -0.5230 0.1274 Mean sum of squares of residuals for the reduced form equations. 1 P 0.39831D+01 2 Q 0.38317D+01 Condition number of the large matrix in Three Stage Least Squares 60.70221 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 SIMEQ STEP KMENTA TEST DATA PAGE 53 TEST CASE FROM KMENTA 1971 PAGE 565 - 582 Three Stage Least Squares Solution for System Number 1 DEMAND EQ. LHS Endogenous Variable No. 2 Q Exogenous Variables (Predetermined) Std. Error t Theil SE Theil t 1 CONSTANT 94.63330 7.920838 11.94738 7.302652 12.95876 2 D 0.3139918 0.4694366E-01 6.688695 0.4327991E-01 7.254908 Endogenous Variables (Jointly Dependent) Std. Error t Theil SE Theil t 3 P -0.2435565 0.9648429E-01 -2.524313 0.8895412E-01 -2.738002 Residual Variance (For Structural Disturbances) 3.286454 Three Stage Least Squares Covariance for System DEMAND EQ. CONSTANT D P 1 2 3 CONSTANT 1 62.74 D 2 0.4930E-01 0.2204E-02 P 3 -0.6734 -0.2642E-02 0.9309E-02 Three Stage Least Squares Solution for System Number 2 SUPPLY EQ. LHS Endogenous Variable No. 2 Q Exogenous Variables (Predetermined) Std. Error t Theil SE Theil t 1 CONSTANT 52.11764 11.89337 4.382074 10.63776 4.899308 2 F 0.2289775 0.4399381E-01 5.204767 0.3934926E-01 5.819106 3 A 0.3579074 0.7288940E-01 4.910281 0.6519426E-01 5.489861 Endogenous Variables (Jointly Dependent) Std. Error t Theil SE Theil t 4 P 0.2289322 0.9967317E-01 2.296828 0.8915039E-01 2.567932 Residual Variance (For Structural Disturbances) 5.360809 Three Stage Least Squares Covariance for System SUPPLY EQ. CONSTANT F A P 1 2 3 4 CONSTANT 1 141.5 F 2 -0.2950 0.1935E-02 A 3 -0.4090 0.2548E-02 0.5313E-02 P 4 -1.083 0.8119E-03 0.1069E-02 0.9935E-02 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 SIMEQ STEP KMENTA TEST DATA PAGE 54 TEST CASE FROM KMENTA 1971 PAGE 565 - 582 Contenporaneous Covariance of Residuals (Structural Disturbances) For Three Stage Least Squares Solution. Condition Number of residual columns, 6.321462 DEMAND E SUPPLY E 1 2 DEMAND E 1 3.286 SUPPLY E 2 4.111 5.361 Correlation Matrix of Residuals DEMAND E SUPPLY E 1 2 DEMAND E 1 1.000 SUPPLY E 2 0.9794 1.000 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 SIMEQ STEP KMENTA TEST DATA PAGE 55 TEST CASE FROM KMENTA 1971 PAGE 565 - 582 Coefficients of the Reduced Form Equations. Three Stage Least Squares Solution using Orthogonal Factorization. Condition number of matrix used to find the reduced form coefficients is no smaller than 4.232905401139098 P Q 1 2 CONSTANT 1 89.98 72.72 D 2 0.6645 0.1521 F 3 -0.4846 0.1180 A 4 -0.7575 0.1845 Mean sum of squares of residuals for the reduced form equations. 1 P 0.19065D+01 2 Q 0.42494D+01 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 DATA STEP TEST DATA FROM LEE-JUDGE-ZELLNER PAGE 56 Variable # Cases Mean Std Deviation Variance Maximum Minimum VAR1 1 5 0.8080000000 0.1917550521 0.3677000000E-01 0.9700000000 0.5000000000 VAR2 2 5 0.1920000000 0.1917550521 0.3677000000E-01 0.5000000000 0.3000000000E-01 SAMPSIZE 3 5 10.00000000 0.000000000 0.000000000 10.00000000 10.00000000 CONSTANT 4 5 1.000000000 0.000000000 0.000000000 1.000000000 1.000000000 Number of observations in data file 5 Current missing variable code 1.000000000000000E+31 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 LIST STEP TEST DATA FROM LEE-JUDGE-ZELLNER PAGE 57 Listing for observation 1 to observation 5. Obs VAR1 VAR2 SAMPSIZE 1 0.50000000 0.50000000 10.000000 2 0.75000000 0.25000000 10.000000 3 0.88000000 0.12000000 10.000000 4 0.94000000 0.60000000E-01 10.000000 5 0.97000000 0.30000000E-01 10.000000 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 TRANSPROB STEP TEST DATA FROM LEE-JUDGE-ZELLNER PAGE 58 TRANSFER PROBABILITY (MARKOV PROBABILITY MODEL) OPTION SELECTED FOR DISCUSSION OF PROCEDURES USED SEE LEE, JUDGE AND ZELLNER (1970) ON MAIN CONTROL CARD NT1, NS, SS, TOL, KDROP, KW, KV, KP, KEY(1)- (9), IKILL, ISMP, ITIT 5 2 0. 0.10000000E-05 2 1 2 1 1 0 1 8 2 0 3 2 0 0 3 1 VARIABLES INPUTED FROM B34S B34S # NAME COL # ON INPUT 1 VAR1 1 2 VAR2 2 NOTE KEY(8).GT.1 - LP ITERATION CANNOT BE PERFORMED SINCE ARRAYS ARE NOT SET BIG ENOUGH FOR THIS TP RUN OF 6000000 SPACE AVAILABLE 315 REQUIRED (NOTE: SPACE GIVEN IN REAL*8) SAMPLE SIZE READ FROM B34S X- 3 NAME = SAMPSIZE B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 TRANSPROB STEP TEST DATA FROM LEE-JUDGE-ZELLNER PAGE 59 TEST DATA FROM TEXT THE OBSERVED PROPORTIONS AND SAMPLE SIZES 1 VAR1 2 VAR2 3 SAMPSIZE 1 0.500000 0.500000 10.0000 2 0.750000 0.250000 10.0000 3 0.880000 0.120000 10.0000 4 0.940000 0.600000E-01 10.0000 5 0.970000 0.300000E-01 10.0000 AS DESIRED,COLUMN 2 IS DROPPED IN FORMING THE SYSTEM. READ THE FOLLOWING MATRICES IN THE SEQUENCE 1 VAR1 2 VAR2 THE WEIGHT MATRIX IS DERIVED FROM THE MLE WITH ELEMENTS N/WR(T)+Z*(N/WJ(T)), Z=1 FOR DIAGONALS AND Z=0 OTHERWISE. GENERALIZED XSX FOR QP INPUT 1 2 1 507.548 69.1939 2 69.1939 23.0422 GENERALIZED XSY FOR QP INPUT 1 542.500 2 80.8333 UNRESTRICTED ESTIMATOR OF THE TRANSITION MATRIX 0.9999988 0.1152761E-05 0.5051406 0.4948594 PREDICTIONS USING TRANSFER PROBABILITY MATRIX 20 PERIODS AHEAD 1 VAR1 2 VAR2 1 0.985153 0.148469E-01 2 0.992652 0.734826E-02 3 0.996362 0.363750E-02 4 0.998199 0.180120E-02 5 0.999108 0.892492E-03 6 0.999557 0.442810E-03 7 0.999780 0.220281E-03 8 0.999890 0.110160E-03 9 0.999944 0.556666E-04 10 0.999971 0.286998E-04 11 0.999985 0.153551E-04 12 0.999991 0.875136E-05 13 0.999995 0.548344E-05 14 0.999996 0.386629E-05 15 0.999997 0.306603E-05 16 0.999997 0.267001E-05 17 0.999998 0.247404E-05 18 0.999998 0.237706E-05 19 0.999998 0.232907E-05 20 0.999998 0.230532E-05 EIGENVALUES FOR TRANSITION MATRIX 1 1.0000000 + , - 0.0000000 IMAGINARY 2 0.49485824 + , - 0.0000000 IMAGINARY THEIL MEASURE OF CONVERGENCE RATE = 0.24488467 , ACCURACY OF CONVERGENCE MEASURE = 0.0000000 Eigenvector matrix rcond = 3.906327433136840E-03 EIGENVECTOR MATRIX 1 2 1 0.390622E-02 -0.228207E-05 2 0.390622E-02 1.00001 ASYMPTOTIC PREDICTION - CALCULATED USING EIGENVALUE DECOMPOSITION OF TRANSITION MATRIX 1 VAR1 2 VAR2 1 0.999998 0.228205E-05 STATISTICAL DECOMPOSITION OF ASYMPTOTIC TRANSITION MATRIX - FOR A DETAILED DISCUSSION SEE THEIL(1972) FUNDAMENTAL MATRIX Z 1 / CONDITION 0.33792002 1 VAR1 2 VAR2 1 1.00000 -0.223560E-05 2 -0.979640 1.97964 EXCHANGE MATRIX (BIG PI) - PROB OF EXCHANGE BETWEEN TWO STATES IN SUCCESSIVE STEPS AFTER EQUILIBRIUM 1 VAR1 2 VAR2 1 0.999997 0.115276E-05 2 0.115276E-05 0.112930E-05 MEAN FIRST PASSAGE ( MEAN RECURRENCE WHEN I=J ) TIME ( MATRIX M) 1 VAR1 2 VAR2 1 1.00000 867483. 2 1.97965 438202. DECOMPOSITION OF MEAN PASSAGE MATRIX INTO TRAVEL TIME (TAU) AND WAITING TIME (OMEGA) TRAVEL TIME (TAU) MATRIX 1 VAR1 2 VAR2 1 0.00000 429281. 2 0.979645 0.00000 WAITING TIME (OMEGA) 1 VAR1 2 VAR2 1 1.00000 438202. CAN FURTHER BREAK DOWN TRAVEL TIME MATRIX (TAU) INTO DISTANCE MATRIX (S) AND DESTINATION EFFECT DISTANCE MATRIX WILL ONLY BE MEANINGFUL IF EXCHANGE MATRIX (BIG PHI) IS SYMMETRIC OR ALMOST SYMMETRIC FURTHER DECOMPOSITION IS POSSIBLE IF STATES CAN BE RANK ORDERED - FOR FURTHER RESULTS SEE THEIL(1972) DISTANCE MATRIX (S) 1 VAR1 2 VAR2 1 -0.223560E-05 0.979642 2 0.979642 -429280. DESTINATION EFFECT MATRIX (IN ROW FORM) 1 VAR1 2 VAR2 1 0.223560E-05 429280. LEAVING DECOMPOSITION SECTION OF B34S TRAPB - THE ABOVE LISTED MATRIXES MUST BE INTERPRETED GIVEN ASSUMPTIONS IN THEIL(1972) DISPERSION MATRIX OF THE ML (GLS, MCS) ESTIMATOR P I,J), OR THE INVERSE OF XSX FOR ANYTHING ELSE. 1 2 1 0.333595E-02 -0.100176E-01 2 -0.100176E-01 0.734807E-01 PREDICTED PROPORTIONS WITHIN SAMPLE 1 VAR1 2 VAR2 2 0.752570 0.247430 3 0.876284 0.123716 4 0.940616 0.593841E-01 5 0.970307 0.296926E-01 6 0.985153 0.148469E-01 SUM OF SQUARED ERROR = 0.41767540E-04 MEAN SQUARED ERROR = 0.52209425E-05 CHI SQUARE VALUE = 0.17288640E-02 MODIFIED CHI SQUARE STATISTIC = 0.17593333E-02 THE UNRESTRICTED ESTIMATOR IS PERFECT. BAYESIAN ESTIMATION OF THE TRANSITION PROBILITIES PRIOR PARAMETERS A(I,J) 99.00 1.000 50.00 50.00 MULTI-BETA PRIOR MEANS 0.9900 0.1000E-01 0.5000 0.5000 MULTI-BETA PRIOR COVARIANCE MATRIX 1 2 1 0.980198E-04 0.00000 2 0.00000 0.247525E-02 THE FOLLOWING XSX AND XSY DENOTE XSX+S(0) AND XSY+S(0) RESPECTIVELY GENERALIZED XSX FOR QP INPUT 1 2 1 10406.5 69.1939 2 69.1939 415.042 GENERALIZED XSY FOR QP INPUT 1 10441.5 2 276.833 UNRESTRICTED ESTIMATOR OF THE TRANSITION MATRIX 1.000032 -0.3226352E-04 0.5002798 0.4997202 PREDICTED PROPORTIONS WITHIN SAMPLE 1 VAR1 2 VAR2 2 0.750156 0.249844 3 0.875094 0.124906 4 0.940062 0.599380E-01 5 0.970047 0.299529E-01 6 0.985040 0.149603E-01 SUM OF SQUARED ERROR = 0.48195477E-04 MEAN SQUARED ERROR = 0.60244346E-05 CHI SQUARE VALUE = 0.22046080E-02 MODIFIED CHI SQUARE STATISTIC = 0.22818455E-02 THE UNRESTRICTED ESTIMATOR VIOLATES THE PROPERTIES OF PROBABILITY. HENCE, THE ITERATION PROCEDURE IS REQUIRED. THE FOLLOWINGS ARE QP SOLUTIONS # of iterations, piviot row, new basis, obj. value before iteration 1 1 3 5 10718.3 2 4 4 0 242.592 3 3 1 0 0.335379 NUMBER OF CYCLES = 3 ORIGINAL VALUE FOR LP OR ROUNDING ERROR FOR QP= 0.000000 I J B(I) 1 3 1.0000000 2 6 0.49971480 3 1 0.33537935 4 4 0.50028520 HENCE, THE BAYESIAN ESTIMATOR OF THE TRANSITION MATRIX IS 1 2 1 1.00000 0.00000 1 2 2 0.500285 0.499715 PREDICTIONS USING TRANSFER PROBABILITY MATRIX 20 PERIODS AHEAD 1 VAR1 2 VAR2 1 0.985009 0.149914E-01 2 0.992509 0.749145E-02 3 0.996256 0.374359E-02 4 0.998129 0.187073E-02 5 0.999065 0.934829E-03 6 0.999533 0.467148E-03 7 0.999767 0.233441E-03 8 0.999883 0.116654E-03 9 0.999942 0.582936E-04 10 0.999971 0.291302E-04 11 0.999985 0.145568E-04 12 0.999993 0.727424E-05 13 0.999996 0.363505E-05 14 0.999998 0.181649E-05 15 0.999999 0.907725E-06 16 1.00000 0.453604E-06 17 1.00000 0.226672E-06 18 1.00000 0.113272E-06 19 1.00000 0.566035E-07 20 1.00000 0.282856E-07 EIGENVALUES FOR TRANSITION MATRIX 1 0.49971480 + , - 0.0000000 IMAGINARY 2 1.0000000 + , - 0.0000000 IMAGINARY THEIL MEASURE OF CONVERGENCE RATE = 0.24971488 , ACCURACY OF CONVERGENCE MEASURE = 0.0000000 Eigenvector matrix rcond = 0.3000000000000000 EIGENVECTOR MATRIX 1 2 1 0.00000 1.00000 2 1.00000 1.00000 ASYMPTOTIC PREDICTION - CALCULATED USING EIGENVALUE DECOMPOSITION OF TRANSITION MATRIX 1 VAR1 2 VAR2 1 -0.300000E-01 0.300000E-01 STATISTICAL DECOMPOSITION OF ASYMPTOTIC TRANSITION MATRIX - FOR A DETAILED DISCUSSION SEE THEIL(1972) FUNDAMENTAL MATRIX Z IN LONGRN MATRIX Z SINGULAR TO MACHINE PRECISION, 1/ COND. 0.0000000 PREDICTED PROPORTIONS WITHIN SAMPLE 1 VAR1 2 VAR2 2 0.750143 0.249857 3 0.875071 0.124929 4 0.940034 0.599658E-01 5 0.970017 0.299829E-01 6 0.985009 0.149914E-01 SUM OF SQUARED ERROR = 0.48627752E-04 MEAN SQUARED ERROR = 0.60784690E-05 CHI SQUARE VALUE = 0.22234698E-02 MODIFIED CHI SQUARE STATISTIC = 0.23017789E-02 ON RECURSIVE CARD NREC,NST,KV,KP,KEY(1)-(9) READ AS 6 3 0 1 0 0 8 2 0 3 2 0 0 RECURSIVE OUTPUT,K= 1 THE WEIGHT MATRIX WILL BE DIVIDED BY THE SCALAR 0.10E+04 MULTI-BETA PRIOR COVARIANCE MATRIX 1 2 1 0.980198E-04 0.00000 2 0.00000 0.247525E-02 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 TRANSPROB STEP TEST DATA FROM LEE-JUDGE-ZELLNER PAGE 60 THE FOLLOWING XSX AND XSY DENOTE XSX+S(0) AND XSY+S(0) RESPECTIVELY UNRESTRICTED ESTIMATOR OF THE TRANSITION MATRIX 1.000000 -0.3516282E-07 0.5001467 0.4998533 PREDICTED PROPORTIONS WITHIN SAMPLE 1 VAR1 2 VAR2 2 0.750073 0.249927 3 0.875037 0.124963 4 0.940018 0.599824E-01 5 0.970009 0.299912E-01 6 0.985004 0.149956E-01 SUM OF SQUARED ERROR = 0.49280355E-04 MEAN SQUARED ERROR = 0.61600444E-05 CHI SQUARE VALUE = 0.22532246E-02 MODIFIED CHI SQUARE STATISTIC = 0.23331727E-02 THE UNRESTRICTED ESTIMATOR VIOLATES THE PROPERTIES OF PROBABILITY. HENCE, THE ITERATION PROCEDURE IS REQUIRED. THE FOLLOWINGS ARE QP SOLUTIONS NUMBER OF CYCLES = 3 ORIGINAL VALUE FOR LP OR ROUNDING ERROR FOR QP= 0.000000 HENCE, THE BAYESIAN ESTIMATOR OF THE TRANSITION MATRIX IS 1 2 1 1.00000 0.00000 1 2 2 0.500147 0.499853 PREDICTIONS USING TRANSFER PROBABILITY MATRIX 20 PERIODS AHEAD 1 VAR1 2 VAR2 1 0.985004 0.149956E-01 2 0.992504 0.749560E-02 3 0.996253 0.374670E-02 4 0.998127 0.187280E-02 5 0.999064 0.936126E-03 6 0.999532 0.467926E-03 7 0.999766 0.233894E-03 8 0.999883 0.116913E-03 9 0.999942 0.584392E-04 10 0.999971 0.292110E-04 11 0.999985 0.146012E-04 12 0.999993 0.729848E-05 13 0.999996 0.364817E-05 14 0.999998 0.182355E-05 15 0.999999 0.911507E-06 16 1.00000 0.455620E-06 17 1.00000 0.227743E-06 18 1.00000 0.113838E-06 19 1.00000 0.569024E-07 20 1.00000 0.284428E-07 EIGENVALUES FOR TRANSITION MATRIX 1 0.49985333 + , - 0.0000000 IMAGINARY 2 1.0000000 + , - 0.0000000 IMAGINARY THEIL MEASURE OF CONVERGENCE RATE = 0.24985335 , ACCURACY OF CONVERGENCE MEASURE = 0.0000000 Eigenvector matrix rcond = 0.3000000000000000 EIGENVECTOR MATRIX 1 2 1 0.00000 1.00000 2 1.00000 1.00000 ASYMPTOTIC PREDICTION - CALCULATED USING EIGENVALUE DECOMPOSITION OF TRANSITION MATRIX 1 VAR1 2 VAR2 1 -0.300000E-01 0.300000E-01 STATISTICAL DECOMPOSITION OF ASYMPTOTIC TRANSITION MATRIX - FOR A DETAILED DISCUSSION SEE THEIL(1972) FUNDAMENTAL MATRIX Z IN LONGRN MATRIX Z SINGULAR TO MACHINE PRECISION, 1/ COND. 0.0000000 PREDICTED PROPORTIONS WITHIN SAMPLE 1 VAR1 2 VAR2 2 0.750073 0.249927 3 0.875037 0.124963 4 0.940018 0.599824E-01 5 0.970009 0.299912E-01 6 0.985004 0.149956E-01 SUM OF SQUARED ERROR = 0.49280856E-04 MEAN SQUARED ERROR = 0.61601069E-05 CHI SQUARE VALUE = 0.22532469E-02 MODIFIED CHI SQUARE STATISTIC = 0.23331963E-02 RECURSIVE DIFFERENCE = 0.000277 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 LIST STEP TEST DATA FROM LEE-JUDGE-ZELLNER PAGE 61 Listing for observation 1 to observation 5. Obs VAR1 VAR2 SAMPSIZE 1 0.97000000 0.30000000E-01 10.000000 2 0.94000000 0.60000000E-01 10.000000 3 0.88000000 0.12000000 10.000000 4 0.75000000 0.25000000 10.000000 5 0.50000000 0.50000000 10.000000 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 DATA STEP PAGE 62 Variable # Cases Mean Std Deviation Variance Maximum Minimum TIME 1 296 148.5000000 85.59205571 7326.000000 296.0000000 1.000000000 GASIN 2 296 -0.5683445946E-01 1.072765504 1.150825827 2.834000000 -2.716000000 GASOUT 3 296 53.50912162 3.202120786 10.25357753 60.50000000 45.60000000 CONSTANT 4 296 1.000000000 0.000000000 0.000000000 1.000000000 1.000000000 Number of observations in data file 296 Current missing variable code 1.000000000000000E+31 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 4 DESCRIBE STEP PAGE 63 Describe Command. Version 1 July 1997 Series TIME Label: Number of observations 296 Number of nonmissing observations 296 Mean of series 148.5000000000000 Median of series 148.5000000000000 Standard deviation of series 85.59205570612264 Variance of series 7326.000000000001 Skewness of series 0.000000000000000E+00 Kurtosis of series -1.212168825766799 C6 7.000540186922194 Coefficient of Variation 2.027027027027027E-02 Maximum of Series 296.0000000000000 Minimum of Series 1.000000000000000 1st Quartile 74.50000000000000 3rd Quartile 223.0000000000000 Maximim - Minimum 295.0000000000000 Q3 - Q1 148.5000000000000 Series GASIN Label: Number of observations 296 Number of nonmissing observations 296 Mean of series -5.683445945945951E-02 Median of series 0.000000000000000E+00 Standard deviation of series 1.072765504078465 Variance of series 1.150825826740724 Skewness of series -5.164336009813296E-02 Kurtosis of series -0.2713048212859461 C6 0.2461730608307597 Coefficient of Variation -4.938580464467111E-02 Maximum of Series 2.834000000000000 Minimum of Series -2.716000000000000 1st Quartile -0.8360000000000000 3rd Quartile 0.7090000000000000 Maximim - Minimum 5.550000000000001 Q3 - Q1 1.545000000000000 Series GASOUT Label: Number of observations 296 Number of nonmissing observations 296 Mean of series 53.50912162162156 Median of series 53.50000000000000 Standard deviation of series 3.202120786435257 Variance of series 10.25357753092075 Skewness of series -5.173145345413963E-02 Kurtosis of series -0.6089697605545719 C6 2.113810959374490 Coefficient of Variation 5.218580681743433 Maximum of Series 60.50000000000000 Minimum of Series 45.60000000000000 1st Quartile 51.20000000000000 3rd Quartile 56.00000000000000 Maximim - Minimum 14.90000000000000 Q3 - Q1 4.799999999999997 VAR=GASIN SERIES # 1 FROM BJ -- GAS INPUT Listing of Observed Series 1- 8 -0.10900E+00 0.00000E+00 0.17800E+00 0.33900E+00 0.37300E+00 0.44100E+00 0.46100E+00 0.34800E+00 9- 16 0.12700E+00 -0.18000E+00 -0.58800E+00 -0.10550E+01 -0.14210E+01 -0.15200E+01 -0.13020E+01 -0.81400E+00 17- 24 -0.47500E+00 -0.19300E+00 0.88000E-01 0.43500E+00 0.77100E+00 0.86600E+00 0.87500E+00 0.89100E+00 25- 32 0.98700E+00 0.12630E+01 0.17750E+01 0.19760E+01 0.19340E+01 0.18660E+01 0.18320E+01 0.17670E+01 33- 40 0.16080E+01 0.12650E+01 0.79000E+00 0.36000E+00 0.11500E+00 0.88000E-01 0.33100E+00 0.64500E+00 41- 48 0.96000E+00 0.14090E+01 0.26700E+01 0.28340E+01 0.28120E+01 0.24830E+01 0.19290E+01 0.14850E+01 49- 56 0.12140E+01 0.12390E+01 0.16080E+01 0.19050E+01 0.20230E+01 0.18150E+01 0.53500E+00 0.12200E+00 57- 64 0.90000E-02 0.16400E+00 0.67100E+00 0.10190E+01 0.11460E+01 0.11550E+01 0.11120E+01 0.11210E+01 65- 72 0.12230E+01 0.12570E+01 0.11570E+01 0.91300E+00 0.62000E+00 0.25500E+00 -0.28000E+00 -0.10800E+01 73- 80 -0.15510E+01 -0.17990E+01 -0.18250E+01 -0.14560E+01 -0.94400E+00 -0.57000E+00 -0.43100E+00 -0.57700E+00 81- 88 -0.96000E+00 -0.16160E+01 -0.18750E+01 -0.18910E+01 -0.17460E+01 -0.14740E+01 -0.12010E+01 -0.92700E+00 89- 96 -0.52400E+00 0.40000E-01 0.78800E+00 0.94300E+00 0.93000E+00 0.10060E+01 0.11370E+01 0.11980E+01 97- 104 0.10540E+01 0.59500E+00 -0.80000E-01 -0.31400E+00 -0.28800E+00 -0.15300E+00 -0.10900E+00 -0.18700E+00 105- 112 -0.25500E+00 -0.22900E+00 -0.70000E-02 0.25400E+00 0.33000E+00 0.10200E+00 -0.42300E+00 -0.11390E+01 113- 120 -0.22750E+01 -0.25940E+01 -0.27160E+01 -0.25100E+01 -0.17900E+01 -0.13460E+01 -0.10810E+01 -0.91000E+00 121- 128 -0.87600E+00 -0.88500E+00 -0.80000E+00 -0.54400E+00 -0.41600E+00 -0.27100E+00 0.00000E+00 0.40300E+00 129- 136 0.84100E+00 0.12850E+01 0.16070E+01 0.17460E+01 0.16830E+01 0.14850E+01 0.99300E+00 0.64800E+00 137- 144 0.57700E+00 0.57700E+00 0.63200E+00 0.74700E+00 0.90000E+00 0.99300E+00 0.96800E+00 0.79000E+00 145- 152 0.39900E+00 -0.16100E+00 -0.55300E+00 -0.60300E+00 -0.42400E+00 -0.19400E+00 -0.49000E-01 0.60000E-01 153- 160 0.16100E+00 0.30100E+00 0.51700E+00 0.56600E+00 0.56000E+00 0.57300E+00 0.59200E+00 0.67100E+00 161- 168 0.93300E+00 0.13370E+01 0.14600E+01 0.13530E+01 0.77200E+00 0.21800E+00 -0.23700E+00 -0.71400E+00 169- 176 -0.10990E+01 -0.12690E+01 -0.11750E+01 -0.67600E+00 0.33000E-01 0.55600E+00 0.64300E+00 0.48400E+00 177- 184 0.10900E+00 -0.31000E+00 -0.69700E+00 -0.10470E+01 -0.12180E+01 -0.11830E+01 -0.87300E+00 -0.33600E+00 185- 192 0.63000E-01 0.84000E-01 0.00000E+00 0.10000E-02 0.20900E+00 0.55600E+00 0.78200E+00 0.85800E+00 193- 200 0.91800E+00 0.86200E+00 0.41600E+00 -0.33600E+00 -0.95900E+00 -0.18130E+01 -0.23780E+01 -0.24990E+01 201- 208 -0.24730E+01 -0.23300E+01 -0.20530E+01 -0.17390E+01 -0.12610E+01 -0.56900E+00 -0.13700E+00 -0.24000E-01 209- 216 -0.50000E-01 -0.13500E+00 -0.27600E+00 -0.53400E+00 -0.87100E+00 -0.12430E+01 -0.14390E+01 -0.14220E+01 217- 224 -0.11750E+01 -0.81300E+00 -0.63400E+00 -0.58200E+00 -0.62500E+00 -0.71300E+00 -0.84800E+00 -0.10390E+01 225- 232 -0.13460E+01 -0.16280E+01 -0.16190E+01 -0.11490E+01 -0.48800E+00 -0.16000E+00 -0.70000E-02 -0.92000E-01 233- 240 -0.62000E+00 -0.10860E+01 -0.15250E+01 -0.18580E+01 -0.20290E+01 -0.20240E+01 -0.19610E+01 -0.19520E+01 241- 248 -0.17940E+01 -0.13020E+01 -0.10300E+01 -0.91800E+00 -0.79800E+00 -0.86700E+00 -0.10470E+01 -0.11230E+01 249- 256 -0.87600E+00 -0.39500E+00 0.18500E+00 0.66200E+00 0.70900E+00 0.60500E+00 0.50100E+00 0.60300E+00 257- 264 0.94300E+00 0.12230E+01 0.12490E+01 0.82400E+00 0.10200E+00 0.25000E-01 0.38200E+00 0.92200E+00 265- 272 0.10320E+01 0.86600E+00 0.52700E+00 0.93000E-01 -0.45800E+00 -0.74800E+00 -0.94700E+00 -0.10290E+01 273- 280 -0.92800E+00 -0.64500E+00 -0.42400E+00 -0.27600E+00 -0.15800E+00 -0.33000E-01 0.10200E+00 0.25100E+00 281- 288 0.28000E+00 0.00000E+00 -0.49300E+00 -0.75900E+00 -0.82400E+00 -0.74000E+00 -0.52800E+00 -0.20400E+00 289- 296 0.34000E-01 0.20400E+00 0.25300E+00 0.19500E+00 0.13100E+00 0.17000E-01 -0.18200E+00 -0.26200E+00 VAR=GASIN SERIES # 1 FROM BJ -- GAS INPUT Variable 2.834 * * * * * * * * * * * * * * * * * ** * * * * * * * * ** * * * * * * * * * * * * * * * *** * * * ** * * * * * * * ** * * * * * * * * * * * * * * * * * ** * * * * * * * * ** ** * ** * * * ** * * * * * ** * * * * * * * * * * ** * * * ** * ** * * * * ** * * * * * * * * * ** * * * * * ** * ** * * * * * * * * * * ** * * ** * * * * * * *** * * * * * * * * * * * * * * * * * * * * * * * ** * * ** * * * * * * * * * * * ** * * * * ** * *** * * ** * * * * ** * * * * * * * * ** * * * * * * ** * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * * * * ** * * * * * * * ** * ** * * * -2.716 ***************************************************************************************************** 1.000 296.0 Time VAR=GASOUT SERIES # 2 FROM BJ -- GAS OUTPUT Listing of Observed Series 1- 8 0.53800E+02 0.53600E+02 0.53500E+02 0.53500E+02 0.53400E+02 0.53100E+02 0.52700E+02 0.52400E+02 9- 16 0.52200E+02 0.52000E+02 0.52000E+02 0.52400E+02 0.53000E+02 0.54000E+02 0.54900E+02 0.56000E+02 17- 24 0.56800E+02 0.56800E+02 0.56400E+02 0.55700E+02 0.55000E+02 0.54300E+02 0.53200E+02 0.52300E+02 25- 32 0.51600E+02 0.51200E+02 0.50800E+02 0.50500E+02 0.50000E+02 0.49200E+02 0.48400E+02 0.47900E+02 33- 40 0.47600E+02 0.47500E+02 0.47500E+02 0.47600E+02 0.48100E+02 0.49000E+02 0.50000E+02 0.51100E+02 41- 48 0.51800E+02 0.51900E+02 0.51700E+02 0.51200E+02 0.50000E+02 0.48300E+02 0.47000E+02 0.45800E+02 49- 56 0.45600E+02 0.46000E+02 0.46900E+02 0.47800E+02 0.48200E+02 0.48300E+02 0.47900E+02 0.47200E+02 57- 64 0.47200E+02 0.48100E+02 0.49400E+02 0.50600E+02 0.51500E+02 0.51600E+02 0.51200E+02 0.50500E+02 65- 72 0.50100E+02 0.49800E+02 0.49600E+02 0.49400E+02 0.49300E+02 0.49200E+02 0.49300E+02 0.49700E+02 73- 80 0.50300E+02 0.51300E+02 0.52800E+02 0.54400E+02 0.56000E+02 0.56900E+02 0.57500E+02 0.57300E+02 81- 88 0.56600E+02 0.56000E+02 0.55400E+02 0.55400E+02 0.56400E+02 0.57200E+02 0.58000E+02 0.58400E+02 89- 96 0.58400E+02 0.58100E+02 0.57700E+02 0.57000E+02 0.56000E+02 0.54700E+02 0.53200E+02 0.52100E+02 97- 104 0.51600E+02 0.51000E+02 0.50500E+02 0.50400E+02 0.51000E+02 0.51800E+02 0.52400E+02 0.53000E+02 105- 112 0.53400E+02 0.53600E+02 0.53700E+02 0.53800E+02 0.53800E+02 0.53800E+02 0.53300E+02 0.53000E+02 113- 120 0.52900E+02 0.53400E+02 0.54600E+02 0.56400E+02 0.58000E+02 0.59400E+02 0.60200E+02 0.60000E+02 121- 128 0.59400E+02 0.58400E+02 0.57600E+02 0.56900E+02 0.56400E+02 0.56000E+02 0.55700E+02 0.55300E+02 129- 136 0.55000E+02 0.54400E+02 0.53700E+02 0.52800E+02 0.51600E+02 0.50600E+02 0.49400E+02 0.48800E+02 137- 144 0.48500E+02 0.48700E+02 0.49200E+02 0.49800E+02 0.50400E+02 0.50700E+02 0.50900E+02 0.50700E+02 145- 152 0.50500E+02 0.50400E+02 0.50200E+02 0.50400E+02 0.51200E+02 0.52300E+02 0.53200E+02 0.53900E+02 153- 160 0.54100E+02 0.54000E+02 0.53600E+02 0.53200E+02 0.53000E+02 0.52800E+02 0.52300E+02 0.51900E+02 161- 168 0.51600E+02 0.51600E+02 0.51400E+02 0.51200E+02 0.50700E+02 0.50000E+02 0.49400E+02 0.49300E+02 169- 176 0.49700E+02 0.50600E+02 0.51800E+02 0.53000E+02 0.54000E+02 0.55300E+02 0.55900E+02 0.55900E+02 177- 184 0.54600E+02 0.53500E+02 0.52400E+02 0.52100E+02 0.52300E+02 0.53000E+02 0.53800E+02 0.54600E+02 185- 192 0.55400E+02 0.55900E+02 0.55900E+02 0.55200E+02 0.54400E+02 0.53700E+02 0.53600E+02 0.53600E+02 193- 200 0.53200E+02 0.52500E+02 0.52000E+02 0.51400E+02 0.51000E+02 0.50900E+02 0.52400E+02 0.53500E+02 201- 208 0.55600E+02 0.58000E+02 0.59500E+02 0.60000E+02 0.60400E+02 0.60500E+02 0.60200E+02 0.59700E+02 209- 216 0.59000E+02 0.57600E+02 0.56400E+02 0.55200E+02 0.54500E+02 0.54100E+02 0.54100E+02 0.54400E+02 217- 224 0.55500E+02 0.56200E+02 0.57000E+02 0.57300E+02 0.57400E+02 0.57000E+02 0.56400E+02 0.55900E+02 225- 232 0.55500E+02 0.55300E+02 0.55200E+02 0.55400E+02 0.56000E+02 0.56500E+02 0.57100E+02 0.57300E+02 233- 240 0.56800E+02 0.55600E+02 0.55000E+02 0.54100E+02 0.54300E+02 0.55300E+02 0.56400E+02 0.57200E+02 241- 248 0.57800E+02 0.58300E+02 0.58600E+02 0.58800E+02 0.58800E+02 0.58600E+02 0.58000E+02 0.57400E+02 249- 256 0.57000E+02 0.56400E+02 0.56300E+02 0.56400E+02 0.56400E+02 0.56000E+02 0.55200E+02 0.54000E+02 257- 264 0.53000E+02 0.52000E+02 0.51600E+02 0.51600E+02 0.51100E+02 0.50400E+02 0.50000E+02 0.50000E+02 265- 272 0.52000E+02 0.54000E+02 0.55100E+02 0.54500E+02 0.52800E+02 0.51400E+02 0.50800E+02 0.51200E+02 273- 280 0.52000E+02 0.52800E+02 0.53800E+02 0.54500E+02 0.54900E+02 0.54900E+02 0.54800E+02 0.54400E+02 281- 288 0.53700E+02 0.53300E+02 0.52800E+02 0.52600E+02 0.52600E+02 0.53000E+02 0.54300E+02 0.56000E+02 289- 296 0.57000E+02 0.58000E+02 0.58600E+02 0.58500E+02 0.58300E+02 0.57800E+02 0.57300E+02 0.57000E+02 VAR=GASOUT SERIES # 2 FROM BJ -- GAS OUTPUT Variable 60.50 * * * * ** * * * * * * ** * * * * * * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * * * * * ** * * * * * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * * * ** * * * * * ** ** * * * ** * * *** * ** * * * * * * * * * * * * * * * * * * * * * * * * ** * ** * * * * ** * * * ** * * * * * * * ** * * * * * * * * ** * * * * * ** * * * * * * * * ** * ** * * * * * * * ** ** * * * * ** * * * * * * * ** * *** * * * * ** * ** * * * * * * * * * * * * * * * * * ** * ** * * * ** * * * * * ** 45.60 ***************************************************************************************************** 1.000 296.0 Time Autocorrelation Function Data - VAR=GASIN SERIES # 1 FROM BJ -- GAS INPUT 296 Observations Differencing - Original Series is your data Differences below are of order 1 Original Series Mean of the Series -5.683445945945946E-02 St. Dev. of Series 1.070951867102525 Number of observations 296 S. E. of mean 6.235322838747232E-02 T value of mean (against zero) -0.9114918494080466 1- 12 0.95 0.83 0.68 0.53 0.41 0.32 0.26 0.23 0.21 0.21 0.20 0.19 St.E. 0.06 0.10 0.12 0.13 0.14 0.14 0.15 0.15 0.15 0.15 0.15 0.15 Mod. Q 271.3 480.0 620.0 705.2 755.6 786.3 807.0 822.9 836.8 850.2 862.9 874.1 13- 24 0.17 0.14 0.10 0.08 0.05 0.04 0.03 0.04 0.06 0.07 0.08 0.08 St.E. 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 Mod. Q 882.8 888.7 892.2 893.9 894.8 895.2 895.6 896.2 897.2 898.7 900.6 902.5 Mean divided by St. Error (using N in S. D.) 0.9130354438235713 Q Statistic 885.88 DF 24 Prob. 1.0000 Modified Q Statistic 902.52 DF 24 Prob. 1.0000 NOTE: In some cases degrees of freedom for Q and Modified Q Statistics may have to be adjusted. Difference 1 Mean of the Series -5.683445945945946E-02 St. Dev. of Series 1.070951867102525 Number of observations 295 S. E. of mean 1.927548278726943E-02 T value of mean (against zero) -2.690693008940615E-02 1- 12 0.75 0.36 -0.02 -0.28 -0.36 -0.33 -0.27 -0.19 -0.10 0.01 0.08 0.09 St.E. 0.06 0.08 0.09 0.09 0.09 0.10 0.10 0.10 0.10 0.11 0.11 0.11 Mod. Q 166.4 204.7 204.8 228.9 268.6 301.6 323.4 334.9 338.3 338.3 340.5 342.9 13- 24 0.08 0.03 -0.03 -0.06 -0.09 -0.13 -0.12 -0.06 0.01 0.06 0.08 0.06 St.E. 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 Mod. Q 345.1 345.5 345.8 347.0 349.5 354.5 359.2 360.3 360.3 361.5 363.5 364.6 Mean divided by St. Error (using N in S. D.) 2.695265132899106E-02 Q Statistic 357.17 DF 24 Prob. 1.0000 Modified Q Statistic 364.55 DF 24 Prob. 1.0000 NOTE: In some cases degrees of freedom for Q and Modified Q Statistics may have to be adjusted. Difference 2 Mean of the Series -5.683445945945946E-02 St. Dev. of Series 1.070951867102525 Number of observations 294 S. E. of mean 1.374490118239666E-02 T value of mean (against zero) -4.677059036848236E-02 1- 12 0.27 -0.03 -0.21 -0.37 -0.22 -0.06 -0.02 -0.03 -0.04 0.06 0.14 0.01 St.E. 0.06 0.06 0.06 0.06 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.08 Mod. Q 21.4 21.7 35.0 76.5 91.1 92.1 92.2 92.5 93.0 94.3 100.7 100.8 13- 24 0.09 0.03 -0.07 -0.01 0.02 -0.08 -0.11 -0.01 0.04 0.07 0.07 0.02 St.E. 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 Mod. Q 103.2 103.5 105.0 105.0 105.1 107.3 111.3 111.3 111.7 113.2 114.8 115.0 Mean divided by St. Error (using N in S. D.) 4.685033567851064E-02 Q Statistic 112.01 DF 24 Prob. 1.0000 Modified Q Statistic 115.00 DF 24 Prob. 1.0000 NOTE: In some cases degrees of freedom for Q and Modified Q Statistics may have to be adjusted. Partial Autocorrelations Data - VAR=GASIN SERIES # 1 FROM BJ -- GAS INPUT 296 Observations Differencing - Original Series is your data Differences below are of order 1 Original Series Mean of the Series -5.683445945945946E-02 St. Dev. of Series 1.070951867102525 Number of observations 296 S. E. of mean 6.235322838747232E-02 T value of mean (against zero) -0.9114918494080466 1- 12 0.95 -0.79 0.34 0.12 0.06 -0.11 0.05 0.10 0.02 -0.07 -0.09 0.04 13- 24 0.09 -0.14 0.05 0.03 -0.02 0.03 0.09 -0.04 -0.09 0.04 0.04 0.01 Difference 1 Mean of the Series -5.683445945945946E-02 St. Dev. of Series 1.070951867102525 Number of observations 295 S. E. of mean 1.927548278726943E-02 T value of mean (against zero) -2.690693008940615E-02 1- 12 0.75 -0.45 -0.19 -0.11 0.06 -0.11 -0.15 -0.05 0.03 0.05 -0.09 -0.12 13- 24 0.10 -0.09 -0.08 -0.01 -0.06 -0.12 0.01 0.06 -0.07 -0.06 -0.03 -0.02 Difference 2 Mean of the Series -5.683445945945946E-02 St. Dev. of Series 1.070951867102525 Number of observations 294 S. E. of mean 1.374490118239666E-02 T value of mean (against zero) -4.677059036848236E-02 1- 12 0.27 -0.11 -0.19 -0.30 -0.09 -0.06 -0.15 -0.20 -0.19 -0.03 -0.01 -0.22 13- 24 -0.02 -0.03 -0.10 -0.05 0.01 -0.13 -0.16 -0.02 -0.03 -0.06 -0.07 -0.09 Autocorrelation Function Data - VAR=GASOUT SERIES # 2 FROM BJ -- GAS OUTPUT 296 Observations Differencing - Original Series is your data Differences below are of order 1 Original Series Mean of the Series 53.50912162162162 St. Dev. of Series 3.196707222485234 Number of observations 296 S. E. of mean 0.1861194901978001 T value of mean (against zero) 287.4987545084845 1- 12 0.97 0.90 0.79 0.68 0.57 0.49 0.42 0.37 0.33 0.31 0.29 0.27 St.E. 0.06 0.10 0.12 0.14 0.15 0.16 0.16 0.17 0.17 0.17 0.17 0.17 Mod. Q 281.8 522.7 711.8 851.4 951.5 1023.2 1076.0 1116.9 1150.5 1179.5 1205.1 1227.7 13- 24 0.25 0.22 0.19 0.16 0.14 0.12 0.11 0.11 0.11 0.12 0.12 0.13 St.E. 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 Mod. Q 1246.7 1262.1 1273.7 1282.3 1288.5 1293.1 1297.0 1300.7 1304.7 1309.1 1314.0 1319.1 Mean divided by St. Error (using N in S. D.) 287.9856282772601 Q Statistic 1289.5 DF 24 Prob. 1.0000 Modified Q Statistic 1319.1 DF 24 Prob. 1.0000 NOTE: In some cases degrees of freedom for Q and Modified Q Statistics may have to be adjusted. Difference 1 Mean of the Series 53.50912162162162 St. Dev. of Series 3.196707222485234 Number of observations 295 S. E. of mean 4.356494985316111E-02 T value of mean (against zero) 0.2489950674494246 1- 12 0.83 0.52 0.16 -0.13 -0.30 -0.35 -0.33 -0.26 -0.17 -0.07 0.01 0.06 St.E. 0.06 0.09 0.10 0.10 0.10 0.10 0.11 0.11 0.11 0.11 0.11 0.11 Mod. Q 205.0 285.2 292.6 298.0 326.0 362.8 395.1 415.5 424.7 426.2 426.2 427.4 13- 24 0.06 0.04 -0.02 -0.07 -0.12 -0.15 -0.15 -0.10 -0.03 0.03 0.06 0.08 St.E. 0.11 0.11 0.11 0.11 0.11 0.12 0.12 0.12 0.12 0.12 0.12 0.12 Mod. Q 428.6 429.0 429.1 430.8 435.7 442.8 449.7 452.8 453.2 453.5 454.8 456.6 Mean divided by St. Error (using N in S. D.) 0.2494181689736969 Q Statistic 447.44 DF 24 Prob. 1.0000 Modified Q Statistic 456.63 DF 24 Prob. 1.0000 NOTE: In some cases degrees of freedom for Q and Modified Q Statistics may have to be adjusted. Difference 2 Mean of the Series 53.50912162162162 St. Dev. of Series 3.196707222485234 Number of observations 294 S. E. of mean 2.550367139467266E-02 T value of mean (against zero) -1.333674862564387E-02 1- 12 0.41 0.15 -0.21 -0.36 -0.37 -0.19 -0.13 -0.05 -0.05 0.06 0.09 0.14 St.E. 0.06 0.07 0.07 0.07 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.09 Mod. Q 50.6 57.2 70.0 108.2 148.5 159.7 164.8 165.7 166.4 167.4 169.8 176.1 13- 24 0.08 0.09 -0.01 0.00 -0.08 -0.08 -0.14 -0.05 0.01 0.08 0.06 0.04 St.E. 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 Mod. Q 177.9 180.7 180.7 180.7 182.9 184.9 190.8 191.5 191.6 193.8 195.2 195.7 Mean divided by St. Error (using N in S. D.) 1.335948819650543E-02 Q Statistic 190.86 DF 24 Prob. 1.0000 Modified Q Statistic 195.71 DF 24 Prob. 1.0000 NOTE: In some cases degrees of freedom for Q and Modified Q Statistics may have to be adjusted. Partial Autocorrelations Data - VAR=GASOUT SERIES # 2 FROM BJ -- GAS OUTPUT 296 Observations Differencing - Original Series is your data Differences below are of order 1 Original Series Mean of the Series 53.50912162162162 St. Dev. of Series 3.196707222485234 Number of observations 296 S. E. of mean 0.1861194901978001 T value of mean (against zero) 287.4987545084845 1- 12 0.97 -0.80 0.19 0.26 0.06 -0.06 -0.01 0.05 0.01 0.03 -0.12 -0.04 13- 24 0.05 0.05 -0.05 0.03 0.00 0.09 0.02 -0.03 -0.05 0.01 0.05 0.00 Difference 1 Mean of the Series 53.50912162162162 St. Dev. of Series 3.196707222485234 Number of observations 295 S. E. of mean 4.356494985316111E-02 T value of mean (against zero) 0.2489950674494246 1- 12 0.83 -0.54 -0.25 0.05 0.01 -0.03 -0.16 0.00 0.04 0.05 -0.10 -0.05 13- 24 -0.05 0.03 -0.11 -0.04 -0.09 0.01 -0.02 0.04 -0.05 -0.06 -0.02 0.03 Difference 2 Mean of the Series 53.50912162162162 St. Dev. of Series 3.196707222485234 Number of observations 294 S. E. of mean 2.550367139467266E-02 T value of mean (against zero) -1.333674862564387E-02 1- 12 0.41 -0.03 -0.31 -0.21 -0.13 0.00 -0.17 -0.17 -0.17 -0.01 -0.06 -0.06 13- 24 -0.13 0.02 -0.07 -0.01 -0.11 -0.08 -0.12 -0.02 -0.02 -0.06 -0.10 -0.10 Autocorrelation Function Data - VAR=GASIN SERIES # 1 FROM BJ -- GAS INPUT 296 Observations Differencing - Original Series is your data differenced by 1) 1 of order 12 Differences below are of order 1 Original Series Mean of the Series -7.890845070422535E-03 St. Dev. of Series 1.387071651449274 Number of observations 284 S. E. of mean 8.245285120768341E-02 T value of mean (against zero) -9.570130025639699E-02 1- 12 0.95 0.81 0.64 0.47 0.31 0.18 0.05 -0.07 -0.19 -0.30 -0.38 -0.43 St.E. 0.06 0.10 0.12 0.13 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.15 Mod. Q 256.5 447.4 567.5 631.5 660.1 669.4 670.2 671.6 682.0 707.8 750.6 804.6 13- 24 -0.42 -0.38 -0.32 -0.27 -0.23 -0.20 -0.18 -0.17 -0.15 -0.14 -0.12 -0.09 St.E. 0.15 0.16 0.16 0.16 0.16 0.16 0.16 0.17 0.17 0.17 0.17 0.17 Mod. Q 857.5 900.9 932.3 953.8 969.3 981.5 991.9 1000.6 1007.9 1013.6 1017.9 1020.6 Mean divided by St. Error (using N in S. D.) 9.587023472196195E-02 Q Statistic 991.25 DF 24 Prob. 1.0000 Modified Q Statistic 1020.6 DF 24 Prob. 1.0000 NOTE: In some cases degrees of freedom for Q and Modified Q Statistics may have to be adjusted. Difference 1 Mean of the Series -7.890845070422535E-03 St. Dev. of Series 1.387071651449274 Number of observations 283 S. E. of mean 2.688495089644254E-02 T value of mean (against zero) 0.2377622400365152 1- 12 0.72 0.37 0.06 -0.17 -0.19 -0.10 -0.01 -0.01 -0.10 -0.21 -0.35 -0.48 St.E. 0.06 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.10 0.10 Mod. Q 149.8 188.3 189.2 197.2 208.1 211.1 211.1 211.2 214.0 227.4 264.1 332.2 13- 24 -0.33 -0.15 0.00 0.14 0.16 0.07 0.01 -0.01 -0.02 -0.04 -0.05 -0.03 St.E. 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 Mod. Q 364.0 370.7 370.7 376.3 383.8 385.4 385.4 385.5 385.6 386.1 386.8 387.2 Mean divided by St. Error (using N in S. D.) 0.2381834312258942 Q Statistic 375.66 DF 24 Prob. 1.0000 Modified Q Statistic 387.17 DF 24 Prob. 1.0000 NOTE: In some cases degrees of freedom for Q and Modified Q Statistics may have to be adjusted. Difference 2 Mean of the Series -7.890845070422535E-03 St. Dev. of Series 1.387071651449274 Number of observations 282 S. E. of mean 2.002901012993199E-02 T value of mean (against zero) 6.975697308572484E-02 1- 12 0.15 -0.08 -0.16 -0.36 -0.22 0.02 0.15 0.17 0.05 0.05 -0.02 -0.51 St.E. 0.06 0.06 0.06 0.06 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 Mod. Q 6.3 8.3 15.5 51.9 65.7 65.8 72.1 80.3 80.9 81.6 81.8 157.9 13- 24 -0.04 0.05 0.02 0.21 0.19 -0.03 -0.09 -0.01 0.00 -0.01 -0.04 0.02 St.E. 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 Mod. Q 158.5 159.1 159.2 172.8 183.5 183.7 186.2 186.2 186.2 186.3 186.9 187.0 Mean divided by St. Error (using N in S. D.) 6.988098558021992E-02 Q Statistic 179.43 DF 24 Prob. 1.0000 Modified Q Statistic 186.99 DF 24 Prob. 1.0000 NOTE: In some cases degrees of freedom for Q and Modified Q Statistics may have to be adjusted. Partial Autocorrelations Data - VAR=GASIN SERIES # 1 FROM BJ -- GAS INPUT 296 Observations Differencing - Original Series is your data differenced by 1) 1 of order 12 Differences below are of order 1 Original Series Mean of the Series -7.890845070422535E-03 St. Dev. of Series 1.387071651449274 Number of observations 284 S. E. of mean 8.245285120768341E-02 T value of mean (against zero) -9.570130025639699E-02 1- 12 0.95 -0.75 0.15 0.05 0.02 -0.21 -0.18 -0.08 -0.01 0.01 -0.03 0.12 13- 24 0.21 -0.35 0.02 -0.01 -0.07 -0.10 -0.01 -0.08 -0.09 0.05 0.07 0.11 Difference 1 Mean of the Series -7.890845070422535E-03 St. Dev. of Series 1.387071651449274 Number of observations 283 S. E. of mean 2.688495089644254E-02 T value of mean (against zero) 0.2377622400365152 1- 12 0.72 -0.33 -0.14 -0.11 0.15 0.06 -0.07 -0.15 -0.14 -0.06 -0.22 -0.27 13- 24 0.37 -0.17 -0.06 0.02 0.02 -0.09 -0.01 0.00 -0.17 -0.13 -0.15 -0.11 Difference 2 Mean of the Series -7.890845070422535E-03 St. Dev. of Series 1.387071651449274 Number of observations 282 S. E. of mean 2.002901012993199E-02 T value of mean (against zero) 6.975697308572484E-02 1- 12 0.15 -0.11 -0.13 -0.34 -0.19 -0.04 0.02 -0.01 -0.09 0.05 0.04 -0.52 13- 24 0.06 -0.07 -0.14 -0.12 -0.01 -0.09 -0.09 0.07 0.01 0.01 -0.06 -0.34 Autocorrelation Function Data - VAR=GASOUT SERIES # 2 FROM BJ -- GAS OUTPUT 296 Observations Differencing - Original Series is your data differenced by 1) 1 of order 12 Differences below are of order 1 Original Series Mean of the Series 0.1542253521126760 St. Dev. of Series 3.866133622710556 Number of observations 284 S. E. of mean 0.2298177891598510 T value of mean (against zero) 0.6710766502300819 1- 12 0.96 0.87 0.73 0.57 0.42 0.26 0.12 -0.01 -0.14 -0.25 -0.33 -0.38 St.E. 0.06 0.10 0.12 0.14 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.16 Mod. Q 265.8 481.5 634.8 729.9 780.2 800.7 805.0 805.1 810.9 829.1 861.6 905.0 13- 24 -0.40 -0.39 -0.35 -0.31 -0.27 -0.24 -0.20 -0.18 -0.16 -0.13 -0.11 -0.08 St.E. 0.16 0.16 0.17 0.17 0.17 0.17 0.17 0.17 0.18 0.18 0.18 0.18 Mod. Q 952.3 997.0 1034.8 1064.5 1087.0 1104.0 1116.8 1126.7 1134.3 1139.9 1143.6 1145.6 Mean divided by St. Error (using N in S. D.) 0.6722612524764048 Q Statistic 1113.6 DF 24 Prob. 1.0000 Modified Q Statistic 1145.6 DF 24 Prob. 1.0000 NOTE: In some cases degrees of freedom for Q and Modified Q Statistics may have to be adjusted. Difference 1 Mean of the Series 0.1542253521126760 St. Dev. of Series 3.866133622710556 Number of observations 283 S. E. of mean 6.135498681564180E-02 T value of mean (against zero) 0.2994794597397340 1- 12 0.84 0.57 0.26 0.03 -0.08 -0.10 -0.09 -0.14 -0.24 -0.36 -0.46 -0.51 St.E. 0.06 0.09 0.10 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.12 Mod. Q 203.1 295.2 315.3 315.6 317.5 320.3 322.8 328.4 345.0 382.6 444.8 520.7 13- 24 -0.42 -0.27 -0.12 0.00 0.06 0.07 0.04 0.03 0.00 -0.01 -0.02 -0.01 St.E. 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 Mod. Q 572.9 594.7 599.1 599.1 600.3 601.6 602.2 602.4 602.4 602.5 602.6 602.7 Mean divided by St. Error (using N in S. D.) 0.3000099817848788 Q Statistic 585.22 DF 24 Prob. 1.0000 Modified Q Statistic 602.69 DF 24 Prob. 1.0000 NOTE: In some cases degrees of freedom for Q and Modified Q Statistics may have to be adjusted. Difference 2 Mean of the Series 0.1542253521126760 St. Dev. of Series 3.866133622710556 Number of observations 282 S. E. of mean 3.428097090526018E-02 T value of mean (against zero) -0.1344748691848402 1- 12 0.39 0.08 -0.22 -0.39 -0.31 -0.06 0.16 0.18 0.07 -0.06 -0.17 -0.43 St.E. 0.06 0.07 0.07 0.07 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.09 Mod. Q 42.4 44.4 57.9 100.9 128.0 128.9 136.2 145.5 147.0 148.1 156.8 212.4 13- 24 -0.20 0.00 0.08 0.18 0.19 0.07 -0.02 0.01 -0.02 -0.02 -0.06 -0.10 St.E. 0.09 0.09 0.09 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 Mod. Q 224.0 224.0 226.0 236.2 247.4 248.8 248.9 248.9 249.1 249.2 250.3 253.4 Mean divided by St. Error (using N in S. D.) 0.1347139358076711 Q Statistic 244.61 DF 24 Prob. 1.0000 Modified Q Statistic 253.36 DF 24 Prob. 1.0000 NOTE: In some cases degrees of freedom for Q and Modified Q Statistics may have to be adjusted. Partial Autocorrelations Data - VAR=GASOUT SERIES # 2 FROM BJ -- GAS OUTPUT 296 Observations Differencing - Original Series is your data differenced by 1) 1 of order 12 Differences below are of order 1 Original Series Mean of the Series 0.1542253521126760 St. Dev. of Series 3.866133622710556 Number of observations 284 S. E. of mean 0.2298177891598510 T value of mean (against zero) 0.6710766502300819 1- 12 0.96 -0.82 0.11 0.12 -0.03 -0.23 -0.15 -0.03 0.06 0.11 -0.02 0.02 13- 24 0.07 -0.15 -0.08 0.01 -0.07 -0.09 -0.04 -0.01 0.01 0.16 0.00 0.01 Difference 1 Mean of the Series 0.1542253521126760 St. Dev. of Series 3.866133622710556 Number of observations 283 S. E. of mean 6.135498681564180E-02 T value of mean (against zero) 0.2994794597397340 1- 12 0.84 -0.50 -0.15 0.08 0.13 -0.02 -0.19 -0.24 -0.11 -0.05 -0.12 -0.15 13- 24 0.27 -0.09 -0.14 0.05 0.02 -0.09 -0.07 -0.11 -0.19 -0.05 -0.07 -0.04 Difference 2 Mean of the Series 0.1542253521126760 St. Dev. of Series 3.866133622710556 Number of observations 282 S. E. of mean 3.428097090526018E-02 T value of mean (against zero) -0.1344748691848402 1- 12 0.39 -0.08 -0.26 -0.26 -0.08 0.08 0.08 -0.07 -0.12 -0.06 -0.05 -0.41 13- 24 0.01 0.03 -0.17 -0.11 0.00 -0.02 0.01 0.07 -0.10 -0.06 -0.10 -0.34 Cross Correlations Series 1 - VAR=GASIN SERIES # 1 FROM BJ -- GAS INPUT Series 2 - VAR=GASOUT SERIES # 2 FROM BJ -- GAS OUTPUT Mean Series 1 = -5.683445945945946E-02 ST. Dev. Series 1 = 1.070951867102525 Mean Series 2 = 53.50912162162162 ST. Dev. Series 2 = 3.196707222485234 Number of Lags Cross Number of Lags Cross on Series 1 Correlation on Series 2 Correlation S Left S Right Mod S Left Mod S Right 0 -0.484 0 -0.484 69.5 69.5 69.5 69.5 1 -0.598 1 -0.393 175. 115. 176. 115. 2 -0.725 2 -0.329 331. 147. 332. 148. 3 -0.843 3 -0.286 541. 172. 545. 172. 4 -0.925 4 -0.260 794. 192. 801. 192. 5 -0.950 5 -0.243 0.106E+04 209. 0.107E+04 210. 6 -0.915 6 -0.227 0.131E+04 224. 0.133E+04 226. 7 -0.829 7 -0.206 0.151E+04 237. 0.153E+04 239. 8 -0.717 8 -0.179 0.166E+04 246. 0.169E+04 248. 9 -0.600 9 -0.149 0.177E+04 253. 0.180E+04 255. 10 -0.495 10 -0.118 0.184E+04 257. 0.188E+04 259. 11 -0.411 11 -0.093 0.189E+04 260. 0.193E+04 262. 12 -0.348 12 -0.075 0.193E+04 261. 0.196E+04 264. 13 -0.305 13 -0.066 0.196E+04 263. 0.199E+04 265. 14 -0.278 14 -0.066 0.198E+04 264. 0.202E+04 267. 15 -0.263 15 -0.073 0.200E+04 265. 0.204E+04 268. 16 -0.255 16 -0.083 0.202E+04 267. 0.206E+04 270. 17 -0.246 17 -0.093 0.204E+04 270. 0.208E+04 273. 18 -0.233 18 -0.100 0.205E+04 273. 0.210E+04 276. 19 -0.213 19 -0.103 0.207E+04 276. 0.211E+04 280. 20 -0.187 20 -0.103 0.208E+04 279. 0.212E+04 283. 21 -0.157 21 -0.102 0.208E+04 282. 0.213E+04 286. 22 -0.127 22 -0.101 0.209E+04 285. 0.213E+04 290. 23 -0.103 23 -0.100 0.209E+04 288. 0.214E+04 293. 24 -0.087 24 -0.100 0.209E+04 291. 0.214E+04 296. 25 -0.080 25 -0.103 0.210E+04 295. 0.214E+04 300. 26 -0.081 26 -0.110 0.210E+04 298. 0.214E+04 304. 27 -0.085 27 -0.118 0.210E+04 302. 0.215E+04 308. 28 -0.087 28 -0.124 0.210E+04 307. 0.215E+04 313. 29 -0.087 29 -0.121 0.211E+04 311. 0.215E+04 318. 30 -0.082 30 -0.108 0.211E+04 315. 0.215E+04 322. 31 -0.073 31 -0.088 0.211E+04 317. 0.216E+04 324. 32 -0.064 32 -0.063 0.211E+04 318. 0.216E+04 326. 33 -0.058 33 -0.039 0.211E+04 319. 0.216E+04 326. 34 -0.057 34 -0.017 0.211E+04 319. 0.216E+04 326. 35 -0.061 35 0.001 0.211E+04 319. 0.216E+04 326. 36 -0.072 36 0.015 0.211E+04 319. 0.216E+04 326. 37 -0.087 37 0.025 0.212E+04 319. 0.216E+04 326. 38 -0.102 38 0.035 0.212E+04 319. 0.217E+04 327. 39 -0.112 39 0.049 0.212E+04 320. 0.217E+04 328. 40 -0.110 40 0.069 0.213E+04 321. 0.218E+04 329. 41 -0.098 41 0.094 0.213E+04 324. 0.218E+04 332. 42 -0.077 42 0.124 0.213E+04 328. 0.218E+04 338. 43 -0.053 43 0.153 0.213E+04 335. 0.218E+04 346. 44 -0.031 44 0.179 0.213E+04 345. 0.218E+04 357. 45 -0.014 45 0.200 0.213E+04 357. 0.218E+04 371. 46 -0.001 46 0.213 0.213E+04 370. 0.218E+04 387. 47 0.008 47 0.221 0.213E+04 385. 0.218E+04 404. 48 0.014 48 0.221 0.213E+04 399. 0.218E+04 421. 49 0.018 49 0.215 0.213E+04 413. 0.218E+04 438. 50 0.024 50 0.205 0.213E+04 425. 0.218E+04 453. Number of terms for Sum of Cross Correlations Squared 51 0.72066260E+01 0.14363733E+01 Haugh S Statistic - See JASA June 76 Page 382 S for left side 2133.2 DF 51 Chi Prob 1.000000 S for right side 355.70 DF 50 Chi Prob 1.000000 S for both sides 2488.9 DF 101 CHI Prob 1.000000 Test for feedback plus instantaneous causality S for right side 425.17 DF 51 Chi Prob 1.000000 Haugh Modified S Statistic - See JASA June 76 Page 383 S for left side 2183.3 DF 51 Chi Prob 1.000000 S for right side 383.05 DF 50 Chi Prob 1.000000 S for both sides 2566.3 DF 101 CHI Prob 1.000000 Test for feedback plus instantaneous causality S for right side 452.52 DF 51 Chi Prob 1.000000 Note: Cross correlations on left are for series 2 on lags of series 1 Cross correlations on right are for series 1 on lags of series 2 Note: Degrees of freedom of S Statistics have to be adjusted for transfer function checking. Power spectrum not positive for some frequency Value set to 0.0 Coherence estimate found to be greater than one, set to 1.0 Spectral Analysis of X Series - VAR=GASIN SERIES # 1 FROM BJ -- GAS INPUT Y Series - VAR=GASOUT SERIES # 2 FROM BJ -- GAS OUTPUT X Mean -5.683445945945946E-02 X Variance 1.146937901650384 Y Mean 53.50912162162162 Y Variance 10.21893706628926 Interval 1.000000000000000 Frequency Cospectrum Quad SP Amplitude Phase A Trans X-Y A Trans Y-X Coherence X Pow Spec Y Pow Spec 0.0000 -15.990 -2.2662 16.150 0.52241 3.3603 0.28481 0.95703 4.8061 56.705 0.10000E-01 -12.556 -3.4460 13.020 0.54263 3.2888 0.29116 0.95755 3.9591 44.719 0.20000E-01 -6.2697 -4.7803 7.8842 0.60368 2.9351 0.29946 0.87895 2.6862 26.328 0.30000E-01 -3.6427 -5.4361 6.5437 0.65604 2.8337 0.33682 0.95444 2.3092 19.428 0.40000E-01 -1.7011 -3.6471 4.0243 0.68054 2.7155 0.32461 0.88147 1.4820 12.398 0.50000E-01 -0.31044 -2.8349 2.8519 0.73264 2.6712 0.34483 0.92111 1.0676 8.2705 0.60000E-01 0.65329 -2.2767 2.3686 0.79447 2.3624 0.37549 0.88707 1.0026 6.3079 0.70000E-01 1.1715 -1.6639 2.0350 0.84763 2.4569 0.37308 0.91663 0.82826 5.4544 0.80000E-01 1.4953 -0.94841 1.7707 0.91004 2.2381 0.36631 0.81985 0.79114 4.8338 0.90000E-01 1.3533 -0.48816 1.4386 0.94490 1.9641 0.43722 0.85876 0.73245 3.2903 0.10000 0.60155 -0.10664 0.61093 0.97208 1.8643 0.54925 1.0000 0.32769 1.1123 0.11000 0.33704 -0.41658E-01 0.33961 0.98043 1.9925 0.45659 0.90974 0.17044 0.74379 0.12000 0.26652 0.69235E-01 0.27536 0.40451E-01 1.8275 0.56529 1.0000 0.15067 0.48712 0.13000 0.13341 0.60259E-01 0.14638 0.67523E-01 1.4238 0.51136 0.72804 0.10282 0.28627 0.14000 0.59716E-01 0.13220 0.14507 0.18248 2.1914 0.61544 1.0000 0.66197E-01 0.23571 0.15000 0.19946E-01 0.71073E-01 0.73819E-01 0.20646 1.3301 0.33630 0.44732 0.55497E-01 0.21951 0.16000 0.55951E-02 0.62416E-01 0.62666E-01 0.23577 1.8598 1.4012 1.0000 0.33695E-01 0.44724E-01 0.17000 -0.14300E-01 0.14251E-01 0.20188E-01 0.37527 0.74753 0.26527 0.19830 0.27007E-01 0.76106E-01 0.18000 -0.20670E-01 0.41589E-01 0.46442E-01 0.32341 1.8537 0.92484 1.0000 0.25054E-01 0.50217E-01 0.19000 -0.17322E-02 0.17458E-02 0.24593E-02 0.37438 0.14382 0.68873E-01 0.99053E-02 0.17100E-01 0.35708E-01 0.20000 0.73429E-03 0.17333E-01 0.17349E-01 0.24326 5.6059 0.0000 0.0000 0.30947E-02 0.0000 0.21000 0.19455E-02 -0.11391E-01 0.11556E-01 0.77692 8.2107 1.4603 1.0000 0.14074E-02 0.79134E-02 0.22000 0.16321E-02 0.13783E-01 0.13879E-01 0.23124 71.500 0.0000 0.0000 0.19411E-03 0.0000 0.23000 -0.68793E-04 -0.97054E-02 0.97056E-02 0.74887 3.5531 1.6384 1.0000 0.27316E-02 0.59239E-02 0.24000 -0.13250E-02 0.97744E-02 0.98638E-02 0.27144 0.0000 0.0000 0.0000 0.0000 0.0000 0.25000 0.58009E-03 -0.86546E-02 0.86741E-02 0.76065 29.032 0.82559 1.0000 0.29878E-03 0.10506E-01 0.26000 -0.44390E-03 0.10553E-01 0.10562E-01 0.25669 0.0000 0.0000 0.0000 0.0000 0.0000 0.27000 0.86597E-03 -0.80041E-02 0.80508E-02 0.76715 9.8995 0.86499 1.0000 0.81325E-03 0.93073E-02 0.28000 0.17157E-02 0.75925E-02 0.77839E-02 0.21463 105.79 0.0000 0.0000 0.73580E-04 0.0000 0.29000 0.57556E-03 -0.64775E-02 0.65030E-02 0.76410 2.3007 0.99956 1.0000 0.28265E-02 0.65059E-02 0.30000 -0.50447E-03 0.82502E-02 0.82657E-02 0.25972 4.3031 0.0000 0.0000 0.19209E-02 0.0000 0.31000 0.54265E-03 -0.65439E-02 0.65664E-02 0.76317 4.9185 1.6745 1.0000 0.13350E-02 0.39213E-02 0.32000 0.13612E-03 0.59917E-02 0.59932E-02 0.24638 0.0000 0.0000 0.0000 0.0000 0.0000 0.33000 0.42683E-03 -0.58734E-02 0.58889E-02 0.76155 22.259 1.2445 1.0000 0.26457E-03 0.47318E-02 0.34000 0.61723E-03 0.45536E-02 0.45952E-02 0.22856 0.0000 0.0000 0.0000 0.0000 0.0000 0.35000 0.11884E-02 -0.50243E-02 0.51629E-02 0.78697 4.9527 1.1144 1.0000 0.10425E-02 0.46329E-02 0.36000 0.26428E-03 0.55656E-02 0.55718E-02 0.24245 11.194 0.0000 0.0000 0.49777E-03 0.0000 0.37000 0.71680E-04 -0.31790E-02 0.31798E-02 0.75359 2.1463 0.46341 0.99461 0.14815E-02 0.68616E-02 0.38000 0.40842E-03 0.36204E-02 0.36433E-02 0.23212 21.932 0.0000 0.0000 0.16612E-03 0.0000 0.39000 0.65535E-03 -0.32181E-02 0.32842E-02 0.78197 4.6673 0.49124 1.0000 0.70365E-03 0.66855E-02 0.40000 0.44816E-03 0.35131E-02 0.35416E-02 0.22981 0.0000 0.0000 0.0000 0.0000 0.0000 0.41000 0.86400E-03 -0.28852E-02 0.30118E-02 0.79631 13.920 1.2048 1.0000 0.21636E-03 0.24998E-02 0.42000 0.81791E-03 0.25098E-02 0.26397E-02 0.19986 0.0000 0.0000 0.0000 0.0000 0.0000 0.43000 0.10122E-02 -0.23174E-02 0.25288E-02 0.81554 12.163 0.49073 1.0000 0.20791E-03 0.51532E-02 0.44000 0.79262E-03 0.14552E-02 0.16571E-02 0.17062 0.0000 0.0000 0.0000 0.0000 0.0000 0.45000 0.93947E-03 -0.16030E-02 0.18580E-02 0.83437 3.9210 0.58955 1.0000 0.47385E-03 0.31515E-02 0.46000 0.69248E-03 0.10555E-02 0.12624E-02 0.15759 0.0000 0.0000 0.0000 0.0000 0.0000 0.47000 0.96026E-03 -0.11321E-02 0.14845E-02 0.86196 6.0255 0.61753 1.0000 0.24637E-03 0.24039E-02 0.48000 0.73296E-03 0.25048E-03 0.77458E-03 0.52408E-01 0.0000 0.0000 0.0000 0.0000 0.0000 0.49000 0.87656E-03 -0.95639E-03 0.12973E-02 0.86807 11.666 0.20368 1.0000 0.11121E-03 0.63694E-02 0.50000 0.83242E-03 -0.22982E-02 0.24443E-02 0.80531 0.0000 0.0000 0.0000 0.0000 0.0000 Plot of the Amplitude of the Transfer Function of Series X mapping to Series Y AMPL 105.8 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 0.000 ***************************************************************************************************** 0.000 0.5000 FREQ Plot of the Amplitude of the Transfer Function of Series Y mapping to Series X AMPL 1.675 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *** * * * * * * * * * * * * * * * * * * * * * * * * * * * * 0.000 ***************************************************************************************************** 0.000 0.5000 FREQ Analysis for Prewhitened input 1 ------------------------------ Specification of Prewhitening Transformation applied to input series 1 Data - X1 = VAR=GASIN SERIES # 1 FROM BJ -- GAS INPUT Observations 296 Differencing on X1 - None Transformations Examined - None. Univariate Model Parameters. Parameter Beginning # Type Order Value 1 Mean -0.6100E-01 2 Autoregressive 1 1 1.975 3 Autoregressive 1 2 -1.373 4 Autoregressive 1 3 0.3424 Specification of Prewhitening Transformation Applied to Output Series Data - Y = VAR=GASOUT SERIES # 2 FROM BJ -- GAS OUTPUT Observations 296 Differencing on Y - None Transformations Examined - None. Univariate Model Parameters. Parameter Beginning # Type Order Value 1 Mean 53.51 2 Autoregressive 1 1 1.975 3 Autoregressive 1 2 -1.373 4 Autoregressive 1 3 0.3424 Other Transfer Function Identification Information Effective number of observations for cross correlation 293 Number of Impulse Response Weights estimated = 24 Number of Impulse Response Weights used to generate Noise Series 24 Cross Correlations Series 1 - Prewhitened VAR=GASIN SERIES # 1 FROM BJ -- GAS INPUT Series 2 - Prewhitened VAR=GASOUT SERIES # 2 FROM BJ -- GAS OUTPUT Mean Series 1 = -4.432591808873746E-04 ST. Dev. Series 1 = 0.1887146792440929 Mean Series 2 = 2.927767337201386E-03 ST. Dev. Series 2 = 0.3629305906132739 Number of Lags Cross Number of Lags Cross on Series 1 Correlation on Series 2 Correlation S Left S Right Mod S Left Mod S Right 0 -0.002 0 -0.002 0.123E-02 0.123E-02 0.123E-02 0.123E-02 1 0.054 1 -0.030 0.845 0.272 0.847 0.273 2 -0.025 2 0.009 1.03 0.297 1.04 0.298 3 -0.283 3 -0.049 24.5 1.01 24.7 1.02 4 -0.331 4 -0.016 56.6 1.09 57.3 1.10 5 -0.456 5 -0.003 118. 1.09 119. 1.10 6 -0.268 6 -0.120 139. 5.33 141. 5.43 7 -0.168 7 -0.026 147. 5.53 149. 5.63 8 -0.025 8 -0.089 147. 7.86 150. 8.03 9 0.031 9 0.001 147. 7.86 150. 8.03 10 -0.055 10 0.022 148. 8.00 151. 8.18 11 -0.034 11 0.007 149. 8.02 151. 8.19 12 -0.018 12 -0.005 149. 8.02 151. 8.20 13 -0.070 13 0.013 150. 8.07 153. 8.25 14 0.000 14 0.013 150. 8.12 153. 8.30 15 -0.014 15 0.027 150. 8.34 153. 8.53 16 -0.059 16 -0.034 151. 8.67 154. 8.88 17 -0.048 17 -0.058 152. 9.65 154. 9.92 18 -0.029 18 -0.048 152. 10.3 155. 10.6 19 -0.116 19 0.039 156. 10.8 159. 11.1 20 0.014 20 -0.063 156. 11.9 159. 12.4 21 -0.053 21 0.030 157. 12.2 160. 12.7 22 -0.022 22 -0.047 157. 12.8 160. 13.4 23 0.063 23 -0.025 158. 13.0 161. 13.5 24 0.008 24 -0.029 158. 13.3 161. 13.8 Number of terms for Sum of Cross Correlations Squared 25 0.53995001E+00 0.45277279E-01 Haugh S Statistic - See JASA June 76 Page 382 S for left side 158.21 DF 25 Chi Prob 1.000000 S for right side 13.265 DF 24 Chi Prob 0.038450 S for both sides 171.47 DF 49 CHI Prob 1.000000 Test for feedback plus instantaneous causality S for right side 13.266 DF 25 Chi Prob 0.026932 Haugh Modified S Statistic - See JASA June 76 Page 383 S for left side 161.30 DF 25 Chi Prob 1.000000 S for right side 13.805 DF 24 Chi Prob 0.049076 S for both sides 175.10 DF 49 CHI Prob 1.000000 Test for feedback plus instantaneous causality S for right side 13.807 DF 25 Chi Prob 0.035001 Note: Cross correlations on left are for series 2 on lags of series 1 Cross correlations on right are for series 1 on lags of series 2 Note: Degrees of freedom of S Statistics have to be adjusted for transfer function checking. Spectral Analysis of X Series - Prewhitened VAR=GASIN SERIES # 1 FROM BJ -- GAS INPUT Y Series - Prewhitened VAR=GASOUT SERIES # 2 FROM BJ -- GAS OUTPUT X Mean -4.432591808873746E-04 X Variance 3.561323016220088E-02 Y Mean 2.927767337201386E-03 Y Variance 0.1317186136028998 Interval 1.000000000000000 Frequency Cospectrum Quad SP Amplitude Phase A Trans X-Y A Trans Y-X Coherence X Pow Spec Y Pow Spec 0.0000 -0.51146E-01 -0.66798E-02 0.51580E-01 0.52067 3.4238 0.27644 0.94648 0.15065E-01 0.18659 0.10000E-01 -0.41906E-01 -0.11404E-01 0.43430E-01 0.54229 3.3031 0.28757 0.94986 0.13148E-01 0.15102 0.20000E-01 -0.23410E-01 -0.19388E-01 0.30396E-01 0.61009 2.8854 0.29484 0.85072 0.10534E-01 0.10309 0.30000E-01 -0.16531E-01 -0.24861E-01 0.29855E-01 0.65661 2.8029 0.33682 0.94407 0.10652E-01 0.88639E-01 0.40000E-01 -0.87948E-02 -0.20673E-01 0.22466E-01 0.68598 2.7774 0.31769 0.88236 0.80888E-02 0.70716E-01 0.50000E-01 -0.16131E-02 -0.20671E-01 0.20734E-01 0.73761 2.6689 0.35003 0.93420 0.77687E-02 0.59235E-01 0.60000E-01 0.71482E-02 -0.21733E-01 0.22879E-01 0.80057 2.3465 0.38116 0.89439 0.97502E-02 0.60023E-01 0.70000E-01 0.15348E-01 -0.20581E-01 0.25674E-01 0.85198 2.3700 0.37844 0.89690 0.10833E-01 0.67840E-01 0.80000E-01 0.28177E-01 -0.17797E-01 0.33326E-01 0.91034 2.1811 0.38351 0.83645 0.15280E-01 0.86900E-01 0.90000E-01 0.32621E-01 -0.12159E-01 0.34813E-01 0.94322 1.9084 0.43827 0.83641 0.18242E-01 0.79432E-01 0.10000 0.19955E-01 -0.50571E-02 0.20586E-01 0.96050 1.8752 0.47409 0.88903 0.10978E-01 0.43421E-01 0.11000 0.19144E-01 -0.14614E-02 0.19200E-01 0.98787 1.8899 0.46485 0.87853 0.10159E-01 0.41303E-01 0.12000 0.20721E-01 0.32737E-02 0.20978E-01 0.24939E-01 1.7137 0.50554 0.86634 0.12241E-01 0.41496E-01 0.13000 0.13813E-01 0.11035E-01 0.17679E-01 0.10728 1.5421 0.44166 0.68110 0.11464E-01 0.40029E-01 0.14000 0.75487E-02 0.18890E-01 0.20342E-01 0.18949 1.7067 0.44495 0.75941 0.11919E-01 0.45718E-01 0.15000 0.35816E-02 0.17938E-01 0.18292E-01 0.21864 1.4103 0.46259 0.65239 0.12971E-01 0.39543E-01 0.16000 0.10946E-03 0.12757E-01 0.12758E-01 0.24863 1.1061 0.43684 0.48319 0.11534E-01 0.29205E-01 0.17000 -0.82537E-02 0.10721E-01 0.13530E-01 0.35442 1.1133 0.43415 0.48335 0.12153E-01 0.31164E-01 0.18000 -0.87149E-02 0.13808E-01 0.16328E-01 0.33961 1.0259 0.47968 0.49211 0.15916E-01 0.34039E-01 0.19000 -0.25817E-02 0.10984E-01 0.11284E-01 0.28674 0.88053 0.44917 0.39551 0.12815E-01 0.25121E-01 0.20000 -0.16175E-02 0.24449E-02 0.29315E-02 0.34302 0.52827 0.28054 0.14820 0.55492E-02 0.10449E-01 0.21000 0.32296E-03 0.59613E-03 0.67799E-03 0.17098 0.22531 0.14715 0.33155E-01 0.30091E-02 0.46075E-02 0.22000 -0.58855E-03 0.17605E-02 0.18563E-02 0.30135 0.40519 0.21414 0.86766E-01 0.45812E-02 0.86685E-02 0.23000 -0.27726E-02 -0.15048E-02 0.31546E-02 0.57914 0.48943 0.26829 0.13131 0.64454E-02 0.11758E-01 0.24000 -0.25812E-02 -0.15845E-02 0.30288E-02 0.58762 0.73677 0.28037 0.20657 0.41109E-02 0.10803E-01 0.25000 -0.95284E-03 0.16896E-02 0.19398E-02 0.33172 0.84441 0.19578 0.16532 0.22972E-02 0.99081E-02 0.26000 -0.24001E-02 0.40125E-02 0.46755E-02 0.33579 1.2767 0.35277 0.45039 0.36621E-02 0.13254E-01 0.27000 0.14663E-04 0.29203E-02 0.29203E-02 0.24920 0.54563 0.15346 0.83734E-01 0.53522E-02 0.19030E-01 0.28000 0.10881E-02 -0.22223E-02 0.24743E-02 0.82246 0.27885 0.10021 0.27945E-01 0.88735E-02 0.24690E-01 0.29000 -0.46583E-02 0.11130E-02 0.47894E-02 0.46267 0.25742 0.17495 0.45036E-01 0.18605E-01 0.27376E-01 0.30000 -0.55103E-02 0.43648E-02 0.70296E-02 0.39338 0.34136 0.26342 0.89920E-01 0.20593E-01 0.26686E-01 0.31000 -0.17218E-02 -0.19814E-02 0.26249E-02 0.63614 0.22102 0.14441 0.31917E-01 0.11877E-01 0.18177E-01 0.32000 -0.39943E-02 0.91719E-04 0.39953E-02 0.49635 0.63152 0.15526 0.98051E-01 0.63265E-02 0.25733E-01 0.33000 -0.43500E-02 -0.20328E-02 0.48016E-02 0.56957 0.83049 0.13511 0.11221 0.57816E-02 0.35538E-01 0.34000 -0.20609E-03 -0.48330E-02 0.48374E-02 0.74322 0.44557 0.20583 0.91712E-01 0.10857E-01 0.23502E-01 0.35000 0.17158E-02 0.19563E-02 0.26022E-02 0.13541 0.16381 0.10471 0.17153E-01 0.15885E-01 0.24852E-01 0.36000 -0.76381E-02 0.14611E-01 0.16487E-01 0.32666 0.77210 0.34740 0.26823 0.21354E-01 0.47459E-01 0.37000 -0.93408E-02 0.95406E-02 0.13352E-01 0.37332 0.56078 0.41012 0.22999 0.23810E-01 0.32556E-01 0.38000 -0.33091E-02 -0.17053E-02 0.37227E-02 0.57573 0.20172 0.23532 0.47470E-01 0.18454E-01 0.15819E-01 0.39000 -0.36502E-02 0.19236E-02 0.41261E-02 0.42281 0.25771 0.11422 0.29435E-01 0.16010E-01 0.36125E-01 0.40000 -0.28444E-02 0.55882E-02 0.62705E-02 0.32493 0.43818 0.15536 0.68077E-01 0.14310E-01 0.40361E-01 0.41000 -0.21148E-02 -0.64118E-03 0.22098E-02 0.54685 0.23814 0.94639E-01 0.22537E-01 0.92798E-02 0.23350E-01 0.42000 0.26180E-02 -0.27775E-08 0.26180E-02 1.0000 0.31709 0.10108 0.32053E-01 0.82562E-02 0.25899E-01 0.43000 0.36309E-02 -0.52591E-02 0.63907E-02 0.84617 0.66058 0.13745 0.90796E-01 0.96744E-02 0.46496E-01 0.44000 0.32289E-02 -0.98341E-02 0.10351E-01 0.80049 0.79599 0.23622 0.18803 0.13003E-01 0.43818E-01 0.45000 0.45621E-02 -0.38905E-02 0.59958E-02 0.88762 0.39050 0.19051 0.74393E-01 0.15354E-01 0.31472E-01 0.46000 0.21324E-02 -0.91128E-03 0.23190E-02 0.93573 0.16306 0.10020 0.16339E-01 0.14222E-01 0.23143E-01 0.47000 0.14736E-02 -0.45637E-02 0.47958E-02 0.79971 0.41548 0.18896 0.78508E-01 0.11543E-01 0.25380E-01 0.48000 0.52297E-02 -0.66424E-02 0.84541E-02 0.85615 0.71501 0.19022 0.13601 0.11824E-01 0.44443E-01 0.49000 0.25534E-02 -0.94860E-02 0.98236E-02 0.79185 1.1703 0.11967 0.14005 0.83941E-02 0.82088E-01 0.50000 -0.26885E-02 -0.79028E-02 0.83476E-02 0.69781 1.1820 0.80746E-01 0.95443E-01 0.70622E-02 0.10338 Plot of the Amplitude of the Transfer Function of Series X mapping to Series Y AMPL 3.424 ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 0.1631 ***************************************************************************************************** 0.000 0.5000 FREQ Plot of the Amplitude of the Transfer Function of Series Y mapping to Series X AMPL 0.5055 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 0.8075E-01 ***************************************************************************************************** 0.000 0.5000 FREQ Est. Impulse Response Weights Reverse Response Weights K V(K) K V(K) 0 -0.39459766E-02 0 -0.10668877E-02 1 0.10317942 1 -0.15815001E-01 2 -0.48576931E-01 2 0.47786353E-02 3 -0.54394127 3 -0.25653853E-01 4 -0.63668488 4 -0.83532194E-02 5 -0.87730949 5 -0.16072142E-02 6 -0.51584498 6 -0.62554041E-01 7 -0.32366805 7 -0.13571899E-01 8 -0.48790929E-01 8 -0.46425726E-01 9 0.59676904E-01 9 0.42465464E-03 10 -0.10532795 10 0.11299051E-01 11 -0.64739970E-01 11 0.34170984E-02 12 -0.34896474E-01 12 -0.25061005E-02 13 -0.13379578 13 0.65532784E-02 14 0.52069257E-03 14 0.70086624E-02 15 -0.26410815E-01 15 0.14210855E-01 16 -0.11253674 16 -0.17465852E-01 17 -0.91446023E-01 17 -0.30027042E-01 18 -0.55665997E-01 18 -0.24924557E-01 19 -0.22223554 19 0.20377688E-01 20 0.27438489E-01 20 -0.32805153E-01 21 -0.10155944 21 0.15755329E-01 22 -0.42391889E-01 22 -0.24308831E-01 23 0.12095204 23 -0.12746610E-01 24 0.14488762E-01 24 -0.14962323E-01 SCA file created by B34SFL on unit 9 Autocorrelation Function Data - The Generated Noise Series 272 Observations Original Series Mean of the Series 2.388902800196126E-02 St. Dev. of Series 0.9412932134536537 Number of observations 272 S. E. of mean 5.717949061046255E-02 T value of mean (against zero) 0.4177901507501381 1- 12 0.91 0.75 0.56 0.38 0.23 0.12 0.05 0.01 -0.01 -0.01 -0.01 -0.02 St.E. 0.06 0.10 0.12 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 Mod. Q 226.7 381.0 467.3 507.0 522.0 526.2 526.9 526.9 527.0 527.0 527.0 527.1 13- 24 -0.04 -0.07 -0.11 -0.13 -0.15 -0.15 -0.13 -0.08 -0.02 0.03 0.08 0.10 St.E. 0.13 0.13 0.13 0.13 0.13 0.13 0.14 0.14 0.14 0.14 0.14 0.14 Mod. Q 527.7 529.2 532.5 537.6 544.3 550.8 555.5 557.4 557.5 557.8 559.5 562.6 Mean divided by St. Error (using N in S. D.) 0.4185602714972680 Q Statistic 552.30 DF 24 Prob. 1.0000 Modified Q Statistic 562.62 DF 24 Prob. 1.0000 NOTE: In some cases degrees of freedom for Q and Modified Q Statistics may have to be adjusted. Partial Autocorrelations Data - The Generated Noise Series 272 Observations Original Series Mean of the Series 2.388902800196126E-02 St. Dev. of Series 0.9412932134536537 Number of observations 272 S. E. of mean 5.717949061046255E-02 T value of mean (against zero) 0.4177901507501381 1- 12 0.91 -0.44 -0.15 0.01 0.04 0.00 -0.01 0.01 -0.01 0.06 -0.07 -0.10 13- 24 -0.04 0.03 -0.05 0.01 -0.02 0.05 0.07 0.05 -0.01 -0.01 0.03 -0.01 Preliminary estimates option selected Preliminary estimates main control card ib (number of backorder) = 0 ir (number of output terms) = 3 is (number of input terms) = 3 ip (print control) = 1 ih (h and a matrix print control) = 1 nrw (number of response weights - if 0 - response weights read off file iunrw) = 0 iunrw (unit to read response weights) = 9 rufile (file name, sca procedure name and variable name ) = SDATA5 Output model orders 1 2 3 Input model orders 1 2 3 PROCEDURE SDATA5 FOUND ON UNIT 9 Number of observations found 25 OF 12000000 SPACE ALLOWED, 1300 WILL BE USED A MATRIX 1 2 3 1 -0.485769E-01 0.103179 -0.394598E-02 2 -0.543941 -0.485769E-01 0.103179 3 -0.636685 -0.543941 -0.485769E-01 H VECTOR -0.543941 -0.636685 -0.877309 GIVEN 25 IMPULSE RESPONSE WEIGHTS LISTED BELOW TERM # ORDER RESPONSE WEIGHT 1 0 -0.39459766E-02 2 1 0.10317942 3 2 -0.48576931E-01 4 3 -0.54394127 5 4 -0.63668488 6 5 -0.87730949 7 6 -0.51584498 8 7 -0.32366805 9 8 -0.48790929E-01 10 9 0.59676904E-01 11 10 -0.10532795 12 11 -0.64739970E-01 13 12 -0.34896474E-01 14 13 -0.13379578 15 14 0.52069257E-03 16 15 -0.26410815E-01 17 16 -0.11253674 18 17 -0.91446023E-01 19 18 -0.55665997E-01 20 19 -0.22223554 21 20 0.27438489E-01 22 21 -0.10155944 23 22 -0.42391889E-01 24 23 0.12095204 25 24 0.14488762E-01 STARTING VALUES FOR NUMERATOR POLYNOMIAL ORDER STARTING VALUE 1 -0.39459766E-02 2 -0.11659926 3 0.41242198 STARTING VALUES FOR DENOMINATOR POLYNOMIAL ORDER STARTING VALUE 1 3.4008923 2 -3.2800384 3 10.213923 Time Series Parameter Estimation for Model 1 Data - Z = VAR=GASIN Observations 296 Differencing on Z - None Transformations Examined - None. Univariate Model Parameters. Parameter Beginning # Type Order Value 1 Mean 0.5000 2 Autoregressive 1 1 0.9700 3 Autoregressive 1 2 -0.9400 4 Autoregressive 1 3 0.5000 Output at each iteration has been suppressed. Residual output has been suppressed. Initial sum of Squares 118.4792984188001 Iteration stops - Relative parameter change < 4.000000189989805E-03 Correlation Matrix of the Parameters. 1/Cond = 0.1347E-02 1 2 3 4 1 1.0000 2 -0.0009 1.0000 3 -0.0003 -0.9410 1.0000 4 -0.0011 0.7899 -0.9410 1.0000 End of Estimation for Model 1 Summary of model 1 Data - Z = VAR=GASIN Observations 296 Differencing on Z - None Univariate Model Parameters. Parameter Estimated 95 Per Cent # Type Order Value Lower Limit t Upper Limit Std. Error 1 Mean -0.6894E-01 -0.4666 -0.3467 0.3287 0.1988 2 Autoregressive 1 1 1.975 1.864 35.74 2.085 0.5526E-01 3 Autoregressive 1 2 -1.373 -1.574 -13.71 -1.173 0.1001 4 Autoregressive 1 3 0.3424 0.2319 6.195 0.4530 0.5528E-01 Other Information and results. Residual Sum of Squares 10.434676 289 D.F. Residual Mean Square 3.610614602651619E-02 Number of residuals 293 Residual Standard error 0.1900161730656530 Backforecasting not used in Estimation Autocorrelation Function Data - THE ESTIMATED RESIDUALS - MODEL 1 293 Observations Original Series Mean of the Series -2.758565560279432E-13 St. Dev. of Series 0.1887146771112735 Number of observations 293 S. E. of mean 1.104369115092541E-02 T value of mean (against zero) -2.497865543847880E-11 1- 12 -0.04 0.07 0.06 -0.15 -0.01 0.06 0.02 0.00 -0.05 0.04 0.14 -0.08 St.E. 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 Mod. Q 0.5 1.9 2.9 9.2 9.2 10.3 10.4 10.4 11.2 11.7 18.0 19.9 13- 24 0.10 0.04 -0.08 0.01 0.06 -0.05 -0.08 0.02 0.01 0.03 0.04 0.00 St.E. 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 Mod. Q 22.8 23.3 25.4 25.5 26.7 27.7 29.6 29.8 29.9 30.1 30.7 30.7 Mean divided by St. Error (using N in S. D.) 2.502139055174033E-11 Q Statistic 29.391 DF 20 Prob. 0.91965 Modified Q Statistic 30.680 DF 20 Prob. 0.94044 NOTE: In some cases degrees of freedom for Q and Modified Q Statistics may have to be adjusted. Partial Autocorrelations Data - THE ESTIMATED RESIDUALS - MODEL 1 293 Observations Original Series Mean of the Series -2.758565560279432E-13 St. Dev. of Series 0.1887146771112735 Number of observations 293 S. E. of mean 1.104369115092541E-02 T value of mean (against zero) -2.497865543847880E-11 1- 12 -0.04 0.07 0.06 -0.15 -0.03 0.08 0.04 -0.03 -0.07 0.06 0.18 -0.08 13- 24 0.03 0.06 -0.02 -0.03 0.06 -0.02 -0.11 0.02 0.05 0.03 0.01 -0.05 Time Series Forecasting for Model 1 Data - Z = VAR=GASIN Observations 296 Differencing on Z - None Transformations Examined - None. Univariate Model Parameters. Parameter Beginning # Type Order Value 1 Mean -0.6894E-01 2 Autoregressive 1 1 1.975 3 Autoregressive 1 2 -1.373 4 Autoregressive 1 3 0.3424 Number of time origins for Forecasts 1 Number of forecasts at each time origin 24 Forecast Time Origins date T= 296 Backforecasting was suppressed in this analysis. REGULAR Forecast results in terms of THE ORIGINAL DATA ****************************************************** Model 1 Forecasts at base period 296 with 95 per cent confidence limits Period L. Conf. Forecast U. Conf. Actual % Error 297 -0.63797021 -0.26553850 0.10689320 298 -1.0552664 -0.23081413 0.59363813 299 -1.4360188 -0.18477104 1.0664767 300 -1.7298303 -0.14273423 1.4443618 301 -1.9294886 -0.11105007 1.7073884 302 -2.0516278 -0.90434430E-01 1.8707589 303 -2.1201104 -0.78833967E-01 1.9624424 304 -2.1560960 -0.73383633E-01 2.0093288 305 -2.1743622 -0.71489933E-01 2.0313823 306 -2.1836146 -0.71262052E-01 2.0410905 307 -2.1883663 -0.71546064E-01 2.0452742 308 -2.1907870 -0.71771429E-01 2.0472442 309 -2.1919247 -0.71748464E-01 2.0484278 310 -2.1923339 -0.71490887E-01 2.0493522 311 -2.1923443 -0.71090895E-01 2.0501625 312 -2.1921631 -0.70646775E-01 2.0508695 313 -2.1919172 -0.70230733E-01 2.0514558 314 -2.1916774 -0.69881974E-01 2.0519134 315 -2.1914758 -0.69612427E-01 2.0522510 316 -2.1913212 -0.69416540E-01 2.0524881 317 -2.1912095 -0.69280391E-01 2.0526487 318 -2.1911314 -0.69188199E-01 2.0527550 319 -2.1910772 -0.69126006E-01 2.0528252 320 -2.1910389 -0.69083157E-01 2.0528725 Weights used in calculating confidence limits J PS(J) 0 1.000000 1 1.974961 2 2.527235 3 2.621546 4 2.383272 5 1.972302 6 1.520155 7 1.109944 8 0.7799655 9 0.5367526 10 0.3690810 11 0.2589261 12 0.1883407 13 0.1427880 14 0.1120319 15 0.8967292E-01 16 0.7215098E-01 17 0.5771782E-01 18 0.4561797E-01 19 0.3554110E-01 20 0.2731310E-01 21 0.2075754E-01 22 0.1565879E-01 23 0.1177367E-01 24 0.8857599E-02 Time Series Parameter Estimation for Model 1 Data - Y = VAR=GASOUT Observations 296 Differencing on Y - None Transformations Examined - None. Noise Series. Differencing on Noise - None Noise Model Parameters Parameter Beginning # Type Order Value 1 Mean 53.51 2 Autoregressive 1 1 0.8000 3 Autoregressive 1 2 0.7600 Input Series 1 DATA - X1 = VAR=GASIN Differencing on X1 - None (Assumed mean of series = -0.6100E-01 ) Value of lag parameter is 3 Transfer function parameters 4 Output Lag 1 1 0.6000 5 Output Lag 1 2 0.2000 6 Input Lag 1 0 -0.5300 7 Input Lag 1 1 0.4000 8 Input Lag 1 2 0.6000 Output at each iteration has been suppressed. Residual output has been suppressed. Initial sum of Squares 1392.945350337510 Iteration stops - Relative parameter change < 4.000000189989805E-03 Correlation Matrix of the Parameters. 1/Cond = 0.1282E-02 1 2 3 4 5 6 7 8 1 1.0000 2 -0.0458 1.0000 3 0.0765 -0.9270 1.0000 4 0.0027 -0.0058 0.0057 1.0000 5 -0.0029 0.0093 -0.0105 -0.9849 1.0000 6 0.0059 -0.0034 0.0224 -0.1148 0.1159 1.0000 7 -0.0024 0.0096 -0.0094 -0.7150 0.7240 0.5791 1.0000 8 -0.0011 0.0043 -0.0033 -0.8083 0.7349 -0.0482 0.3025 1.0000 End of Estimation for Model 1 Summary of model 1 Data - Y = VAR=GASOUT Observations 296 Differencing on Y - None Noise Series. Differencing on Noise - None Noise Model Parameters Parameter Estimated 95 Per Cent # Type Order Value Lower Limit t Upper Limit Std. Error 1 Mean 53.56 53.28 373.8 53.85 0.1433 2 Autoregressive 1 1 1.531 1.436 32.12 1.627 0.4768E-01 3 Autoregressive 1 2 -0.6321 -0.7325 -12.59 -0.5316 0.5022E-01 Input Series 1 DATA - X1 = VAR=GASIN Differencing on X1 - None (Assumed mean of series = -0.6100E-01 ) Value of lag parameter is 3 Transfer function parameters Parameter 95 Per Cent # Type Order Value Lower Limit t Upper Limit Std. Error 4 Output Lag 1 1 0.5709 0.1417 2.661 1.000 0.2146 5 Output Lag 1 2 -0.1564E-01 -0.3179 -0.1034 0.2867 0.1512 6 Input Lag 1 0 -0.5305 -0.6818 -7.015 -0.3793 0.7562E-01 7 Input Lag 1 1 0.3683 0.6660E-01 2.441 0.6700 0.1509 8 Input Lag 1 2 0.5072 0.1888 3.186 0.8256 0.1592 Other Information and results. Residual Sum of Squares 16.593754 281 D.F. Residual Mean Square 5.905250364714099E-02 Number of residuals 289 Residual Standard error 0.2430072090435611 Backforecasting not used in Estimation Autocorrelation Function Data - THE ESTIMATED RESIDUALS - MODEL 1 289 Observations Original Series Mean of the Series 1.954374326686871E-04 St. Dev. of Series 0.2396201036434864 Number of observations 289 S. E. of mean 1.411975001624438E-02 T value of mean (against zero) 1.384142300280400E-02 1- 12 0.02 0.06 -0.07 -0.06 -0.05 0.12 0.03 0.03 -0.08 0.05 0.02 0.10 St.E. 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 Mod. Q 0.2 1.1 2.7 3.6 4.4 8.9 9.2 9.6 11.6 12.4 12.5 15.5 13- 24 -0.04 0.05 -0.09 -0.01 -0.08 0.00 -0.12 0.00 -0.01 0.08 0.02 -0.01 St.E. 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 Mod. Q 16.0 16.8 19.4 19.4 21.3 21.3 25.6 25.6 25.6 27.4 27.6 27.6 Mean divided by St. Error (using N in S. D.) 1.386543242761841E-02 Q Statistic 26.291 DF 21 Prob. 0.80442 Modified Q Statistic 27.595 DF 21 Prob. 0.84799 NOTE: In some cases degrees of freedom for Q and Modified Q Statistics may have to be adjusted. Partial Autocorrelations Data - THE ESTIMATED RESIDUALS - MODEL 1 289 Observations Original Series Mean of the Series 1.954374326686871E-04 St. Dev. of Series 0.2396201036434864 Number of observations 289 S. E. of mean 1.411975001624438E-02 T value of mean (against zero) 1.384142300280400E-02 1- 12 0.02 0.06 -0.08 -0.06 -0.04 0.13 0.02 0.01 -0.08 0.07 0.05 0.07 13- 24 -0.06 0.04 -0.05 -0.01 -0.08 -0.04 -0.11 -0.02 0.01 0.05 0.03 -0.04 Cross Correlations Series 1 - PREWHITENED VAR=GASIN Series 2 - THE ESTIMATED RESIDUALS - MODEL 1 Mean Series 1 = -7.311710726643630E-04 ST. Dev. Series 1 = 0.1898705768026324 Mean Series 2 = 1.954374326686871E-04 ST. Dev. Series 2 = 0.2396201036434864 Number of Lags Cross Number of Lags Cross on Series 1 Correlation on Series 2 Correlation S Left S Right Mod S Left Mod S Right 0 -0.056 0 -0.056 0.923 0.923 0.923 0.923 1 0.026 1 -0.045 1.11 1.50 1.11 1.50 2 -0.015 2 0.035 1.18 1.86 1.18 1.86 3 0.002 3 -0.044 1.18 2.40 1.18 2.41 4 0.004 4 -0.012 1.18 2.44 1.19 2.45 5 0.005 5 -0.003 1.19 2.45 1.19 2.46 6 0.010 6 -0.095 1.22 5.03 1.22 5.10 7 -0.043 7 0.015 1.76 5.10 1.78 5.17 8 0.028 8 -0.030 1.98 5.35 2.01 5.43 9 0.075 9 0.048 3.63 6.02 3.70 6.11 10 -0.028 10 0.051 3.86 6.77 3.94 6.89 11 -0.021 11 -0.005 3.98 6.77 4.06 6.90 12 -0.024 12 -0.019 4.14 6.88 4.24 7.01 13 -0.111 13 -0.002 7.73 6.88 7.99 7.01 14 0.012 14 -0.019 7.77 6.98 8.04 7.11 15 0.047 15 -0.014 8.42 7.04 8.72 7.17 16 0.040 16 -0.056 8.89 7.95 9.22 8.14 17 0.017 17 -0.025 8.97 8.12 9.30 8.32 18 0.012 18 0.024 9.01 8.29 9.35 8.50 19 -0.142 19 0.082 14.8 10.2 15.6 10.6 20 -0.030 20 -0.049 15.1 10.9 15.9 11.3 21 -0.074 21 0.030 16.7 11.2 17.5 11.6 22 -0.079 22 -0.082 18.5 13.1 19.5 13.7 23 0.023 23 -0.075 18.6 14.7 19.7 15.5 24 -0.016 24 -0.053 18.7 15.5 19.7 16.3 Number of terms for Sum of Cross Correlations Squared 25 0.64642899E-01 0.53804448E-01 Haugh S Statistic - See JASA June 76 Page 382 S for left side 18.682 DF 25 Chi Prob 0.187883 S for right side 14.627 DF 24 Chi Prob 0.068799 S for both sides 33.309 DF 49 CHI Prob 0.042192 Test for feedback plus instantaneous causality S for right side 15.549 DF 25 Chi Prob 0.072414 Haugh Modified S Statistic - See JASA June 76 Page 383 S for left side 19.738 DF 25 Chi Prob 0.239566 S for right side 15.420 DF 24 Chi Prob 0.092120 S for both sides 35.157 DF 49 CHI Prob 0.068378 Test for feedback plus instantaneous causality S for right side 16.342 DF 25 Chi Prob 0.095741 Note: Cross correlations on left are for series 2 on lags of series 1 Cross correlations on right are for series 1 on lags of series 2 Note: Degrees of freedom of S Statistics have to be adjusted for transfer function checking. Input series 1 *************** Model Implied Estimated Correct Lag Impulse Response Weights Impulse Response Weights Difference Sum Implied WGT Sum Corr WGT 0 0.0000000 -0.44654458E-01 -0.44654458E-01 0.00000 -0.446545E-01 1 0.0000000 0.63722795E-01 0.63722795E-01 0.00000 0.190683E-01 2 0.0000000 -0.40252619E-01 -0.40252619E-01 0.00000 -0.211843E-01 3 -0.53051900 -0.51849451 0.12024492E-01 -0.530519 -0.539679 4 -0.67118710 -0.66422806 0.69590388E-02 -1.20171 -1.20391 5 -0.88209022 -0.87644372 0.56465036E-02 -2.08380 -2.08035 6 -0.49308704 -0.48002708 0.13059961E-01 -2.57688 -2.56038 7 -0.26770932 -0.32625836 -0.58549045E-01 -2.84459 -2.88664 8 -0.14512442 -0.81879840E-01 0.63244576E-01 -2.98972 -2.96852 9 -0.78665126E-01 -0.15304628E-03 0.78512080E-01 -3.06838 -2.96867 10 -0.42640484E-01 -0.12066305 -0.78022565E-01 -3.11102 -3.08933 11 -0.23113298E-01 -0.24710788E-01 -0.15974909E-02 -3.13414 -3.11404 12 -0.12528575E-01 -0.29348218E-01 -0.16819643E-01 -3.14666 -3.14339 13 -0.67911209E-02 -0.13154992 -0.12475880 -3.15346 -3.27494 14 -0.36811307E-02 0.68018194E-01 0.71699325E-01 -3.15714 -3.20692 15 -0.19953589E-02 0.33934170E-01 0.35929528E-01 -3.15913 -3.17299 16 -0.10815854E-02 0.19106857E-01 0.20188442E-01 -3.16021 -3.15388 17 -0.58627392E-03 0.59940229E-03 0.11856762E-02 -3.16080 -3.15328 18 -0.31779009E-03 0.10969209E-01 0.11286999E-01 -3.16112 -3.14231 19 -0.17225829E-03 -0.18279651 -0.18262425 -3.16129 -3.32511 20 -0.93372698E-04 0.46233637E-01 0.46327009E-01 -3.16138 -3.27888 21 -0.50612721E-04 -0.86951839E-01 -0.86901227E-01 -3.16143 -3.36583 22 -0.27434652E-04 -0.67495124E-01 -0.67467690E-01 -3.16146 -3.43332 23 -0.14870968E-04 0.66775537E-01 0.66790408E-01 -3.16148 -3.36655 24 -0.80608162E-05 -0.40432030E-01 -0.40423970E-01 -3.16148 -3.40698 Graph of ESTIMATED CORRECT WGHTS. Graph Interval is 0.2191E-01 -.1096E+01 0.0000E+00 0.1096E+01 values .+++++++++.+++++++++.+++++++++.+++++++++.+++++++++.+++++++++.+++++++++.+++++++++.+++++++++.+++++++++. X 0 XXX -0.4465E-01 X 1 XXXX 0.6372E-01 X 2 XXX -0.4025E-01 X 3 XXXXXXXXXXXXXXXXXXXXXXXXX -0.5185 X 4 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX -0.6642 X 5 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX -0.8764 X 6 XXXXXXXXXXXXXXXXXXXXXXX -0.4800 X 7 XXXXXXXXXXXXXXXX -0.3263 X 8 XXXXX -0.8188E-01 X 9 X -0.1530E-03 X 10 XXXXXXX -0.1207 X 11 XX -0.2471E-01 X 12 XX -0.2935E-01 X 13 XXXXXXX -0.1315 X 14 XXXX 0.6802E-01 X 15 XXX 0.3393E-01 X 16 XX 0.1911E-01 X 17 X 0.5994E-03 X 18 XX 0.1097E-01 X 19 XXXXXXXXX -0.1828 X 20 XXX 0.4623E-01 X 21 XXXXX -0.8695E-01 X 22 XXXX -0.6750E-01 X 23 XXXX 0.6678E-01 X 24 XXX -0.4043E-01 Time Series Forecasting for Model 1 Data - Y = VAR=GASOUT Observations 296 Differencing on Y - None Transformations Examined - None. Noise Series. Differencing on Noise - None Noise Model Parameters Parameter Beginning # Type Order Value 1 Mean 53.56 2 Autoregressive 1 1 1.531 3 Autoregressive 1 2 -0.6321 Input Series 1 DATA - X1 = VAR=GASIN Differencing on X1 - None (Assumed mean of series = -0.6100E-01 ) Value of lag parameter is 3 Transfer function parameters 4 Output Lag 1 1 0.5709 5 Output Lag 1 2 -0.1564E-01 6 Input Lag 1 0 -0.5305 7 Input Lag 1 1 0.3683 8 Input Lag 1 2 0.5072 Number of time origins for Forecasts 1 Number of forecasts at each time origin 24 Forecast Time Origins date T= 296 Backforecasting was suppressed in this analysis. Time Series Forecasting for INPUT SERIES 1 Data - X1 = VAR=GASIN Observations 296 Differencing on X1 - None Transformations Examined - None. Univariate Model Parameters. Parameter Beginning # Type Order Value 1 Mean -0.6100E-01 2 Autoregressive 1 1 1.975 3 Autoregressive 1 2 -1.373 4 Autoregressive 1 3 0.3424 REGULAR Forecast results in terms of THE ORIGINAL DATA ****************************************************** INPUT SERIES 1 Model 1 Forecasts at base period 296 with 95 per cent confidence limits Period L. Conf. Forecast U. Conf. Actual % Error 297 -0.63753025 -0.26509854 0.10733317 298 -1.0539449 -0.22949957 0.59494580 299 -1.4335610 -0.18233083 1.0688993 300 -1.7261827 -0.13912083 1.4479411 301 -1.9247451 -0.10636672 1.7120116 302 -2.0459621 -0.84864696E-01 1.8762327 303 -2.1137213 -0.72582337E-01 1.9685566 304 -2.1491711 -0.66636985E-01 2.0158972 305 -2.1670581 -0.64399113E-01 2.0382599 306 -2.1760504 -0.63938130E-01 2.0481742 307 -2.1806258 -0.64065071E-01 2.0524957 308 -2.1829255 -0.64182548E-01 2.0545604 309 -2.1839772 -0.64082401E-01 2.0558124 310 -2.1843225 -0.63766763E-01 2.0567890 311 -2.1842834 -0.63321142E-01 2.0576411 312 -2.1840627 -0.62840212E-01 2.0583823 313 -2.1837853 -0.62394255E-01 2.0589967 314 -2.1835202 -0.62021350E-01 2.0594775 315 -2.1832988 -0.61732603E-01 2.0598335 316 -2.1831287 -0.61521722E-01 2.0600853 317 -2.1830052 -0.61374069E-01 2.0602571 318 -2.1829183 -0.61273179E-01 2.0603719 319 -2.1828575 -0.61204478E-01 2.0604485 320 -2.1828142 -0.61156783E-01 2.0605007 Weights used in calculating confidence limits J PS(J) 0 1.000000 1 1.974940 2 2.527188 3 2.621457 4 2.383105 5 1.972014 6 1.519717 7 1.109354 8 0.7792512 9 0.5359598 10 0.3682638 11 0.2581344 12 0.1876128 13 0.1421473 14 0.1114878 15 0.8922364E-01 16 0.7178752E-01 17 0.5742756E-01 18 0.4538755E-01 19 0.3535820E-01 20 0.2716734E-01 21 0.2064068E-01 22 0.1556457E-01 23 0.1169740E-01 24 0.8795763E-02 REGULAR Forecast results in terms of THE ORIGINAL DATA ****************************************************** Output Series Forecasts Model 1 Forecasts at base period 296 with 95 per cent confidence limits Period L. Conf. Forecast U. Conf. Actual % Error 297 56.058946 56.535240 57.011534 298 55.195277 56.066446 56.937615 299 54.447797 55.641500 56.835202 300 53.821422 55.265767 56.710112 301 53.152271 54.877120 56.601969 302 52.240657 54.484952 56.729246 303 51.099756 54.123688 57.147620 304 49.940980 53.824265 57.707549 305 48.947353 53.602906 58.258459 306 48.200838 53.460416 58.719994 307 47.701917 53.386395 59.070872 308 47.406193 53.364657 59.323122 309 47.255090 53.377861 59.500633 310 47.194847 53.410577 59.626306 311 47.184653 53.450818 59.716982 312 47.197478 53.490384 59.783290 313 47.217429 53.524473 59.831517 314 47.236297 53.550933 59.865568 315 47.250622 53.569452 59.888282 316 47.259605 53.580833 59.902061 317 47.263782 53.586426 59.909069 318 47.264235 53.587733 59.911230 319 47.262146 53.586166 59.910186 320 47.258578 53.582917 59.907257 Weights USED in calculating confidence limits j PS(J) 1 V(J) 0 1.000000 0.000000 1 1.531487 0.000000 2 1.713400 0.000000 3 1.656072 -0.5305190 4 1.453295 -1.718930 5 1.178980 -3.548366 6 0.8870349 -5.322111 7 0.6133066 -6.494505 8 0.3786193 -6.878020 9 0.1922093 -6.566378 10 0.5505917E-01 -5.789665 11 -0.3716374E-01 -4.795438 12 -0.9171600E-01 -3.781191 13 -0.1169724 -2.871702 14 -0.1211725 -2.124746 15 -0.1116415 -1.549501 16 -0.9439028E-01 -1.126822 17 -0.7399429E-01 -0.8257308 18 -0.5366178E-01 -0.6142834 19 -0.3541411E-01 -0.4652756 20 -0.2031925E-01 -0.3581810 21 -0.8735131E-02 -0.2788507 22 -0.5349274E-03 -0.2181972 23 0.4701816E-02 -0.1706645 24 0.7538870E-02 -0.1329104 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 64 Multivariate Time Series Modeling Option Selected Set up to run for 296 Observations Series # B34S Variable # Name 1 2 GASIN 2 3 GASOUT OF 12000000 SIZE AVAILABLE 8882 USED IDENTIFICATION RUN WITH GAS DATA Number of observations = 296 Number of series = 2 Number of lags = 36 Series 1: VAR= B-J GAS INPUT DATA 1 1 12 1 Differencing = (1-B ) * (1-B ) Series 2: VAR= B-J GAS OUTPUT DATA After any transformation and/or differencing. Series 1 has sample mean = 0.63922261E-02 Sample standard deviation = 0.45147510 Series 2 has sample mean = 53.537456 Sample standard deviation = 3.2638197 Sample covariance matrix = GAMZ IS 0.20382976 0.55443973 10.652519 Eigenvalues of GAMZ : 0.17449186 10.681857 Eigenvectors of GAMZ are 1 2 0.99860296 0.52840590E-01 -0.52840590E-01 0.99860296 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 65 Estimated sample auto correlations based on 283 observations of the series. Approximate. SE ACF: 0.5944E-01 VAR= B-J GAS INPUT DATA Mean: 0.6392E-02, St. Dev.: 0.4515 LAG -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . + 0 + * . * X+ 1.000 1 . * . * X . 0.724 2 . * . * X . 0.366 3 . * . X * . 0.056 4 . X * . * . -0.167 5 + X * . * + -0.194 6 . *X . * . -0.100 7 . * X. * . -0.015 8 . * X * . -0.010 9 . *X . * . -0.098 10 + X * . * + -0.213 11 . X * . * . -0.352 12 . X * . * . -0.479 13 . X * . * . -0.326 14 . X* . * . -0.149 15 + * X * + -0.001 16 . * . *X . 0.137 17 . * . * X . 0.157 18 . * . X * . 0.074 19 . * X * . 0.005 20 + * X. * + -0.013 21 . * X. * . -0.024 22 . * X . * . -0.039 23 . * X . * . -0.048 24 . * X . * . -0.034 25 + * X . * + -0.030 26 . * X * . -0.005 27 . * .X * . 0.021 28 . * X. * . -0.017 29 . * X . * . -0.035 30 + * .X * + 0.012 31 . * . X * . 0.057 32 . * . X * . 0.089 33 . * . X . 0.124 34 . * . X . 0.121 35 + * . X* + 0.094 36 . * . X * . 0.049 + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . + -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 66 Estimated sample auto correlations based on 283 observations of the series. Approximate. SE ACF: 0.5944E-01 VAR= B-J GAS OUTPUT DATA Mean: 53.54 , St. Dev.: 3.264 LAG -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . + 0 + * . * X+ 1.000 1 . * . * X . 0.971 2 . * . * X . 0.897 3 . * . * X . 0.795 4 . * . * X . 0.684 5 + * . * X + 0.580 6 . * . * X . 0.493 7 . * . * X . 0.424 8 . * . * X . 0.374 9 . * . * X . 0.339 10 + * . * X + 0.314 11 . * . * X . 0.294 12 . * . * X . 0.273 13 . * . * X . 0.249 14 . * . * X . 0.220 15 + * . * X + 0.190 16 . * . * X . 0.160 17 . * . *X . 0.133 18 . * . X . 0.113 19 . * . X* . 0.101 20 + * . X* + 0.097 21 . * . X* . 0.099 22 . * . X* . 0.103 23 . * . X* . 0.108 24 . * . X . 0.111 25 + * . X + 0.111 26 . * . X* . 0.108 27 . * . X* . 0.102 28 . * . X* . 0.095 29 . * . X * . 0.087 30 + * . X * + 0.083 31 . * . X * . 0.084 32 . * . X * . 0.089 33 . * . X* . 0.096 34 . * . X* . 0.098 35 + * . X* + 0.093 36 . * . X * . 0.079 + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . + -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 67 Estimated Sample Cross Correlations based on 283 observations of each series. Approximate SE CCF 0.5944E-01 1. VAR= B-J GAS INPUT DATA Mean: 0.6392E-02 St. Dev: 0.4515 2. VAR= B-J GAS OUTPUT DATA Mean: 53.54 St. Dev: 3.264 Note: Series one assumed to be input series - Significant spikes at negative lags imply feedback from series 2 to series 1 LAG -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . + -36 . * . X * . 0.036 -35 + * . X * + 0.050 -34 . * . X * . 0.063 -33 . * . X * . 0.071 -32 . * . X * . 0.072 -31 . * . X * . 0.061 -30 + * . X * + 0.043 -29 . * .X * . 0.023 -28 . * X * . 0.002 -27 . * X. * . -0.014 -26 . * X. * . -0.025 -25 + * X . * + -0.035 -24 . * X . * . -0.049 -23 . * X . * . -0.063 -22 . * X . * . -0.074 -21 . * X . * . -0.076 -20 + * X . * + -0.069 -19 . * X . * . -0.060 -18 . * X . * . -0.057 -17 . * X . * . -0.068 -16 . * X . * . -0.088 -15 + X . * + -0.115 -14 . X * . * . -0.151 -13 . X * . * . -0.190 -12 . X * . * . -0.222 -11 . X * . * . -0.231 -10 + X * . * + -0.195 -9 . *X . * . -0.106 -8 . * .X * . 0.018 -7 . * . *X . 0.150 -6 . * . * X . 0.255 -5 + * . * X + 0.321 -4 . * . * X . 0.347 -3 . * . * X . 0.351 -2 . * . * X . 0.355 -1 . * . * X . 0.365 0 + * . * X + 0.376 1 . * . * X . 0.370 2 . * . * X . 0.321 3 . * . * X . 0.223 4 . * . X* . 0.091 5 + * X . * + -0.044 6 . X* . * . -0.146 7 . X * . * . -0.196 8 . X * . * . -0.199 9 . X * . * . -0.172 10 + X* . * + -0.140 11 . X . * . -0.113 12 . *X . * . -0.093 13 . * X . * . -0.076 14 . * X . * . -0.056 15 + * X . * + -0.039 16 . * X . * . -0.033 17 . * X . * . -0.035 18 . * X . * . -0.044 19 . * X . * . -0.062 20 + * X . * + -0.079 21 . *X . * . -0.090 22 . *X . * . -0.093 23 . * X . * . -0.087 24 . * X . * . -0.075 25 + * X . * + -0.055 26 . * X . * . -0.031 27 . * X * . -0.005 28 . * .X * . 0.020 29 . * . X * . 0.034 30 + * . X * + 0.033 31 . * .X * . 0.029 32 . * .X * . 0.024 33 . * .X * . 0.019 34 . * .X * . 0.019 35 + * .X * + 0.021 36 . * .X * . 0.023 + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . + -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 Summaries or cross correlation matrices using +,-,., where + denotes a value greater that G/SQRT(NOBE) - denotes a value less than -G/SQRT(NOBE) . denotes a non-significant value based on the above criterion, where G = 2.000 . Behavior of values in (i,j)th position of cross correlation matrix over all outputted lags ++.--....--- +++..-----.. --.++....... ............ ........++.. ............ +++++++..--- ++++++++++++ --.......... +++++....... ............ ............ Cross Correlation Matrices in terms of +, -, . Note: Series i is lagged for each term P(i,j) Lags 1 through 6 + + + + . + - . - . . - + + + + + + + + + + + + Lags 7 through 12 . - . - . - - - - . - . + + . + . + - + - + - + Lags 13 through 18 - . - . . . + . + . . . - + - + . + . + . + . . Lags 19 through 24 . . . . . . . . . . . . . . . . . . . . . . . . Lags 25 through 30 . . . . . . . . . . . . . . . . . . . . . . . . Lags 31 through 36 . . . . + . + . . . . . . . . . . . . . . . . . Summary Table for VAR= B-J GAS INPUT DATA Mean= 0.63922261E-02 Variance= 0.20382976 Standard Deviation= 0.45147510 Skewness= -0.63327744 Kurtosis= 3.2916540 # of observations 283 Hinich bispectrum summary table. M G L BICOH Lamda 9 1.3147740 -5.1833340 1.5097272 0.10000000E-15 10 1.9335630 -4.4405674 1.5697293 0.10000000E-15 11 1.6808697 -3.8160138 1.5634914 0.10000000E-15 12 4.7365216 -3.3284579 1.8752641 0.10000000E-15 13 4.8402078 -2.7451557 1.9261581 0.10000000E-15 14 1.7160432 -2.8636684 1.6016467 0.10000000E-15 15 5.2205453 -1.7319598 2.0514512 0.10000000E-15 16 0.96667057 -1.9520824 1.5331053 0.10000000E-15 17 2.8582574 -1.6144566 1.7966106 0.10000000E-15 Mean for G = 2.8074947 Mean for L = -3.0750773 For the above table NWD = 51 WT = 14.925034 M = # of terms averaged to estimate bispectrum. G = (Z) statistic to test for Gaussianity. L = (Z) statistic to test for linearity. BICOH = average skewness (measure of nonlinear predictability). LAMDA = estimate of non-centrality. WT = whiteness statistic. Smoothing has not been done. MARTINGALE DIFFERENCE TEST FOR SERIES VAR= B-J GAS INPUT DATA NO. OBERVATIONS INPUTTED= 283 DESCRIPTIVE STATISTICS OF DATA... MEAN = 0.63922261E-02 VARIANCE = 0.20455257 STANDARD DEVIATION = 0.45227488 SKEWNESS = -0.62992382 KURTOSIS = 3.2472685 SAMPLE 6TH ORDER CUMULANT= 58.702681 MAX VALUE DATA= 1.2950000 MIN VALUE DATA= -2.5410000 V MART KERNEL FILTER WIDTH = 0.00% SQUARE ROOT OF NUMBER OF OBSERVATIONS= 16.822604 ********************************************************************* RUN # BLOCKSIZE # OBS. V INT. Z BEFORE FILTER D. F. 1 14 280 0 10.256915 20 2 15 270 0 6.7327104 24 3 16 272 0 11.282465 28 4 17 272 0 10.888789 32 5 18 270 0 25.121343 38 VAR= B-J GAS INPUT DATA Dickey-Fuller Unit Root Test (I) Lag 0 t test -6.7044710 Prob of I(1) 0.0100 Aug. Dickey-Fuller Test (II) Lag 0 t test -6.6943342 Prob of I(1) 0.0100 Aug. Dickey-Fuller Test (II) Lag 0 t test -6.6943342 Prob of I(1) 0.0100 Summary Table for VAR= B-J GAS OUTPUT DATA Mean= 53.537456 Variance= 10.652519 Standard Deviation= 3.2638197 Skewness= -0.75865736E-01 Kurtosis= -0.68128705 # of observations 283 Hinich bispectrum summary table. M G L BICOH Lamda 9 168.70203 10.898291 13.917296 182.45024 10 156.93673 8.0183743 14.225685 194.52822 11 161.10896 19.244722 15.997432 254.75087 12 158.28179 13.871627 16.931616 290.07694 13 164.19398 39.020545 18.913328 341.38110 14 164.81928 36.951611 19.837142 394.37343 15 155.40899 23.783053 20.538371 441.76193 16 152.35179 12.864656 21.076841 530.30210 17 154.65469 22.635256 22.453489 527.49414 Mean for G = 159.60647 Mean for L = 20.809793 For the above table NWD = 51 WT = 10.290141 M = # of terms averaged to estimate bispectrum. G = (Z) statistic to test for Gaussianity. L = (Z) statistic to test for linearity. BICOH = average skewness (measure of nonlinear predictability). LAMDA = estimate of non-centrality. WT = whiteness statistic. Smoothing has not been done. MARTINGALE DIFFERENCE TEST FOR SERIES VAR= B-J GAS OUTPUT DATA NO. OBERVATIONS INPUTTED= 283 DESCRIPTIVE STATISTICS OF DATA... MEAN = 53.537456 VARIANCE = 10.690294 STANDARD DEVIATION = 3.2696015 SKEWNESS = -0.75463976E-01 KURTOSIS = -0.69764477 SAMPLE 6TH ORDER CUMULANT= 2.8220470 MAX VALUE DATA= 60.500000 MIN VALUE DATA= 45.600000 V MART KERNEL FILTER WIDTH = 0.00% SQUARE ROOT OF NUMBER OF OBSERVATIONS= 16.822604 ********************************************************************* RUN # BLOCKSIZE # OBS. V INT. Z BEFORE FILTER D. F. 1 14 280 0 0.50236942 20 2 15 270 0 -2.0789411 24 3 16 272 0 -1.7231582 28 4 17 272 0 -3.5875010 32 5 18 270 0 1.9294250 38 VAR= B-J GAS OUTPUT DATA Dickey-Fuller Unit Root Test (I) Lag 0 t test 0.12433713 Prob of I(1) 0.1000 Aug. Dickey-Fuller Test (II) Lag 0 t test -1.8161241 Prob of I(1) 0.1000 Aug. Dickey-Fuller Test (II) Lag 0 t test -1.8161241 Prob of I(1) 0.1000 Multivariate Q Statistic Portmanteau statistic for multivariate time series Orig-Q => Ljung Box (1978) LM-Q => Li and McLeod (1981) LB-Q => Hosking (1980, 1981) Code developed by Tsay (1990) Changes 2001 by H. H. Stokes Suggested # of Lags = 5 m Orig-Q LM-Q LB-Q d.f. 1 398.0904 398.1045 399.5021 0 2 647.7743 647.8167 650.9631 4 3 830.1485 830.2333 835.2913 8 4 995.4117 995.5530 1002.9238 12 5 1134.6170 1134.8290 1144.6328 16 6 1242.9896 1243.2865 1255.3529 20 7 1337.1197 1337.5155 1351.8704 24 8 1424.5050 1425.0138 1441.7978 28 9 1505.8338 1506.4699 1525.7980 32 10 1588.7469 1589.5243 1611.7481 36 11 1680.7469 1681.6797 1707.4687 40 12 1788.9148 1790.0173 1820.4264 44 13 1856.2953 1857.5815 1891.0510 48 14 1895.0473 1896.5314 1931.8199 52 15 1923.4965 1925.1926 1961.8615 56 16 1957.0067 1958.9290 1997.3798 60 17 1986.6776 1988.8402 2028.9469 64 18 2002.2890 2004.7059 2045.6187 68 19 2013.2398 2015.9254 2057.3577 72 20 2025.2029 2028.1711 2070.2305 76 21 2038.5415 2041.8065 2084.6382 80 22 2052.1346 2055.7106 2099.3771 84 23 2064.5625 2068.4636 2112.9043 88 24 2075.5130 2079.7533 2124.8696 92 25 2084.1651 2088.7587 2134.3600 96 26 2090.8905 2095.8517 2141.7659 100 27 2096.0553 2101.3981 2147.4754 104 28 2099.0844 2104.8229 2150.8371 108 29 2101.9911 2108.1395 2154.0756 112 30 2103.9857 2110.5582 2156.3068 116 31 2106.7098 2113.7204 2159.3660 120 32 2111.1083 2118.5712 2164.3252 124 33 2118.3392 2126.2685 2172.5106 128 34 2125.5142 2133.9241 2180.6654 132 35 2130.5846 2139.4892 2186.4514 136 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 68 36 2132.9611 2142.3746 2189.1742 140 Significance of Q statistics 1 1.0000 1.0000 1.0000 0 2 1.0000 1.0000 1.0000 4 3 1.0000 1.0000 1.0000 8 4 1.0000 1.0000 1.0000 12 5 1.0000 1.0000 1.0000 16 6 1.0000 1.0000 1.0000 20 7 1.0000 1.0000 1.0000 24 8 1.0000 1.0000 1.0000 28 9 1.0000 1.0000 1.0000 32 10 1.0000 1.0000 1.0000 36 11 1.0000 1.0000 1.0000 40 12 1.0000 1.0000 1.0000 44 13 1.0000 1.0000 1.0000 48 14 1.0000 1.0000 1.0000 52 15 1.0000 1.0000 1.0000 56 16 1.0000 1.0000 1.0000 60 17 1.0000 1.0000 1.0000 64 18 1.0000 1.0000 1.0000 68 19 1.0000 1.0000 1.0000 72 20 1.0000 1.0000 1.0000 76 21 1.0000 1.0000 1.0000 80 22 1.0000 1.0000 1.0000 84 23 1.0000 1.0000 1.0000 88 24 1.0000 1.0000 1.0000 92 25 1.0000 1.0000 1.0000 96 26 1.0000 1.0000 1.0000 100 27 1.0000 1.0000 1.0000 104 28 1.0000 1.0000 1.0000 108 29 1.0000 1.0000 1.0000 112 30 1.0000 1.0000 1.0000 116 31 1.0000 1.0000 1.0000 120 32 1.0000 1.0000 1.0000 124 33 1.0000 1.0000 1.0000 128 34 1.0000 1.0000 1.0000 132 35 1.0000 1.0000 1.0000 136 36 1.0000 1.0000 1.0000 140 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 69 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 70 Multivariate Time Series Modeling Option Selected Set up to run for 296 Observations Series # B34S Variable # Name 1 2 GASIN 2 3 GASOUT Of 12000000 size available, 5968 was used. ********** IDENTIFICATION RUN WITH GAS DATA ********** Number of observations (NOB) = 296 Number of series (K) = 2 Number of nonseasonal lags (P) = 6 Number of seasonal lags (PS) = 0 Seasonal lag factor (S) = 0 The 6 lags to be regressed on are: 1 2 3 4 5 6 Series 1: VAR= B-J GAS INPUT DATA Series 2: VAR= B-J GAS OUTPUT DATA After any transformations and/or differencing. Series 1 has sample mean = -0.56834459E-01 and sample Std. Dev. = 1.0709519 Series 2 has sample mean = 53.509122 and sample Std. Dev. = 3.1967072 Determinant of S(0) = 9.323 1/Condition = 0.74290701E-01 Note: S(0) is the sample covariance matrix of W(MAXLAG+1),...,W(NOBE) MAXLAG = 6 is the maximum lag to be regressed on NOBE = 296 is the effective number of observations. B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 71 ************ P = 6, PS = 0, S = 0, J = 1, Lags: 1 ********** PHI( 1) ********** ******** Std. Errors ******** ** Significance ** 0.995E+00 0.295E-01 0.198E-01 0.663E-02 + + -0.495E+00 0.894E+00 0.363E-01 0.122E-01 - + ******** Residual Covariance Matrix S(J) ******** ******** Residual Correlation Matrix RS(J) ******** 0.101E+00 1.00 0.888E-01 0.341E+00 0.48 1.00 Sum of squared Residuals for Equations 1,...,k 1 29.36534011088258 2 98.91452371351579 Granger Test for Causality. F(i,j) tests whether jth series Granger causes ith series. Granger Causality F(i,j) 1 2 1 2508.80 19.6418 2 184.524 5344.13 Significance of F(i,j) 1 2 1 1.00000 0.999987 2 1.00000 1.00000 Impulse Response Functions calculated by normalizing by diagonal polynomial. For ith row, jth col is effect of jth variable on ith variable where all X variables are on the left. K + 1 col = 1 / diagonal polynomial IRF row 1 1 2 3 1 1.00000 0.00000 1.00000 2 0.00000 -0.295352E-01 0.994979 3 0.00000 -0.293869E-01 0.989982 4 0.00000 -0.292393E-01 0.985011 5 0.00000 -0.290925E-01 0.980065 6 0.00000 -0.289464E-01 0.975143 7 0.00000 -0.288011E-01 0.970247 8 0.00000 -0.286564E-01 0.965375 9 0.00000 -0.285125E-01 0.960527 10 0.00000 -0.283694E-01 0.955704 11 0.00000 -0.282269E-01 0.950905 12 0.00000 -0.280852E-01 0.946130 IRF row 2 1 2 3 1 0.00000 1.00000 1.00000 2 0.495245 0.00000 0.894129 3 0.442813 0.00000 0.799467 4 0.395932 0.00000 0.714826 5 0.354014 0.00000 0.639147 6 0.316534 0.00000 0.571480 7 0.283023 0.00000 0.510977 8 0.253059 0.00000 0.456879 9 0.226267 0.00000 0.408509 10 0.202312 0.00000 0.365260 11 0.180893 0.00000 0.326589 12 0.161742 0.00000 0.292013 Note: Model as estimated is in the form AR(0)=MA(0)=I and SIGMA-N not a diagonal matrix. Model can be written in form AR(0) NE I and MA(0) = I where SIGMA-U is a diagonal matrix. The former case being model A and the latter being model C on page 223 of Granger and Newbold (1977). Diagonal elements of diagonal matrix SIGMA-U 0.101260 0.263226 AR(0) Matrix 1 2 1 1.00000 2 -0.876871 1.00000 ******** Eigenvalues and Eigenvectors of S(J) ******** Eigenvalues Eigenvectors 0.7196E-01 0.9496 -0.3133 0.3704 0.3133 0.9496 Determinant of S(J) = 0.2665E-01, 1/condition = 0.17399669 leading to a value of the test statistic M = -W*LN(U) = 1678.12 approximately distributed as a chi square with 4 DF and Prob.= 1.000 where U = Det(S(J))/Det(S(J-1)) S(J) = RESIDUAL COVARIANCE MATRIX AFTER JTH FIT W = (NOBE-MAXLAG-1)-J*K-.5, AND DF = K*K. Summaries or cross correlation matrices using +,-,., where + denotes a value greater that G/SQRT(NOBE) - denotes a value less than -G/SQRT(NOBE) . denotes a non-significant value based on the above criterion, where G = 2.000 . Behavior of values in (i,j)th position of cross correlation matrix over all outputted lags ++.----..+++ +++-----.+++ +.-----..+++ ++-----...++ Cross Correlation Matrices in terms of +, -, . Note: Series i is lagged for each term P(i,j) Lags 1 through 6 + + + + . + - - - - - - + + . + - - - - - - - - Lags 7 through 12 - - . - . . + + + + + + - - . . . . + . + + + + Summary Table for Residuals for equation 1 Mean= 0.40580566E-15 Variance= 0.10125979 Standard Deviation= 0.31821344 Skewness= -0.16287344 Kurtosis= 1.0833077 # of observations 290 Hinich bispectrum summary table. M G L BICOH Lamda 9 5.6378187 -5.6844630 1.8192455 0.10000000E-15 10 8.6719351 -5.1064401 2.1199151 0.10000000E-15 11 6.3080267 -3.8893807 1.9647418 0.10000000E-15 12 -0.11794981 -3.5917625 1.3992440 0.10000000E-15 13 0.30878470E-01 -2.2418684 1.4136774 0.10000000E-15 14 1.2867904 -3.0080459 1.5536548 0.10000000E-15 15 2.3601603 -2.2413931 1.6837908 0.10000000E-15 16 3.5231729 -2.4068903 1.8631483 0.10000000E-15 17 1.3362952 -1.5973267 1.5894978 0.10000000E-15 18 3.3145757 -1.2561860 1.8852464 0.10000000E-15 Mean for G = 3.2351704 Mean for L = -3.1023757 For the above table NWD = 53 WT = 16.101142 M = # of terms averaged to estimate bispectrum. G = (Z) statistic to test for Gaussianity. L = (Z) statistic to test for linearity. BICOH = average skewness (measure of nonlinear predictability). LAMDA = estimate of non-centrality. WT = whiteness statistic. Smoothing has not been done. MARTINGALE DIFFERENCE TEST FOR SERIES Residuals for equation 1 NO. OBERVATIONS INPUTTED= 290 DESCRIPTIVE STATISTICS OF DATA... MEAN = 0.40580566E-15 VARIANCE = 0.10161017 STANDARD DEVIATION = 0.31876351 SKEWNESS = -0.16203172 KURTOSIS = 1.0551956 SAMPLE 6TH ORDER CUMULANT= 5.8621113 MAX VALUE DATA= 1.3179440 MIN VALUE DATA= -1.1243395 V MART KERNEL FILTER WIDTH = 0.00% SQUARE ROOT OF NUMBER OF OBSERVATIONS= 17.029386 ********************************************************************* RUN # BLOCKSIZE # OBS. V INT. Z BEFORE FILTER D. F. 1 14 280 0 8.5394490 20 2 15 285 0 7.8388697 24 3 16 288 0 5.7288870 28 4 17 289 0 19.986598 32 5 18 288 0 14.165790 38 Residuals for equation 1 Dickey-Fuller Unit Root Test (I) Lag 0 t test -6.7660461 Prob of I(1) 0.1000 Aug. Dickey-Fuller Test (II) Lag 0 t test -6.7542038 Prob of I(1) 0.1000 Aug. Dickey-Fuller Test (II) Lag 0 t test -6.7542038 Prob of I(1) 0.1000 Summary Table for Residuals for equation 2 Mean= -0.98005895E-16 Variance= 0.34108456 Standard Deviation= 0.58402446 Skewness= 0.41646623 Kurtosis= 1.0903168 # of observations 290 Hinich bispectrum summary table. M G L BICOH Lamda 9 12.993987 -6.2922229 2.3501312 0.10000000E-15 10 9.6362424 -5.1675921 2.1986505 0.10000000E-15 11 7.0092545 -5.1037839 2.0262436 0.10000000E-15 12 4.4727622 -4.4146744 1.8494003 0.10000000E-15 13 3.5353043 -4.2677351 1.7713464 0.10000000E-15 14 2.9003404 -3.4630449 1.7340551 0.10000000E-15 15 3.2253993 -3.3204322 1.7843728 0.10000000E-15 16 4.4933993 -2.8216559 1.9884040 0.10000000E-15 17 4.5178306 -3.0596415 2.0224499 0.10000000E-15 18 9.1442596 -2.5379620 2.7266888 0.10000000E-15 Mean for G = 6.1928780 Mean for L = -4.0448745 For the above table NWD = 53 WT = 21.307388 M = # of terms averaged to estimate bispectrum. G = (Z) statistic to test for Gaussianity. L = (Z) statistic to test for linearity. BICOH = average skewness (measure of nonlinear predictability). LAMDA = estimate of non-centrality. WT = whiteness statistic. Smoothing has not been done. MARTINGALE DIFFERENCE TEST FOR SERIES Residuals for equation 2 NO. OBERVATIONS INPUTTED= 290 DESCRIPTIVE STATISTICS OF DATA... MEAN = -0.98005895E-16 VARIANCE = 0.34226479 STANDARD DEVIATION = 0.58503401 SKEWNESS = 0.41431395 KURTOSIS = 1.0621564 SAMPLE 6TH ORDER CUMULANT= 1.9192283 MAX VALUE DATA= 2.3688554 MIN VALUE DATA= -1.6843629 V MART KERNEL FILTER WIDTH = 0.00% SQUARE ROOT OF NUMBER OF OBSERVATIONS= 17.029386 ********************************************************************* RUN # BLOCKSIZE # OBS. V INT. Z BEFORE FILTER D. F. 1 14 280 0 19.609716 20 2 15 285 0 16.357100 24 3 16 288 0 21.736897 28 4 17 289 0 21.468963 32 5 18 288 0 20.019241 38 Residuals for equation 2 Dickey-Fuller Unit Root Test (I) Lag 0 t test -6.5303210 Prob of I(1) 0.1000 Aug. Dickey-Fuller Test (II) Lag 0 t test -6.5189811 Prob of I(1) 0.1000 Aug. Dickey-Fuller Test (II) Lag 0 t test -6.5189811 Prob of I(1) 0.1000 Multivariate Q Statistic Portmanteau statistic for multivariate time series Orig-Q => Ljung Box (1978) LM-Q => Li and McLeod (1981) LB-Q => Hosking (1980, 1981) Code developed by Tsay (1990) Changes 2001 by H. H. Stokes Suggested # of Lags = 5 m Orig-Q LM-Q LB-Q d.f. 1 317.8867 317.9005 318.9866 0 2 423.8276 423.8690 425.6632 4 3 455.3324 455.4151 457.4973 8 4 521.9216 522.0595 525.0179 12 5 642.4000 642.6069 647.6100 16 6 759.9977 760.2874 767.6921 20 7 813.8129 814.1991 822.8384 24 8 820.0876 820.5842 829.2911 28 9 829.6608 830.2815 839.1709 32 10 848.3666 849.1252 858.5448 36 11 873.7181 874.6285 884.8958 40 12 902.5190 903.5949 914.9399 44 Significance of Q statistics 1 1.0000 1.0000 1.0000 0 2 1.0000 1.0000 1.0000 4 3 1.0000 1.0000 1.0000 8 4 1.0000 1.0000 1.0000 12 5 1.0000 1.0000 1.0000 16 6 1.0000 1.0000 1.0000 20 7 1.0000 1.0000 1.0000 24 8 1.0000 1.0000 1.0000 28 9 1.0000 1.0000 1.0000 32 10 1.0000 1.0000 1.0000 36 11 1.0000 1.0000 1.0000 40 12 1.0000 1.0000 1.0000 44 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 72 ************ P = 6, PS = 0, S = 0, J = 2, Lags: 1 2 ********** PHI( 1) ********** ******** Std. Errors ******** ** Significance ** 0.181E+01-0.754E-01 0.401E-01 0.219E-01 + - 0.234E+00 0.145E+01 0.548E-01 0.298E-01 + + ********** PHI( 2) ********** ******** Std. Errors ******** ** Significance ** -0.961E+00 0.462E-01 0.476E-01 0.194E-01 - + -0.642E+00-0.580E+00 0.650E-01 0.265E-01 - - ******** Residual Covariance Matrix S(J) ******** ******** Residual Correlation Matrix RS(J) ******** 0.365E-01 1.00 -0.379E-02 0.679E-01 -0.08 1.00 Sum of squared Residuals for Equations 1,...,k 1 10.57853145741411 2 19.69804368800116 Granger Test for Causality. F(i,j) tests whether jth series Granger causes ith series. Granger Causality F(i,j) 1 2 1 3469.85 16.5732 2 172.646 8221.29 Significance of F(i,j) 1 2 1 1.00000 1.00000 2 1.00000 1.00000 Impulse Response Functions calculated by normalizing by diagonal polynomial. For ith row, jth col is effect of jth variable on ith variable where all X variables are on the left. K + 1 col = 1 / diagonal polynomial IRF row 1 1 2 3 1 1.00000 0.00000 1.00000 2 0.00000 0.754224E-01 1.81276 3 0.00000 0.905470E-01 2.32550 4 0.00000 0.916885E-01 2.47421 5 0.00000 0.792290E-01 2.25126 6 0.00000 0.555463E-01 1.70424 7 0.00000 0.245840E-01 0.926800 8 0.00000 -0.879355E-02 0.429534E-01 9 0.00000 -0.395563E-01 -0.812431 10 0.00000 -0.632589E-01 -1.51401 11 0.00000 -0.766752E-01 -1.96410 12 0.00000 -0.782266E-01 -2.10608 IRF row 2 1 2 3 1 0.00000 1.00000 1.00000 2 -0.234066 0.00000 1.44657 3 0.303318 0.00000 1.51244 4 0.574555 0.00000 1.34868 5 0.655173 0.00000 1.07356 6 0.614444 0.00000 0.770591 7 0.508760 0.00000 0.491923 8 0.379507 0.00000 0.264570 9 0.253844 0.00000 0.973458E-01 10 0.147044 0.00000 -0.126635E-01 11 0.654513E-01 0.00000 -0.747902E-01 12 0.937703E-02 0.00000 -0.100843 Note: Model as estimated is in the form AR(0)=MA(0)=I and SIGMA-N not a diagonal matrix. Model can be written in form AR(0) NE I and MA(0) = I where SIGMA-U is a diagonal matrix. The former case being model A and the latter being model C on page 223 of Granger and Newbold (1977). Diagonal elements of diagonal matrix SIGMA-U 0.364777E-01 0.675297E-01 AR(0) Matrix 1 2 1 1.00000 2 0.104012 1.00000 ******** Eigenvalues and Eigenvectors of S(J) ******** Eigenvalues Eigenvectors 0.3603E-01 0.9930 0.1181 0.6838E-01 -0.1181 0.9930 Determinant of S(J) = 0.2463E-02, 1/condition = 0.56856620 leading to a value of the test statistic M = -W*LN(U) = 677.52 approximately distributed as a chi square with 4 DF and Prob.= 1.000 where U = Det(S(J))/Det(S(J-1)) S(J) = RESIDUAL COVARIANCE MATRIX AFTER JTH FIT W = (NOBE-MAXLAG-1)-J*K-.5, AND DF = K*K. Summaries or cross correlation matrices using +,-,., where + denotes a value greater that G/SQRT(NOBE) - denotes a value less than -G/SQRT(NOBE) . denotes a non-significant value based on the above criterion, where G = 2.000 . Behavior of values in (i,j)th position of cross correlation matrix over all outputted lags +..-.+...... .+..-..++... ............ ++...+...... Cross Correlation Matrices in terms of +, -, . Note: Series i is lagged for each term P(i,j) Lags 1 through 6 + . . + . . - . . - + . . + . + . . . . . . . + Lags 7 through 12 . . . + . + . . . . . . . . . . . . . . . . . . Summary Table for Residuals for equation 1 Mean= -0.10596887E-14 Variance= 0.36477695E-01 Standard Deviation= 0.19099135 Skewness= -0.40263584E-01 Kurtosis= 5.0656981 # of observations 290 Hinich bispectrum summary table. M G L BICOH Lamda 9 9.2939043 6.6932077 2.0831007 0.10000000E-15 10 10.503597 5.9797794 2.2694696 0.89737352 11 5.5136020 4.6273594 1.8950662 0.13291895 12 10.329714 7.4871185 2.4237217 0.33952651 13 4.4930323 4.6774571 1.8690941 0.58433422E-01 14 5.3402730 2.9532295 2.0068479 0.54838999 15 2.8140463 2.8285203 1.7365540 0.18991984 16 5.1667229 6.1937984 2.0753297 0.10000000E-15 17 7.1940719 0.20721094 2.3866402 2.8994501 18 5.8685652 1.7309678 2.2538830 1.8896483 Mean for G = 6.6517529 Mean for L = 4.3378649 For the above table NWD = 53 WT = -0.85008351 M = # of terms averaged to estimate bispectrum. G = (Z) statistic to test for Gaussianity. L = (Z) statistic to test for linearity. BICOH = average skewness (measure of nonlinear predictability). LAMDA = estimate of non-centrality. WT = whiteness statistic. Smoothing has not been done. MARTINGALE DIFFERENCE TEST FOR SERIES Residuals for equation 1 NO. OBERVATIONS INPUTTED= 290 DESCRIPTIVE STATISTICS OF DATA... MEAN = -0.10596887E-14 VARIANCE = 0.36603915E-01 STANDARD DEVIATION = 0.19132150 SKEWNESS = -0.40055504E-01 KURTOSIS = 5.0101685 SAMPLE 6TH ORDER CUMULANT= 63.217862 MAX VALUE DATA= 1.0047451 MIN VALUE DATA= -0.95039339 V MART KERNEL FILTER WIDTH = 0.00% SQUARE ROOT OF NUMBER OF OBSERVATIONS= 17.029386 ********************************************************************* RUN # BLOCKSIZE # OBS. V INT. Z BEFORE FILTER D. F. 1 14 280 0 -0.20257887E-01 20 2 15 285 0 0.46509947 24 3 16 288 0 0.38086087 28 4 17 289 0 4.2591473 32 5 18 288 0 2.0607596 38 Residuals for equation 1 Dickey-Fuller Unit Root Test (I) Lag 0 t test -14.986762 Prob of I(1) 0.1000 Aug. Dickey-Fuller Test (II) Lag 0 t test -14.960622 Prob of I(1) 0.1000 Aug. Dickey-Fuller Test (II) Lag 0 t test -14.960622 Prob of I(1) 0.1000 Summary Table for Residuals for equation 2 Mean= 0.12128229E-14 Variance= 0.67924289E-01 Standard Deviation= 0.26062289 Skewness= 1.2882228 Kurtosis= 5.9721027 # of observations 290 Hinich bispectrum summary table. M G L BICOH Lamda 9 15.490791 6.8572862 2.5303225 0.44086616 10 17.348915 15.532728 2.8283875 0.50564422 11 16.341254 12.208821 2.8447141 0.18639384 12 16.724638 10.379112 3.0507956 0.55988657 13 16.576061 10.178299 3.1023131 0.54476063 14 16.215509 10.640843 3.2227362 1.2233011 15 16.009026 6.2461154 3.2704392 1.7716860 16 16.508694 5.2684281 3.5395719 2.6101178 17 16.544751 6.0219179 3.6591066 3.3309168 18 16.995477 7.2553582 3.8599144 2.8276997 Mean for G = 16.475512 Mean for L = 9.0588909 For the above table NWD = 53 WT = 0.96405055E-01 M = # of terms averaged to estimate bispectrum. G = (Z) statistic to test for Gaussianity. L = (Z) statistic to test for linearity. BICOH = average skewness (measure of nonlinear predictability). LAMDA = estimate of non-centrality. WT = whiteness statistic. Smoothing has not been done. MARTINGALE DIFFERENCE TEST FOR SERIES Residuals for equation 2 NO. OBERVATIONS INPUTTED= 290 DESCRIPTIVE STATISTICS OF DATA... MEAN = 0.12128229E-14 VARIANCE = 0.68159321E-01 STANDARD DEVIATION = 0.26107340 SKEWNESS = 1.2815654 KURTOSIS = 5.9103328 SAMPLE 6TH ORDER CUMULANT= 90.748939 MAX VALUE DATA= 1.5800063 MIN VALUE DATA= -0.88384537 V MART KERNEL FILTER WIDTH = 0.00% SQUARE ROOT OF NUMBER OF OBSERVATIONS= 17.029386 ********************************************************************* RUN # BLOCKSIZE # OBS. V INT. Z BEFORE FILTER D. F. 1 14 280 0 24.899161 20 2 15 285 0 27.839753 24 3 16 288 0 29.854750 28 4 17 289 0 28.655091 32 5 18 288 0 29.907879 38 Residuals for equation 2 Dickey-Fuller Unit Root Test (I) Lag 0 t test -14.120861 Prob of I(1) 0.1000 Aug. Dickey-Fuller Test (II) Lag 0 t test -14.095592 Prob of I(1) 0.1000 Aug. Dickey-Fuller Test (II) Lag 0 t test -14.095592 Prob of I(1) 0.1000 Multivariate Q Statistic Portmanteau statistic for multivariate time series Orig-Q => Ljung Box (1978) LM-Q => Li and McLeod (1981) LB-Q => Hosking (1980, 1981) Code developed by Tsay (1990) Changes 2001 by H. H. Stokes Suggested # of Lags = 5 m Orig-Q LM-Q LB-Q d.f. 1 15.2504 15.2642 15.3032 0 2 30.2502 30.2916 30.4071 4 3 38.2715 38.3543 38.5123 8 4 45.3205 45.4584 45.6598 12 5 50.4624 50.6693 50.8920 16 6 69.5068 69.7964 70.3387 20 7 73.3156 73.7018 74.2418 24 8 78.5117 79.0083 79.5853 28 9 97.8841 98.5048 99.5781 32 10 101.4134 102.1720 103.2334 36 11 104.8291 105.7394 106.7838 40 12 112.1763 113.2522 114.4482 44 Significance of Q statistics 1 1.0000 1.0000 1.0000 0 2 1.0000 1.0000 1.0000 4 3 1.0000 1.0000 1.0000 8 4 1.0000 1.0000 1.0000 12 5 1.0000 1.0000 1.0000 16 6 1.0000 1.0000 1.0000 20 7 1.0000 1.0000 1.0000 24 8 1.0000 1.0000 1.0000 28 9 1.0000 1.0000 1.0000 32 10 1.0000 1.0000 1.0000 36 11 1.0000 1.0000 1.0000 40 12 1.0000 1.0000 1.0000 44 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 73 ************ P = 6, PS = 0, S = 0, J = 3, Lags: 1 2 3 ********** PHI( 1) ********** ******** Std. Errors ******** ** Significance ** 0.194E+01-0.549E-01 0.581E-01 0.429E-01 + . 0.105E+00 0.161E+01 0.770E-01 0.569E-01 . + ********** PHI( 2) ********** ******** Std. Errors ******** ** Significance ** -0.127E+01 0.609E-01 0.114E+00 0.654E-01 - . -0.319E+00-0.934E+00 0.151E+00 0.867E-01 - - ********** PHI( 3) ********** ******** Std. Errors ******** ** Significance ** 0.229E+00-0.225E-01 0.800E-01 0.313E-01 + . -0.197E+00 0.195E+00 0.106E+00 0.415E-01 . + ******** Residual Covariance Matrix S(J) ******** ******** Residual Correlation Matrix RS(J) ******** 0.354E-01 1.00 -0.223E-02 0.622E-01 -0.05 1.00 Sum of squared Residuals for Equations 1,...,k 1 10.25973296709942 2 18.03849855625813 Granger Test for Causality. F(i,j) tests whether jth series Granger causes ith series. Granger Causality F(i,j) 1 2 1 2171.39 1.46232 2 84.6386 3092.05 Significance of F(i,j) 1 2 1 1.00000 0.774968 2 1.00000 1.00000 Impulse Response Functions calculated by normalizing by diagonal polynomial. For ith row, jth col is effect of jth variable on ith variable where all X variables are on the left. K + 1 col = 1 / diagonal polynomial IRF row 1 1 2 3 1 1.00000 0.00000 1.00000 2 0.00000 0.548570E-01 1.93761 3 0.00000 0.453773E-01 2.48834 4 0.00000 0.409701E-01 2.59735 5 0.00000 0.344944E-01 2.32598 6 0.00000 0.253566E-01 1.78825 7 0.00000 0.148403E-01 1.11483 8 0.00000 0.454984E-02 0.428660 9 0.00000 -0.416732E-02 -0.171432 10 0.00000 -0.104375E-01 -0.619643 11 0.00000 -0.139065E-01 -0.885468 12 0.00000 -0.146855E-01 -0.970471 IRF row 2 1 2 3 1 0.00000 1.00000 1.00000 2 -0.104987 0.00000 1.61212 3 0.149799 0.00000 1.66458 4 0.536563 0.00000 1.37174 5 0.704616 0.00000 0.969721 6 0.663728 0.00000 0.605425 7 0.516027 0.00000 0.336804 8 0.348812 0.00000 0.165927 9 0.209291 0.00000 0.705743E-01 10 0.111872 0.00000 0.242584E-01 11 0.526534E-01 0.00000 0.544384E-02 12 0.210695E-01 0.00000 -0.160959E-03 Note: Model as estimated is in the form AR(0)=MA(0)=I and SIGMA-N not a diagonal matrix. Model can be written in form AR(0) NE I and MA(0) = I where SIGMA-U is a diagonal matrix. The former case being model A and the latter being model C on page 223 of Granger and Newbold (1977). Diagonal elements of diagonal matrix SIGMA-U 0.353784E-01 0.620616E-01 AR(0) Matrix 1 2 1 1.00000 2 0.629390E-01 1.00000 ******** Eigenvalues and Eigenvectors of S(J) ******** Eigenvalues Eigenvectors 0.3519E-01 0.9966 0.8217E-01 0.6239E-01 -0.8217E-01 0.9966 Determinant of S(J) = 0.2196E-02, 1/condition = 0.62481079 leading to a value of the test statistic M = -W*LN(U) = 32.50 approximately distributed as a chi square with 4 DF and Prob.= 1.000 where U = Det(S(J))/Det(S(J-1)) S(J) = RESIDUAL COVARIANCE MATRIX AFTER JTH FIT W = (NOBE-MAXLAG-1)-J*K-.5, AND DF = K*K. Summaries or cross correlation matrices using +,-,., where + denotes a value greater that G/SQRT(NOBE) - denotes a value less than -G/SQRT(NOBE) . denotes a non-significant value based on the above criterion, where G = 2.000 . Behavior of values in (i,j)th position of cross correlation matrix over all outputted lags ...-........ ........+... ............ .+...+...... Cross Correlation Matrices in terms of +, -, . Note: Series i is lagged for each term P(i,j) Lags 1 through 6 . . . . . . - . . . . . . . . + . . . . . . . + Lags 7 through 12 . . . . . + . . . . . . . . . . . . . . . . . . Summary Table for Residuals for equation 1 Mean= -0.58458985E-15 Variance= 0.35378390E-01 Standard Deviation= 0.18809144 Skewness= -0.75107962E-01 Kurtosis= 6.0280005 # of observations 290 Hinich bispectrum summary table. M G L BICOH Lamda 9 11.285354 6.1464855 2.2268212 0.38283329 10 11.761669 5.7327543 2.3721909 0.97858902 11 7.3914978 5.7482617 2.0597685 0.12466134 12 12.211114 5.2969562 2.6082082 0.85728571 13 5.7734448 4.2170019 1.9997756 0.12835876 14 7.0433545 1.9351558 2.1972582 0.67242935 15 4.0264279 1.8243463 1.8774904 0.63572331 16 6.2505948 8.3822587 2.2152570 0.10000000E-15 17 8.3913640 4.7925590 2.5495711 1.8177375 18 6.5342887 0.78797518 2.3499719 1.7053662 Mean for G = 8.0669110 Mean for L = 4.4863755 For the above table NWD = 53 WT = -1.2848669 M = # of terms averaged to estimate bispectrum. G = (Z) statistic to test for Gaussianity. L = (Z) statistic to test for linearity. BICOH = average skewness (measure of nonlinear predictability). LAMDA = estimate of non-centrality. WT = whiteness statistic. Smoothing has not been done. MARTINGALE DIFFERENCE TEST FOR SERIES Residuals for equation 1 NO. OBERVATIONS INPUTTED= 290 DESCRIPTIVE STATISTICS OF DATA... MEAN = -0.58458985E-15 VARIANCE = 0.35500806E-01 STANDARD DEVIATION = 0.18841658 SKEWNESS = -0.74719808E-01 KURTOSIS = 5.9658457 SAMPLE 6TH ORDER CUMULANT= 71.098868 MAX VALUE DATA= 0.97592415 MIN VALUE DATA= -0.94086045 V MART KERNEL FILTER WIDTH = 0.00% SQUARE ROOT OF NUMBER OF OBSERVATIONS= 17.029386 ********************************************************************* RUN # BLOCKSIZE # OBS. V INT. Z BEFORE FILTER D. F. 1 14 280 0 -1.3702977 20 2 15 285 0 -1.0678520 24 3 16 288 0 -0.99345803 28 4 17 289 0 1.9167421 32 5 18 288 0 0.20449808 38 Residuals for equation 1 Dickey-Fuller Unit Root Test (I) Lag 0 t test -17.133143 Prob of I(1) 0.1000 Aug. Dickey-Fuller Test (II) Lag 0 t test -17.103308 Prob of I(1) 0.1000 Aug. Dickey-Fuller Test (II) Lag 0 t test -17.103308 Prob of I(1) 0.1000 Summary Table for Residuals for equation 2 Mean= 0.49002947E-15 Variance= 0.62201719E-01 Standard Deviation= 0.24940272 Skewness= 1.3191721 Kurtosis= 5.8296766 # of observations 290 Hinich bispectrum summary table. M G L BICOH Lamda 9 13.446275 3.1159598 2.3827723 0.86468816 10 15.415749 4.0857344 2.6705452 1.5213616 11 14.723361 7.1275134 2.7028155 0.61283793E-01 12 16.075195 9.4065379 2.9871124 1.1329641 13 16.358520 10.140010 3.0801104 0.50105229 14 16.144130 3.2916513 3.2147559 1.8823016 15 16.455206 5.8614520 3.3223066 2.4850083 16 16.801945 4.5565668 3.5774305 2.9553781 17 16.308748 1.5189535 3.6269906 4.2705372 18 16.364142 2.5103080 3.7687890 5.1132630 Mean for G = 15.809327 Mean for L = 5.1614687 For the above table NWD = 53 WT = 0.38593784 M = # of terms averaged to estimate bispectrum. G = (Z) statistic to test for Gaussianity. L = (Z) statistic to test for linearity. BICOH = average skewness (measure of nonlinear predictability). LAMDA = estimate of non-centrality. WT = whiteness statistic. Smoothing has not been done. MARTINGALE DIFFERENCE TEST FOR SERIES Residuals for equation 2 NO. OBERVATIONS INPUTTED= 290 DESCRIPTIVE STATISTICS OF DATA... MEAN = 0.49002947E-15 VARIANCE = 0.62416950E-01 STANDARD DEVIATION = 0.24983384 SKEWNESS = 1.3123547 KURTOSIS = 5.7688873 SAMPLE 6TH ORDER CUMULANT= 94.329762 MAX VALUE DATA= 1.5227113 MIN VALUE DATA= -0.78902253 V MART KERNEL FILTER WIDTH = 0.00% SQUARE ROOT OF NUMBER OF OBSERVATIONS= 17.029386 ********************************************************************* RUN # BLOCKSIZE # OBS. V INT. Z BEFORE FILTER D. F. 1 14 280 0 10.773672 20 2 15 285 0 15.768618 24 3 16 288 0 15.117825 28 4 17 289 0 14.631708 32 5 18 288 0 15.095192 38 Residuals for equation 2 Dickey-Fuller Unit Root Test (I) Lag 0 t test -17.588707 Prob of I(1) 0.1000 Aug. Dickey-Fuller Test (II) Lag 0 t test -17.557561 Prob of I(1) 0.1000 Aug. Dickey-Fuller Test (II) Lag 0 t test -17.557561 Prob of I(1) 0.1000 Multivariate Q Statistic Portmanteau statistic for multivariate time series Orig-Q => Ljung Box (1978) LM-Q => Li and McLeod (1981) LB-Q => Hosking (1980, 1981) Code developed by Tsay (1990) Changes 2001 by H. H. Stokes Suggested # of Lags = 5 m Orig-Q LM-Q LB-Q d.f. 1 0.6437 0.6574 0.6459 0 2 19.0553 19.0967 19.1854 4 3 20.0570 20.1398 20.1976 8 4 26.5242 26.6621 26.7552 12 5 30.0729 30.2798 30.3662 16 6 40.4326 40.7223 40.9448 20 7 41.3783 41.7645 41.9139 24 8 43.8302 44.3267 44.4353 28 9 53.7040 54.3247 54.6253 32 10 54.7296 55.4882 55.6875 36 11 58.7025 59.6129 59.8171 40 12 64.4679 65.5437 65.8313 44 Significance of Q statistics 1 0.7819 0.7825 0.7851 0 2 0.9992 0.9993 0.9992 4 3 0.9899 0.9904 0.9902 8 4 0.9910 0.9916 0.9914 12 5 0.9824 0.9838 0.9834 16 6 0.9956 0.9962 0.9960 20 7 0.9849 0.9868 0.9863 24 8 0.9711 0.9749 0.9742 28 9 0.9905 0.9924 0.9918 32 10 0.9765 0.9808 0.9800 36 11 0.9716 0.9773 0.9763 40 12 0.9763 0.9819 0.9808 44 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 74 ************ P = 6, PS = 0, S = 0, J = 4, Lags: 1 2 3 4 ********** PHI( 1) ********** ******** Std. Errors ******** ** Significance ** 0.193E+01-0.545E-01 0.587E-01 0.446E-01 + . 0.840E-01 0.157E+01 0.752E-01 0.571E-01 . + ********** PHI( 2) ********** ******** Std. Errors ******** ** Significance ** -0.120E+01 0.977E-01 0.128E+00 0.831E-01 - . -0.142E+00-0.653E+00 0.164E+00 0.107E+00 . - ********** PHI( 3) ********** ******** Std. Errors ******** ** Significance ** 0.940E-01-0.689E-01 0.137E+00 0.771E-01 . . -0.554E+00-0.182E+00 0.175E+00 0.989E-01 - . ********** PHI( 4) ********** ******** Std. Errors ******** ** Significance ** 0.101E+00 0.175E-01 0.816E-01 0.324E-01 . . 0.284E+00 0.163E+00 0.105E+00 0.415E-01 + + ******** Residual Covariance Matrix S(J) ******** ******** Residual Correlation Matrix RS(J) ******** 0.352E-01 1.00 -0.305E-02 0.578E-01 -0.07 1.00 Sum of squared Residuals for Equations 1,...,k 1 10.19667592946189 2 16.76235733125049 Granger Test for Causality. F(i,j) tests whether jth series Granger causes ith series. Granger Causality F(i,j) 1 2 1 1624.42 0.439473 2 66.5088 1423.02 Significance of F(i,j) 1 2 1 1.00000 0.219960 2 1.00000 1.00000 Impulse Response Functions calculated by normalizing by diagonal polynomial. For ith row, jth col is effect of jth variable on ith variable where all X variables are on the left. K + 1 col = 1 / diagonal polynomial IRF row 1 1 2 3 1 1.00000 0.00000 1.00000 2 0.00000 0.545425E-01 1.92751 3 0.00000 0.747854E-02 2.51907 4 0.00000 0.180786E-01 2.64387 5 0.00000 0.135249E-01 2.36546 6 0.00000 0.106795E-01 1.82925 7 0.00000 0.686512E-02 1.20049 8 0.00000 0.356350E-02 0.616443 9 0.00000 0.103287E-02 0.164148 10 0.00000 -0.542854E-03 -0.122538 11 0.00000 -0.125035E-02 -0.252797 12 0.00000 -0.130208E-02 -0.262717 IRF row 2 1 2 3 1 0.00000 1.00000 1.00000 2 -0.840191E-01 0.00000 1.57231 3 0.982187E-02 0.00000 1.81948 4 0.624279 0.00000 1.65282 5 0.706430 0.00000 1.28850 6 0.687782 0.00000 0.872856 7 0.508477 0.00000 0.527704 8 0.323984 0.00000 0.295342 9 0.167717 0.00000 0.171407 10 0.719784E-01 0.00000 0.123157 11 0.277346E-01 0.00000 0.114136 12 0.189742E-01 0.00000 0.116079 Note: Model as estimated is in the form AR(0)=MA(0)=I and SIGMA-N not a diagonal matrix. Model can be written in form AR(0) NE I and MA(0) = I where SIGMA-U is a diagonal matrix. The former case being model A and the latter being model C on page 223 of Granger and Newbold (1977). Diagonal elements of diagonal matrix SIGMA-U 0.351610E-01 0.575369E-01 AR(0) Matrix 1 2 1 1.00000 2 0.866997E-01 1.00000 ******** Eigenvalues and Eigenvectors of S(J) ******** Eigenvalues Eigenvectors 0.3476E-01 0.9914 0.1311 0.5820E-01 -0.1311 0.9914 Determinant of S(J) = 0.2023E-02, 1/condition = 0.63792762 leading to a value of the test statistic M = -W*LN(U) = 22.96 approximately distributed as a chi square with 4 DF and Prob.= 0.9999 where U = Det(S(J))/Det(S(J-1)) S(J) = RESIDUAL COVARIANCE MATRIX AFTER JTH FIT W = (NOBE-MAXLAG-1)-J*K-.5, AND DF = K*K. Summaries or cross correlation matrices using +,-,., where + denotes a value greater that G/SQRT(NOBE) - denotes a value less than -G/SQRT(NOBE) . denotes a non-significant value based on the above criterion, where G = 2.000 . Behavior of values in (i,j)th position of cross correlation matrix over all outputted lags ...-........ ............ ............ .....+...... Cross Correlation Matrices in terms of +, -, . Note: Series i is lagged for each term P(i,j) Lags 1 through 6 . . . . . . - . . . . . . . . . . . . . . . . + Lags 7 through 12 . . . . . . . . . . . . . . . . . . . . . . . . Summary Table for Residuals for equation 1 Mean= 0.99537237E-17 Variance= 0.35160951E-01 Standard Deviation= 0.18751254 Skewness= -0.70332113E-02 Kurtosis= 5.9808299 # of observations 290 Hinich bispectrum summary table. M G L BICOH Lamda 9 10.625219 7.4565121 2.1791801 0.35569506E-02 10 11.106306 6.2545099 2.3186807 0.94583855 11 6.7779650 7.2367928 2.0059582 0.10000000E-15 12 11.897933 5.1248990 2.5774983 1.0612012 13 5.2200929 2.5795158 1.9432994 0.55869054 14 6.7049444 3.1547026 2.1594228 0.47343592 15 3.4529266 2.2978599 1.8108223 0.29902062 16 6.0109437 6.6550726 2.1843182 0.10952403 17 7.6319353 1.7242154 2.4462259 2.4185591 18 5.6713334 0.59952964 2.2254150 1.5196755 Mean for G = 7.5099600 Mean for L = 4.3083610 For the above table NWD = 53 WT = -1.2605314 M = # of terms averaged to estimate bispectrum. G = (Z) statistic to test for Gaussianity. L = (Z) statistic to test for linearity. BICOH = average skewness (measure of nonlinear predictability). LAMDA = estimate of non-centrality. WT = whiteness statistic. Smoothing has not been done. MARTINGALE DIFFERENCE TEST FOR SERIES Residuals for equation 1 NO. OBERVATIONS INPUTTED= 290 DESCRIPTIVE STATISTICS OF DATA... MEAN = 0.99537237E-17 VARIANCE = 0.35282616E-01 STANDARD DEVIATION = 0.18783667 SKEWNESS = -0.69968640E-02 KURTOSIS = 5.9190000 SAMPLE 6TH ORDER CUMULANT= 72.222214 MAX VALUE DATA= 0.98790193 MIN VALUE DATA= -0.92406643 V MART KERNEL FILTER WIDTH = 0.00% SQUARE ROOT OF NUMBER OF OBSERVATIONS= 17.029386 ********************************************************************* RUN # BLOCKSIZE # OBS. V INT. Z BEFORE FILTER D. F. 1 14 280 0 -1.0932512 20 2 15 285 0 -0.67969230 24 3 16 288 0 -0.80209483 28 4 17 289 0 2.0750672 32 5 18 288 0 0.58842078 38 Residuals for equation 1 Dickey-Fuller Unit Root Test (I) Lag 0 t test -17.048277 Prob of I(1) 0.1000 Aug. Dickey-Fuller Test (II) Lag 0 t test -17.018618 Prob of I(1) 0.1000 Aug. Dickey-Fuller Test (II) Lag 0 t test -17.018618 Prob of I(1) 0.1000 Summary Table for Residuals for equation 2 Mean= -0.39171731E-14 Variance= 0.57801232E-01 Standard Deviation= 0.24041887 Skewness= 1.2625622 Kurtosis= 6.2647435 # of observations 290 Hinich bispectrum summary table. M G L BICOH Lamda 9 14.011582 8.0607404 2.4235698 0.45596431 10 14.098664 6.7220116 2.5630057 1.1613860 11 12.794168 5.8342134 2.5336141 0.51898001 12 14.173097 7.9844028 2.8005964 1.2626569 13 14.128068 3.3971639 2.8524658 2.0656391 14 14.178719 4.0892129 2.9950162 1.9093880 15 14.099564 2.0715749 3.0484687 2.8865509 16 14.788484 5.4305575 3.3174938 2.2795306 17 14.579461 1.0704110 3.3916644 6.0261095 18 14.950589 2.9892028 3.5647603 5.3296902 Mean for G = 14.180240 Mean for L = 4.7649491 For the above table NWD = 53 WT = -0.60090510 M = # of terms averaged to estimate bispectrum. G = (Z) statistic to test for Gaussianity. L = (Z) statistic to test for linearity. BICOH = average skewness (measure of nonlinear predictability). LAMDA = estimate of non-centrality. WT = whiteness statistic. Smoothing has not been done. MARTINGALE DIFFERENCE TEST FOR SERIES Residuals for equation 2 NO. OBERVATIONS INPUTTED= 290 DESCRIPTIVE STATISTICS OF DATA... MEAN = -0.39171731E-14 VARIANCE = 0.58001236E-01 STANDARD DEVIATION = 0.24083446 SKEWNESS = 1.2560373 KURTOSIS = 6.2009589 SAMPLE 6TH ORDER CUMULANT= 124.61984 MAX VALUE DATA= 1.5203606 MIN VALUE DATA= -0.73894676 V MART KERNEL FILTER WIDTH = 0.00% SQUARE ROOT OF NUMBER OF OBSERVATIONS= 17.029386 ********************************************************************* RUN # BLOCKSIZE # OBS. V INT. Z BEFORE FILTER D. F. 1 14 280 0 11.935253 20 2 15 285 0 18.396633 24 3 16 288 0 17.829484 28 4 17 289 0 16.278290 32 5 18 288 0 17.494724 38 Residuals for equation 2 Dickey-Fuller Unit Root Test (I) Lag 0 t test -17.078700 Prob of I(1) 0.1000 Aug. Dickey-Fuller Test (II) Lag 0 t test -17.048592 Prob of I(1) 0.1000 Aug. Dickey-Fuller Test (II) Lag 0 t test -17.048592 Prob of I(1) 0.1000 Multivariate Q Statistic Portmanteau statistic for multivariate time series Orig-Q => Ljung Box (1978) LM-Q => Li and McLeod (1981) LB-Q => Hosking (1980, 1981) Code developed by Tsay (1990) Changes 2001 by H. H. Stokes Suggested # of Lags = 5 m Orig-Q LM-Q LB-Q d.f. 1 0.1305 0.1443 0.1309 0 2 0.4625 0.5039 0.4653 4 3 4.4490 4.5318 4.4935 8 4 9.2492 9.3871 9.3608 12 5 12.5032 12.7101 12.6719 16 6 22.0285 22.3181 22.3984 20 7 23.2300 23.6162 23.6296 24 8 24.0941 24.5906 24.5182 28 9 32.4754 33.0960 33.1679 32 10 34.2449 35.0035 35.0006 36 11 37.8441 38.7544 38.7418 40 12 43.5464 44.6223 44.6902 44 Significance of Q statistics 1 0.5504 0.5509 0.5637 0 2 0.0230 0.0232 0.0269 4 3 0.1855 0.1899 0.1938 8 4 0.3185 0.3282 0.3304 12 5 0.2913 0.3034 0.3062 16 6 0.6610 0.6807 0.6765 20 7 0.4937 0.5171 0.5163 24 8 0.3234 0.3461 0.3500 28 9 0.5567 0.5900 0.5866 32 10 0.4478 0.4840 0.4842 36 11 0.4323 0.4731 0.4737 40 12 0.5090 0.5573 0.5545 44 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 75 ************ P = 6, PS = 0, S = 0, J = 5, Lags: 1 2 3 4 5 ********** PHI( 1) ********** ******** Std. Errors ******** ** Significance ** 0.192E+01-0.649E-01 0.587E-01 0.461E-01 + . 0.743E-01 0.156E+01 0.749E-01 0.588E-01 . + ********** PHI( 2) ********** ******** Std. Errors ******** ** Significance ** -0.119E+01 0.117E+00 0.128E+00 0.845E-01 - . -0.146E+00-0.615E+00 0.163E+00 0.108E+00 . - ********** PHI( 3) ********** ******** Std. Errors ******** ** Significance ** 0.149E+00-0.532E-01 0.146E+00 0.882E-01 . . -0.416E+00-0.201E+00 0.186E+00 0.113E+00 - . ********** PHI( 4) ********** ******** Std. Errors ******** ** Significance ** -0.266E-01-0.118E-01 0.139E+00 0.775E-01 . . -0.605E-02 0.186E+00 0.177E+00 0.989E-01 . . ********** PHI( 5) ********** ******** Std. Errors ******** ** Significance ** 0.957E-01 0.108E-01 0.832E-01 0.332E-01 . . 0.213E+00-0.178E-01 0.106E+00 0.424E-01 + . ******** Residual Covariance Matrix S(J) ******** ******** Residual Correlation Matrix RS(J) ******** 0.350E-01 1.00 -0.338E-02 0.570E-01 -0.08 1.00 Sum of squared Residuals for Equations 1,...,k 1 10.14832401017147 2 16.51637053085889 Granger Test for Causality. F(i,j) tests whether jth series Granger causes ith series. Granger Causality F(i,j) 1 2 1 1292.73 0.434471 2 53.5684 793.180 Significance of F(i,j) 1 2 1 1.00000 0.175639 2 1.00000 1.00000 Impulse Response Functions calculated by normalizing by diagonal polynomial. For ith row, jth col is effect of jth variable on ith variable where all X variables are on the left. K + 1 col = 1 / diagonal polynomial IRF row 1 1 2 3 1 1.00000 0.00000 1.00000 2 0.00000 0.648590E-01 1.92169 3 0.00000 0.778042E-02 2.49927 4 0.00000 -0.928257E-02 2.65850 5 0.00000 -0.563150E-02 2.38628 6 0.00000 -0.111204E-01 1.83060 7 0.00000 -0.100383E-01 1.18430 8 0.00000 -0.586770E-02 0.615932 9 0.00000 -0.169441E-02 0.234541 10 0.00000 0.200402E-02 0.721700E-01 11 0.00000 0.419948E-02 0.944423E-01 12 0.00000 0.462044E-02 0.227324 IRF row 2 1 2 3 1 0.00000 1.00000 1.00000 2 -0.742627E-01 0.00000 1.56200 3 0.303508E-01 0.00000 1.82470 4 0.509271 0.00000 1.68844 5 0.797775 0.00000 1.38700 6 0.700425 0.00000 1.03392 7 0.507970 0.00000 0.734066 8 0.296458 0.00000 0.513446 9 0.149150 0.00000 0.370604 10 0.646044E-01 0.00000 0.283150 11 0.316017E-01 0.00000 0.229262 12 0.257489E-01 0.00000 0.191892 Note: Model as estimated is in the form AR(0)=MA(0)=I and SIGMA-N not a diagonal matrix. Model can be written in form AR(0) NE I and MA(0) = I where SIGMA-U is a diagonal matrix. The former case being model A and the latter being model C on page 223 of Granger and Newbold (1977). Diagonal elements of diagonal matrix SIGMA-U 0.349942E-01 0.566263E-01 AR(0) Matrix 1 2 1 1.00000 2 0.966244E-01 1.00000 ******** Eigenvalues and Eigenvectors of S(J) ******** Eigenvalues Eigenvectors 0.3449E-01 0.9889 0.1488 0.5746E-01 -0.1488 0.9889 Determinant of S(J) = 0.1982E-02, 1/condition = 0.63407779 leading to a value of the test statistic M = -W*LN(U) = 5.77 approximately distributed as a chi square with 4 DF and Prob.= 0.7828 where U = Det(S(J))/Det(S(J-1)) S(J) = RESIDUAL COVARIANCE MATRIX AFTER JTH FIT W = (NOBE-MAXLAG-1)-J*K-.5, AND DF = K*K. Summaries or cross correlation matrices using +,-,., where + denotes a value greater that G/SQRT(NOBE) - denotes a value less than -G/SQRT(NOBE) . denotes a non-significant value based on the above criterion, where G = 2.000 . Behavior of values in (i,j)th position of cross correlation matrix over all outputted lags ............ ............ ............ ............ Cross Correlation Matrices in terms of +, -, . Note: Series i is lagged for each term P(i,j) Lags 1 through 6 . . . . . . . . . . . . . . . . . . . . . . . . Lags 7 through 12 . . . . . . . . . . . . . . . . . . . . . . . . Summary Table for Residuals for equation 1 Mean= 0.38474970E-16 Variance= 0.34994221E-01 Standard Deviation= 0.18706742 Skewness= 0.26596297E-01 Kurtosis= 5.9130813 # of observations 290 Hinich bispectrum summary table. M G L BICOH Lamda 9 10.470124 7.1455308 2.1679870 0.10000000E-15 10 11.701270 5.5885615 2.3672593 1.3296498 11 6.4960123 7.5144922 1.9812293 0.10000000E-15 12 11.838611 2.3629202 2.5716812 1.3569405 13 5.9888097 2.6797143 2.0217562 0.83756765 14 6.4310256 2.2003149 2.1287977 0.72410087 15 3.7744119 2.7760148 1.8481942 0.46642720 16 6.1033480 5.9368570 2.1962475 0.22540836 17 7.8490054 1.2553633 2.4757654 2.3301346 18 6.0737172 0.62038914 2.2834942 1.6339613 Mean for G = 7.6726334 Mean for L = 3.8080158 For the above table NWD = 53 WT = -1.3715418 M = # of terms averaged to estimate bispectrum. G = (Z) statistic to test for Gaussianity. L = (Z) statistic to test for linearity. BICOH = average skewness (measure of nonlinear predictability). LAMDA = estimate of non-centrality. WT = whiteness statistic. Smoothing has not been done. MARTINGALE DIFFERENCE TEST FOR SERIES Residuals for equation 1 NO. OBERVATIONS INPUTTED= 290 DESCRIPTIVE STATISTICS OF DATA... MEAN = 0.38474970E-16 VARIANCE = 0.35115308E-01 STANDARD DEVIATION = 0.18739079 SKEWNESS = 0.26458848E-01 KURTOSIS = 5.8517178 SAMPLE 6TH ORDER CUMULANT= 71.823055 MAX VALUE DATA= 0.99056181 MIN VALUE DATA= -0.91275266 V MART KERNEL FILTER WIDTH = 0.00% SQUARE ROOT OF NUMBER OF OBSERVATIONS= 17.029386 ********************************************************************* RUN # BLOCKSIZE # OBS. V INT. Z BEFORE FILTER D. F. 1 14 280 0 -0.37449331 20 2 15 285 0 -0.13190622 24 3 16 288 0 -0.39004923 28 4 17 289 0 1.8935327 32 5 18 288 0 1.4637804 38 Residuals for equation 1 Dickey-Fuller Unit Root Test (I) Lag 0 t test -16.816959 Prob of I(1) 0.1000 Aug. Dickey-Fuller Test (II) Lag 0 t test -16.787721 Prob of I(1) 0.1000 Aug. Dickey-Fuller Test (II) Lag 0 t test -16.787721 Prob of I(1) 0.1000 Summary Table for Residuals for equation 2 Mean= -0.12465125E-14 Variance= 0.56953002E-01 Standard Deviation= 0.23864828 Skewness= 1.0857627 Kurtosis= 5.3945510 # of observations 290 Hinich bispectrum summary table. M G L BICOH Lamda 9 11.907715 7.9522754 2.2717362 0.45616713 10 12.159788 6.8242228 2.4046971 0.49830921 11 11.145006 6.3421448 2.3889730 0.10000000E-15 12 12.091241 5.5414195 2.5964537 1.2848320 13 12.007507 2.4629684 2.6360370 1.7959243 14 11.993044 2.1356491 2.7506503 1.8046430 15 12.034233 0.74514829 2.8083789 2.6622118 16 12.926483 3.8563511 3.0771105 2.4902202 17 12.666207 0.41498901 3.1313035 5.3069141 18 13.126325 2.3494823 3.3014503 3.9221212 Mean for G = 12.205755 Mean for L = 3.8624651 For the above table NWD = 53 WT = -0.47707574 M = # of terms averaged to estimate bispectrum. G = (Z) statistic to test for Gaussianity. L = (Z) statistic to test for linearity. BICOH = average skewness (measure of nonlinear predictability). LAMDA = estimate of non-centrality. WT = whiteness statistic. Smoothing has not been done. MARTINGALE DIFFERENCE TEST FOR SERIES Residuals for equation 2 NO. OBERVATIONS INPUTTED= 290 DESCRIPTIVE STATISTICS OF DATA... MEAN = -0.12465125E-14 VARIANCE = 0.57150071E-01 STANDARD DEVIATION = 0.23906081 SKEWNESS = 1.0801516 KURTOSIS = 5.3367574 SAMPLE 6TH ORDER CUMULANT= 87.160790 MAX VALUE DATA= 1.4364192 MIN VALUE DATA= -0.72412080 V MART KERNEL FILTER WIDTH = 0.00% SQUARE ROOT OF NUMBER OF OBSERVATIONS= 17.029386 ********************************************************************* RUN # BLOCKSIZE # OBS. V INT. Z BEFORE FILTER D. F. 1 14 280 0 13.400154 20 2 15 285 0 18.125456 24 3 16 288 0 18.076200 28 4 17 289 0 16.491432 32 5 18 288 0 17.605762 38 Residuals for equation 2 Dickey-Fuller Unit Root Test (I) Lag 0 t test -17.219001 Prob of I(1) 0.1000 Aug. Dickey-Fuller Test (II) Lag 0 t test -17.188777 Prob of I(1) 0.1000 Aug. Dickey-Fuller Test (II) Lag 0 t test -17.188777 Prob of I(1) 0.1000 Multivariate Q Statistic Portmanteau statistic for multivariate time series Orig-Q => Ljung Box (1978) LM-Q => Li and McLeod (1981) LB-Q => Hosking (1980, 1981) Code developed by Tsay (1990) Changes 2001 by H. H. Stokes Suggested # of Lags = 5 m Orig-Q LM-Q LB-Q d.f. 1 0.2381 0.2519 0.2389 0 2 0.3177 0.3591 0.3191 4 3 1.8611 1.9438 1.8786 8 4 7.4742 7.6122 7.5703 12 5 9.8791 10.0860 10.0174 16 6 17.6453 17.9350 17.9476 20 7 18.7191 19.1053 19.0480 24 8 19.6304 20.1270 19.9851 28 9 26.7760 27.3966 27.3595 32 10 28.2095 28.9681 28.8442 36 11 31.9451 32.8554 32.7271 40 12 36.6936 37.7695 37.6806 44 Significance of Q statistics 1 0.6331 0.6336 0.6412 0 2 0.0114 0.0115 0.0143 4 3 0.0150 0.0155 0.0173 8 4 0.1752 0.1823 0.1853 12 5 0.1271 0.1343 0.1379 16 6 0.3892 0.4091 0.4083 20 7 0.2332 0.2506 0.2537 24 8 0.1224 0.1350 0.1402 28 9 0.2717 0.2994 0.3012 32 10 0.1803 0.2042 0.2090 36 11 0.1858 0.2140 0.2188 40 12 0.2253 0.2621 0.2655 44 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 76 ************ P = 6, PS = 0, S = 0, J = 6, Lags: 1 2 3 4 5 6 ********** PHI( 1) ********** ******** Std. Errors ******** ** Significance ** 0.193E+01-0.508E-01 0.581E-01 0.457E-01 + . 0.632E-01 0.155E+01 0.743E-01 0.585E-01 . + ********** PHI( 2) ********** ******** Std. Errors ******** ** Significance ** -0.120E+01 0.999E-01 0.126E+00 0.843E-01 - . -0.133E+00-0.593E+00 0.161E+00 0.108E+00 . - ********** PHI( 3) ********** ******** Std. Errors ******** ** Significance ** 0.170E+00-0.796E-01 0.144E+00 0.881E-01 . . -0.441E+00-0.171E+00 0.184E+00 0.113E+00 - . ********** PHI( 4) ********** ******** Std. Errors ******** ** Significance ** -0.160E+00 0.269E-01 0.145E+00 0.877E-01 . . 0.152E+00 0.132E+00 0.186E+00 0.112E+00 . . ********** PHI( 5) ********** ******** Std. Errors ******** ** Significance ** 0.380E+00-0.414E-01 0.137E+00 0.771E-01 + . -0.120E+00 0.569E-01 0.175E+00 0.985E-01 . . ********** PHI( 6) ********** ******** Std. Errors ******** ** Significance ** -0.214E+00 0.305E-01 0.839E-01 0.328E-01 - . 0.249E+00-0.421E-01 0.107E+00 0.419E-01 + . ******** Residual Covariance Matrix S(J) ******** ******** Residual Correlation Matrix RS(J) ******** 0.341E-01 1.00 -0.229E-02 0.557E-01 -0.05 1.00 Sum of squared Residuals for Equations 1,...,k 1 9.884741203642838 2 16.13858295915805 Granger Test for Causality. F(i,j) tests whether jth series Granger causes ith series. Granger Causality F(i,j) 1 2 1 1098.53 0.957770 2 46.1300 579.715 Significance of F(i,j) 1 2 1 1.00000 0.545745 2 1.00000 1.00000 Impulse Response Functions calculated by normalizing by diagonal polynomial. For ith row, jth col is effect of jth variable on ith variable where all X variables are on the left. K + 1 col = 1 / diagonal polynomial IRF row 1 1 2 3 1 1.00000 0.00000 1.00000 2 0.00000 0.507619E-01 1.93132 3 0.00000 -0.187043E-02 2.52554 4 0.00000 0.148459E-01 2.72111 5 0.00000 0.126884E-01 2.38095 6 0.00000 0.396154E-01 1.82027 7 0.00000 0.528172E-01 1.22555 8 0.00000 0.425095E-01 0.690156 9 0.00000 0.292170E-01 0.279198 10 0.00000 0.949464E-02 -0.518434E-01 11 0.00000 -0.575049E-02 -0.332278 12 0.00000 -0.127772E-01 -0.565442 IRF row 2 1 2 3 1 0.00000 1.00000 1.00000 2 -0.631609E-01 0.00000 1.54523 3 0.358598E-01 0.00000 1.79479 4 0.534097 0.00000 1.68609 5 0.662835 0.00000 1.40926 6 0.813415 0.00000 1.13231 7 0.524383 0.00000 0.909058 8 0.290011 0.00000 0.752503 9 0.114682 0.00000 0.637005 10 0.384554E-01 0.00000 0.541717 11 0.295984E-01 0.00000 0.456085 12 0.372991E-01 0.00000 0.378252 Note: Model as estimated is in the form AR(0)=MA(0)=I and SIGMA-N not a diagonal matrix. Model can be written in form AR(0) NE I and MA(0) = I where SIGMA-U is a diagonal matrix. The former case being model A and the latter being model C on page 223 of Granger and Newbold (1977). Diagonal elements of diagonal matrix SIGMA-U 0.340853E-01 0.554958E-01 AR(0) Matrix 1 2 1 1.00000 2 0.673241E-01 1.00000 ******** Eigenvalues and Eigenvectors of S(J) ******** Eigenvalues Eigenvectors 0.3384E-01 0.9945 0.1047 0.5589E-01 -0.1047 0.9945 Determinant of S(J) = 0.1892E-02, 1/condition = 0.65778949 leading to a value of the test statistic M = -W*LN(U) = 12.85 approximately distributed as a chi square with 4 DF and Prob.= 0.9880 where U = Det(S(J))/Det(S(J-1)) S(J) = RESIDUAL COVARIANCE MATRIX AFTER JTH FIT W = (NOBE-MAXLAG-1)-J*K-.5, AND DF = K*K. Summaries or cross correlation matrices using +,-,., where + denotes a value greater that G/SQRT(NOBE) - denotes a value less than -G/SQRT(NOBE) . denotes a non-significant value based on the above criterion, where G = 2.000 . Behavior of values in (i,j)th position of cross correlation matrix over all outputted lags ...........- ............ ............ ............ Cross Correlation Matrices in terms of +, -, . Note: Series i is lagged for each term P(i,j) Lags 1 through 6 . . . . . . . . . . . . . . . . . . . . . . . . Lags 7 through 12 . . . . . . . . . . - . . . . . . . . . . . . . Summary Table for Residuals for equation 1 Mean= -0.49845185E-15 Variance= 0.34085314E-01 Standard Deviation= 0.18462209 Skewness= 0.33264134E-01 Kurtosis= 6.4218618 # of observations 290 Hinich bispectrum summary table. M G L BICOH Lamda 9 10.861086 5.8015161 2.1962023 0.21326145 10 12.066392 6.2986760 2.3970713 1.4411906 11 7.0446751 6.7687435 2.0293502 0.35584957E-01 12 12.750474 3.0802342 2.6610967 1.4805421 13 5.9925537 2.6303578 2.0221384 0.67583871 14 7.5115334 1.4465441 2.2496022 1.8271821 15 4.9896172 4.0394176 1.9894589 0.26802819 16 6.4668424 3.4031905 2.2431744 0.26659665 17 7.6306709 1.1089245 2.4460538 3.1206068 18 6.4782033 0.60189777 2.3418767 2.0447888 Mean for G = 8.1792047 Mean for L = 3.5179502 For the above table NWD = 53 WT = -1.3462879 M = # of terms averaged to estimate bispectrum. G = (Z) statistic to test for Gaussianity. L = (Z) statistic to test for linearity. BICOH = average skewness (measure of nonlinear predictability). LAMDA = estimate of non-centrality. WT = whiteness statistic. Smoothing has not been done. MARTINGALE DIFFERENCE TEST FOR SERIES Residuals for equation 1 NO. OBERVATIONS INPUTTED= 290 DESCRIPTIVE STATISTICS OF DATA... MEAN = -0.49845185E-15 VARIANCE = 0.34203257E-01 STANDARD DEVIATION = 0.18494123 SKEWNESS = 0.33092227E-01 KURTOSIS = 6.3569955 SAMPLE 6TH ORDER CUMULANT= 84.592394 MAX VALUE DATA= 1.0162176 MIN VALUE DATA= -0.88510488 V MART KERNEL FILTER WIDTH = 0.00% SQUARE ROOT OF NUMBER OF OBSERVATIONS= 17.029386 ********************************************************************* RUN # BLOCKSIZE # OBS. V INT. Z BEFORE FILTER D. F. 1 14 280 0 -1.0435933 20 2 15 285 0 -0.13704353 24 3 16 288 0 -0.73503174 28 4 17 289 0 3.1272254 32 5 18 288 0 0.83853171 38 Residuals for equation 1 Dickey-Fuller Unit Root Test (I) Lag 0 t test -17.068445 Prob of I(1) 0.1000 Aug. Dickey-Fuller Test (II) Lag 0 t test -17.038711 Prob of I(1) 0.1000 Aug. Dickey-Fuller Test (II) Lag 0 t test -17.038711 Prob of I(1) 0.1000 Summary Table for Residuals for equation 2 Mean= -0.37058479E-14 Variance= 0.55650286E-01 Standard Deviation= 0.23590313 Skewness= 1.0691018 Kurtosis= 5.5911437 # of observations 290 Hinich bispectrum summary table. M G L BICOH Lamda 9 11.269996 5.5274579 2.2257128 0.83303883 10 11.857019 4.5153033 2.3799762 0.88937093 11 11.240068 5.2914109 2.3973104 0.10000000E-15 12 12.219749 6.2680417 2.6090549 1.0172540 13 11.185675 4.0006474 2.5521591 1.6430483 14 10.924630 8.4519938 2.6311980 0.66577286 15 11.448641 3.2659575 2.7403052 1.1481693 16 12.909613 3.4586397 3.0749325 1.9372543 17 12.047212 0.16760852 3.0470690 4.3164527 18 12.461484 4.2347046 3.2054889 2.7544375 Mean for G = 11.756409 Mean for L = 4.5181765 For the above table NWD = 53 WT = -0.66316780 M = # of terms averaged to estimate bispectrum. G = (Z) statistic to test for Gaussianity. L = (Z) statistic to test for linearity. BICOH = average skewness (measure of nonlinear predictability). LAMDA = estimate of non-centrality. WT = whiteness statistic. Smoothing has not been done. MARTINGALE DIFFERENCE TEST FOR SERIES Residuals for equation 2 NO. OBERVATIONS INPUTTED= 290 DESCRIPTIVE STATISTICS OF DATA... MEAN = -0.37058479E-14 VARIANCE = 0.55842848E-01 STANDARD DEVIATION = 0.23631091 SKEWNESS = 1.0635768 KURTOSIS = 5.5319966 SAMPLE 6TH ORDER CUMULANT= 95.026222 MAX VALUE DATA= 1.4308147 MIN VALUE DATA= -0.75269978 V MART KERNEL FILTER WIDTH = 0.00% SQUARE ROOT OF NUMBER OF OBSERVATIONS= 17.029386 ********************************************************************* RUN # BLOCKSIZE # OBS. V INT. Z BEFORE FILTER D. F. 1 14 280 0 15.453392 20 2 15 285 0 18.389763 24 3 16 288 0 18.541582 28 4 17 289 0 17.438970 32 5 18 288 0 18.329519 38 Residuals for equation 2 Dickey-Fuller Unit Root Test (I) Lag 0 t test -16.896437 Prob of I(1) 0.1000 Aug. Dickey-Fuller Test (II) Lag 0 t test -16.866902 Prob of I(1) 0.1000 Aug. Dickey-Fuller Test (II) Lag 0 t test -16.866902 Prob of I(1) 0.1000 Multivariate Q Statistic Portmanteau statistic for multivariate time series Orig-Q => Ljung Box (1978) LM-Q => Li and McLeod (1981) LB-Q => Hosking (1980, 1981) Code developed by Tsay (1990) Changes 2001 by H. H. Stokes Suggested # of Lags = 5 m Orig-Q LM-Q LB-Q d.f. 1 0.0311 0.0449 0.0312 0 2 0.1496 0.1910 0.1506 4 3 0.5289 0.6116 0.5337 8 4 0.7075 0.8454 0.7149 12 5 4.5606 4.7674 4.6355 16 6 7.5703 7.8599 7.7088 20 7 9.1289 9.5151 9.3060 24 8 10.1921 10.6886 10.3994 28 9 14.4391 15.0598 14.7824 32 10 17.1210 17.8796 17.5601 36 11 20.2584 21.1687 20.8212 40 12 28.0279 29.1038 28.9261 44 Significance of Q statistics 1 0.3883 0.3887 0.4251 0 2 0.0027 0.0027 0.0043 4 3 0.0002 0.0002 0.0003 8 4 0.0000 0.0000 0.0000 12 5 0.0025 0.0027 0.0032 16 6 0.0056 0.0064 0.0072 20 7 0.0027 0.0031 0.0037 24 8 0.0008 0.0010 0.0013 28 9 0.0032 0.0040 0.0048 32 10 0.0032 0.0042 0.0050 36 11 0.0040 0.0053 0.0063 40 12 0.0291 0.0387 0.0409 44 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 77 ********** Stepwise Autoregressive Summary ********** I I I I I Std. Partial I I Residual I Chi-Sq Prob Lag I AR Coefficients I Signif. I Variances I Test ------+-------------------------------------+-------------+-----------+----------------- 1 I 50.35 4.46 I + + I0.101E+00 I1678.12 1.0000 I -13.65 73.48 I - + I0.341E+00 I ------+-------------------------------------+-------------+-----------+----------------- 2 I -20.17 2.38 I - + I0.365E-01 I 677.52 1.0000 I -9.88 -21.90 I - - I0.679E-01 I ------+-------------------------------------+-------------+-----------+----------------- 3 I 2.86 -0.72 I + . I0.354E-01 I 32.50 1.0000 I -1.86 4.69 I . + I0.622E-01 I ------+-------------------------------------+-------------+-----------+----------------- 4 I 1.24 0.54 I . . I0.352E-01 I 22.96 0.9999 I 2.71 3.92 I + + I0.578E-01 I ------+-------------------------------------+-------------+-----------+----------------- 5 I 1.15 0.33 I . . I0.350E-01 I 5.77 0.7828 I 2.00 -0.42 I + . I0.570E-01 I ------+-------------------------------------+-------------+-----------+----------------- 6 I -2.55 0.93 I - . I0.341E-01 I 12.85 0.9880 I 2.32 -1.00 I + . I0.557E-01 I Note: Degrees of freedom for Chi-Square Stat = 4 Note: The partial autoregression coefficient matrix for lag L is the estimated PHI(L) from the fit where the maximum lag used is L (IE the last coefficient matrix). The elements are standardized by dividing each by its standard error. B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 78 *********Significance of Partial Autoregression coefficients by lag ********* I I LAG L: I Eqn Coeff. of I 1 2 3 4 5 6 ----------------------+------------------------------------------------------------------------------------- I W( 1,T) W( 1,T-L) I + - + . . - I W( 2,T-L) I + + . . . . I I W( 2,T) W( 1,T-L) I - - . + + + I W( 2,T-L) I + - + + . . I B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 79 Multivariate Time Series Modeling Option Selected Set up to run for 296 Observations Series # B34S Variable # Name 1 2 GASIN 2 3 GASOUT Of 6000000 space available 10277 used. Iterations terminated due to: Relative change in determinant of covariance matrix .LE. 0.100000E-02 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 80 Multivariate Time Series Estimation for: ESTIMATION RUN WITH GAS DATA Series 1: VAR= B-J GAS INPUT DATA Series 2: VAR= B-J GAS OUTPUT DATA Specified Model = ( 6, 0) Number of observations = 296 (Effective Number = NOBE = 290) ** Conditional Likelihood Method ** Forecasts Requested: 24 Forecasts, beginning at origin = 296 20 Forecasts, beginning at origin = 250 Final model summary with conditional likelihood parameter estimates Parameter Parameter Final Estimated Number Description Estimate Std. Error t Stat ---------- ----------------------------- ------------ ------------ ------------ 1 Constant( 1) -.412206E-02 0.111513E-01 -0.3696 2 Reg Autoregressive ( 1, 1, 1) 1.97812 0.551121E-01 35.8926 3 Reg Autoregressive ( 1, 2, 2) 1.61373 0.553515E-01 29.1541 4 Reg Autoregressive ( 2, 1, 1) -1.37899 0.998875E-01 -13.8054 5 Reg Autoregressive ( 2, 2, 2) -.592534 0.109950 -5.38915 6 Reg Autoregressive ( 3, 1, 1) 0.345227 0.551459E-01 6.26025 7 Reg Autoregressive ( 3, 2, 1) -.505993 0.764397E-01 -6.61951 8 Reg Autoregressive ( 3, 2, 2) -.144308 0.103224 -1.39800 9 Reg Autoregressive ( 4, 2, 1) 0.182199 0.168566 1.08088 10 Reg Autoregressive ( 4, 2, 2) 0.123219 0.446257E-01 2.76117 11 Reg Autoregressive ( 5, 2, 1) -.130505 0.179083 -.728738 12 Reg Autoregressive ( 6, 2, 1) 0.435631 0.989556E-01 4.40228 Error Covariance Matrix 1 2 1 0.359271E-01 2 -0.190652E-02 0.600987E-01 Error Correlation Matrix 1 2 1 1.00000 2 -0.410296E-01 1.00000 Note: Model as estimated is in the form AR(0)=MA(0)=I and SIGMA-N not a diagonal matrix. Model can be written in form AR(0) NE I and MA(0) = I where SIGMA-U is a diagonal matrix. The former case being model A and the latter being model C on page 223 of Granger and Newbold (1977). Diagonal elements of diagonal matrix SIGMA-U 0.359271E-01 0.599976E-01 AR(0) Matrix 1 2 1 1.00000 2 0.530664E-01 1.00000 Objective Function at final maximum likelihood parameter estimates = 580.00000 Correlation Matrix of the parameters ------------------------------------ 1 2 3 4 5 6 7 8 9 10 11 12 1 1.0 2 . 1.0 3 . . 1.0 4 . -.9 . 1.0 5 . . -.8 . 1.0 6 . .7 . -.9 . 1.0 7 . . . . . . 1.0 8 . . . . -.8 . . 1.0 9 . . . . . . -.8 . 1.0 10 . . . . .5 . . -.9 . 1.0 11 . . . . . . .5 . -.8 . 1.0 12 . . . . . . . . . . -.8 1.0 Diagnostic checks on residuals: Summary Statistics on Residual Series Series Mean Standard Deviation Mean / (Se Mean ) Sum of Squares 1 -0.34684267E-04 0.18954446 -0.31161649E-02 10.418860 2 0.10603100E-02 0.24514814 0.73655169E-01 17.428633 Summary Table for Residuals from equation 1 Mean= -0.34684267E-04 Variance= 0.35927101E-01 Standard Deviation= 0.18954446 Skewness= 0.13692810E-01 Kurtosis= 6.2798087 # of observations 290 Hinich bispectrum summary table. M G L BICOH Lamda 9 11.724259 7.6834322 2.2584965 0.97711168E-01 10 12.512273 5.8597281 2.4334773 0.77781889 11 8.5968790 7.1376873 2.1654875 0.10000000E-15 12 12.739837 7.0316958 2.6600537 0.80766853 13 6.9327889 2.7929748 2.1181007 0.50730348 14 8.0618061 1.3579967 2.3111245 0.79982835 15 4.9657368 1.9419400 1.9866829 0.70717138 16 6.9468800 8.2109590 2.3051470 0.10000000E-15 17 9.2883698 6.5610899 2.6716381 1.6486356 18 6.8950710 0.59467645 2.4020464 1.4915487 Mean for G = 8.8663900 Mean for L = 4.9172180 For the above table NWD = 53 WT = -1.2122907 M = # of terms averaged to estimate bispectrum. G = (Z) statistic to test for Gaussianity. L = (Z) statistic to test for linearity. BICOH = average skewness (measure of nonlinear predictability). LAMDA = estimate of non-centrality. WT = whiteness statistic. Smoothing has not been done. Summary Table for Residuals from equation 1 TABLE 1. SUMMARY STATISTICS FOR ISOSCELES TRIANGLE(IT) FRACTILES FOR LINEARITY TEST. LB G(IT) 0.10 0.25 0.50 0.75 0.80 0.90 0.93 0.95 0.97 0.99 14 1.6 0.22 -0.40 0.79 -0.38 -0.73 -0.40 -0.15E-01 -0.42 -1.1 -2.3 16 1.4 1.7 0.88 0.53 1.1 1.0 1.1 1.0 0.80 0.48 0.15 18 6.8 -1.0 -1.1 0.89 1.4 1.4 1.3 1.2 1.0 0.72 0.45 20 3.0 -0.69 -0.54 1.3 1.0 0.84 0.59 1.2 1.1 0.75 0.42 22 2.4 1.9 0.99 1.4 1.1 0.80 1.5 1.3 1.1 0.86 0.52 24 2.8 1.3 3.1 1.5 1.8 1.8 1.5 1.4 1.2 0.90 0.52 TABLE 2. SUMMARY STATISTICS FOR TRANSIENT TRIANGLE(OT) FRACTILES FOR LINEARITY TEST. LB G(OT) 0.10 0.25 0.50 0.75 0.80 0.90 0.93 0.95 0.97 0.99 WT 14 1.7 1.3 0.48 0.48 0.81 0.98 0.64 0.54 0.42 0.26 0.11 0.27 16 0.59E-01 0.44 -0.28 -0.60 0.28 0.52 0.40 0.24 0.33E-01 -0.31 -0.83 0.27 18 11. -0.88 -1.5 0.21 1.5 1.3 0.88 0.75 0.61 0.42 0.27 0.65 20 2.3 1.5 0.72 0.63 0.44 0.60 0.45 0.24 -0.35E-01 -0.50 -1.2 0.31 22 1.9 1.3 0.91 0.72 0.30 0.18 -0.25E-01 -0.24 -0.66 -1.4 -2.7 0.25 24 0.81 0.33 0.22 0.53 1.0 1.1 0.79 0.69 0.44 0.61E-01 -0.43 0.30 TABLE 3. SUMMARY STATISTICS FOR PRINCIPLE DOMAIN (PD) FRACTILES FOR LINEARITY TEST. LB G(PD) 0.10 0.25 0.50 0.75 0.80 0.90 0.93 0.95 0.97 0.99 14 2.3 0.97 -0.90E-01 0.95 0.82E-01 -0.26 0.77 0.73 0.61 0.22 -0.27 16 1.2 1.1 0.56 0.43 1.0 1.2 1.2 1.1 0.90 0.55 0.17 18 13. -1.5 -1.8 1.1 2.3 2.4 1.7 1.5 1.2 0.83 0.52 20 3.7 -0.33 0.57 1.3 0.37 0.22 0.60 0.95 0.94 0.79 0.37 22 3.0 2.1 1.5 1.7 1.3 1.3 1.4 1.2 1.0 0.97 0.59 24 2.8 1.1 0.93 1.7 2.0 2.1 1.7 1.4 1.2 0.98 0.59 FOR ABOVE TABLES LB = BLOCKSIZE G(IT) = TEST FOR GAUSIANITY FOR CONTINUOUS TIME FRACTILES = LINEARITY TEST G(OT) = TEST FOR ALIASING G(PD) = TEST FOR GAUSIANITY FOR DISCRETE TIME WT = WHITENESS TEST NOTE: IF ALIASING IS SUSPECTED, USE PD REGION MEAN G(IT) = 2.9850813 MEAN G(OT) = 3.0390790 MEAN G(PD) = 4.3645280 MARTINGALE DIFFERENCE TEST FOR SERIES Residuals from equation 1 NO. OBERVATIONS INPUTTED= 290 DESCRIPTIVE STATISTICS OF DATA... MEAN = -0.34684267E-04 VARIANCE = 0.36051416E-01 STANDARD DEVIATION = 0.18987210 SKEWNESS = 0.13622046E-01 KURTOSIS = 6.2159203 SAMPLE 6TH ORDER CUMULANT= 73.042521 MAX VALUE DATA= 0.98811605 MIN VALUE DATA= -0.91911937 V MART KERNEL FILTER WIDTH = 0.00% SQUARE ROOT OF NUMBER OF OBSERVATIONS= 17.029386 ********************************************************************* RUN # BLOCKSIZE # OBS. V INT. Z BEFORE FILTER D. F. 1 14 280 0 -1.9275108 20 Residuals from equation 1 Dickey-Fuller Unit Root Test (I) Lag 0 t test -17.749507 Prob of I(1) 0.1000 Aug. Dickey-Fuller Test (II) Lag 0 t test -17.718643 Prob of I(1) 0.1000 Aug. Dickey-Fuller Test (II) Lag 0 t test -17.718643 Prob of I(1) 0.1000 Summary Table for Residuals from equation 2 Mean= 0.10603100E-02 Variance= 0.60097611E-01 Standard Deviation= 0.24514814 Skewness= 0.60580097 Kurtosis= 5.4582855 # of observations 290 Hinich bispectrum summary table. M G L BICOH Lamda 9 10.459475 7.2245193 2.1672185 0.21261937 10 11.587147 8.1774414 2.3579412 0.38424644 11 11.640923 5.3769666 2.4324678 0.10000000E-15 12 12.311316 4.1908615 2.6180338 0.15328824 13 10.325536 4.8302715 2.4643715 1.6177320 14 9.7599381 4.8915378 2.5009815 0.23766453 15 9.5566073 4.8294051 2.5203608 0.10000000E-15 16 11.136366 5.0653014 2.8460073 0.58389543 17 10.224451 5.7793985 2.7990226 0.45404163 18 10.904541 1.0633526 2.9807636 1.3304750 Mean for G = 10.790630 Mean for L = 5.1429056 For the above table NWD = 53 WT = 0.85493017E-01 M = # of terms averaged to estimate bispectrum. G = (Z) statistic to test for Gaussianity. L = (Z) statistic to test for linearity. BICOH = average skewness (measure of nonlinear predictability). LAMDA = estimate of non-centrality. WT = whiteness statistic. Smoothing has not been done. Summary Table for Residuals from equation 2 TABLE 1. SUMMARY STATISTICS FOR ISOSCELES TRIANGLE(IT) FRACTILES FOR LINEARITY TEST. LB G(IT) 0.10 0.25 0.50 0.75 0.80 0.90 0.93 0.95 0.97 0.99 14 8.3 -0.98 -0.91 0.55 1.5 1.6 1.2 0.99 0.79 0.55 0.35 16 10. 0.54E-01 -0.48 0.59 0.78 0.91 1.3 1.1 0.92 0.64 0.40 18 9.1 -1.2 -2.0 0.69 1.7 1.5 0.86 0.86 0.98 0.72 0.45 20 7.4 1.1 1.6 1.2 2.1 2.4 1.6 1.4 1.1 0.80 0.50 22 11. -0.91 1.6 1.3 2.7 2.7 1.8 1.6 1.3 0.88 0.55 24 9.9 1.1 -0.43E-01 1.6 3.3 2.9 2.0 1.7 1.4 0.96 0.60 TABLE 2. SUMMARY STATISTICS FOR TRANSIENT TRIANGLE(OT) FRACTILES FOR LINEARITY TEST. LB G(OT) 0.10 0.25 0.50 0.75 0.80 0.90 0.93 0.95 0.97 0.99 WT 14 2.9 0.87 -0.83E-01 0.97E-01 0.81 0.82 0.42 0.29 0.12 -0.15 -0.54 0.29 16 0.52 -0.75 -1.3 0.24 0.92 0.77 0.34 0.18 -0.42E-01 -0.42 -0.99 0.14 18 2.2 0.99 1.3 0.63 1.0 0.84 0.38 0.18 -0.87E-01 -0.55 -1.3 0.40 20 0.77 0.58 1.4 0.68 0.61 0.57 0.58 0.39 0.15 -0.24 -0.81 0.24 22 0.80 0.33 0.45 0.83 0.18 0.50 0.48 0.31 0.99E-02 -0.49 -1.2 0.55 24 1.9 3.9 2.2 0.88 1.2 1.1 0.78 0.66 0.40 -0.17E-02 -0.52 0.69 TABLE 3. SUMMARY STATISTICS FOR PRINCIPLE DOMAIN (PD) FRACTILES FOR LINEARITY TEST. LB G(PD) 0.10 0.25 0.50 0.75 0.80 0.90 0.93 0.95 0.97 0.99 14 8.7 -0.97 -1.2 0.63 1.2 1.5 1.3 1.1 0.92 0.64 0.40 16 10. -1.3 0.23E-01 0.82 1.6 1.3 1.4 1.3 1.1 0.73 0.46 18 9.3 -0.63 -0.43 0.96 1.2 2.1 1.5 1.2 1.0 0.83 0.52 20 7.1 1.4 1.5 1.4 1.8 1.7 1.9 1.6 1.3 0.92 0.57 22 11. -0.99E-01 2.0 1.6 2.9 2.7 2.1 1.8 1.5 1.0 0.64 24 9.9 1.5 2.2 1.8 3.3 3.2 2.2 1.9 1.6 1.1 0.70 FOR ABOVE TABLES LB = BLOCKSIZE G(IT) = TEST FOR GAUSIANITY FOR CONTINUOUS TIME FRACTILES = LINEARITY TEST G(OT) = TEST FOR ALIASING G(PD) = TEST FOR GAUSIANITY FOR DISCRETE TIME WT = WHITENESS TEST NOTE: IF ALIASING IS SUSPECTED, USE PD REGION MEAN G(IT) = 9.4006781 MEAN G(OT) = 1.5252448 MEAN G(PD) = 9.3454642 MARTINGALE DIFFERENCE TEST FOR SERIES Residuals from equation 2 NO. OBERVATIONS INPUTTED= 290 DESCRIPTIVE STATISTICS OF DATA... MEAN = 0.10603100E-02 VARIANCE = 0.60305562E-01 STANDARD DEVIATION = 0.24557191 SKEWNESS = 0.60267022 KURTOSIS = 5.4000531 SAMPLE 6TH ORDER CUMULANT= 95.863091 MAX VALUE DATA= 1.4745658 MIN VALUE DATA= -0.91008601 V MART KERNEL FILTER WIDTH = 0.00% SQUARE ROOT OF NUMBER OF OBSERVATIONS= 17.029386 ********************************************************************* RUN # BLOCKSIZE # OBS. V INT. Z BEFORE FILTER D. F. 1 14 280 0 19.130931 20 Residuals from equation 2 Dickey-Fuller Unit Root Test (I) Lag 0 t test -16.845036 Prob of I(1) 0.1000 Aug. Dickey-Fuller Test (II) Lag 0 t test -16.816149 Prob of I(1) 0.1000 Aug. Dickey-Fuller Test (II) Lag 0 t test -16.816149 Prob of I(1) 0.1000 Multivariate Q Statistic Portmanteau statistic for multivariate time series Orig-Q => Ljung Box (1978) LM-Q => Li and McLeod (1981) LB-Q => Hosking (1980, 1981) Code developed by Tsay (1990) Changes 2001 by H. H. Stokes Suggested # of Lags = 5 m Orig-Q LM-Q LB-Q d.f. 1 1.9136 1.9274 1.9202 0 2 4.1171 4.1585 4.1391 4 3 7.5888 7.6715 7.6470 8 4 18.6452 18.7832 18.8581 12 5 24.7240 24.9309 25.0435 16 6 28.4052 28.6949 28.8025 20 7 28.9466 29.3328 29.3573 24 8 29.2957 29.7923 29.7163 28 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 81 9 33.1475 33.7682 33.6914 32 10 38.3061 39.0647 39.0343 36 11 46.4835 47.3938 47.5340 40 12 52.9258 54.0017 54.2545 44 13 56.1088 57.3640 57.5869 48 14 59.9571 61.4054 61.6303 52 15 66.7577 68.4128 68.8018 56 16 69.3530 71.2289 71.5488 60 17 73.4777 75.5881 75.9303 64 18 75.5350 77.8936 78.1237 68 19 88.4815 91.1022 91.9779 72 20 88.8816 91.7781 92.4076 76 21 89.9867 93.1729 93.5990 80 22 95.4574 98.9470 99.5188 84 23 99.7480 103.5549 104.1790 88 24 101.7395 105.8775 106.3502 92 Multivariate Q Statistic for squared series *** m Orig-Q LM-Q LB-Q d.f. 1 80.9111 80.9248 81.1910 0 2 83.2087 83.2500 83.5046 4 3 97.8152 97.8980 98.2638 8 4 121.2239 121.3619 121.9999 12 5 123.7926 123.9995 124.6136 16 6 124.6803 124.9700 125.5201 20 7 125.1925 125.5787 126.0450 24 8 126.0597 126.5562 126.9367 28 9 127.3884 128.0091 128.3080 32 10 127.9437 128.7024 128.8832 36 11 136.4181 137.3284 137.6917 40 12 176.0224 177.0983 179.0055 44 13 189.0917 190.3469 192.6882 48 14 189.6064 191.0547 193.2290 52 15 190.4718 192.1269 194.1416 56 16 192.8163 194.6922 196.6230 60 17 194.2332 196.3435 198.1281 64 18 196.5065 198.8651 200.5519 68 19 198.9812 201.6019 203.2001 72 20 201.1043 204.0009 205.4805 76 21 202.6609 205.8471 207.1586 80 22 209.0540 212.5437 214.0765 84 23 211.2877 215.0945 216.5025 88 24 213.7003 217.8383 219.1329 92 Significance of Q statistics 1 0.9275 0.9279 0.9283 0 2 0.6096 0.6125 0.6150 4 3 0.5254 0.5313 0.5338 8 4 0.9025 0.9080 0.9061 12 5 0.9252 0.9309 0.9289 16 6 0.8999 0.9083 0.9061 20 7 0.7779 0.7930 0.7921 24 8 0.6024 0.6231 0.6268 28 9 0.5890 0.6144 0.6180 32 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 82 10 0.6347 0.6650 0.6662 36 11 0.7772 0.8073 0.8035 40 12 0.8324 0.8617 0.8565 44 13 0.8030 0.8382 0.8332 48 14 0.7905 0.8305 0.8255 52 15 0.8461 0.8830 0.8766 56 16 0.8087 0.8539 0.8479 60 17 0.8045 0.8539 0.8476 64 18 0.7520 0.8120 0.8071 68 19 0.9092 0.9437 0.9363 72 20 0.8520 0.9031 0.8951 76 21 0.7915 0.8582 0.8512 80 22 0.8154 0.8813 0.8733 84 23 0.8157 0.8853 0.8769 88 24 0.7713 0.8546 0.8472 92 Significance of Q statistics for squared series 1 1.0000 1.0000 1.0000 0 2 1.0000 1.0000 1.0000 4 3 1.0000 1.0000 1.0000 8 4 1.0000 1.0000 1.0000 12 5 1.0000 1.0000 1.0000 16 6 1.0000 1.0000 1.0000 20 7 1.0000 1.0000 1.0000 24 8 1.0000 1.0000 1.0000 28 9 1.0000 1.0000 1.0000 32 10 1.0000 1.0000 1.0000 36 11 1.0000 1.0000 1.0000 40 12 1.0000 1.0000 1.0000 44 13 1.0000 1.0000 1.0000 48 14 1.0000 1.0000 1.0000 52 15 1.0000 1.0000 1.0000 56 16 1.0000 1.0000 1.0000 60 17 1.0000 1.0000 1.0000 64 18 1.0000 1.0000 1.0000 68 19 1.0000 1.0000 1.0000 72 20 1.0000 1.0000 1.0000 76 21 1.0000 1.0000 1.0000 80 22 1.0000 1.0000 1.0000 84 23 1.0000 1.0000 1.0000 88 24 1.0000 1.0000 1.0000 92 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 83 Sample correlation matrices for 24 Lags. Note: Series i is lagged for each term P(i,j). P(i,j) is is interpreted as the transpose of the way VAR(i,j) and VMA(i,j) terms are interpreted. *************** Lag = 1 *************** -0.0451 0.0572 -0.0359 0.0074 *************** Lag = 2 *************** 0.0686 0.0057 0.0315 -0.0421 *************** Lag = 3 *************** 0.0575 -0.0034 -0.0506 -0.0773 *************** Lag = 4 *************** -0.1446 -0.0015 -0.0028 -0.1301 *************** Lag = 5 *************** -0.0060 -0.0008 -0.0037 -0.1442 *************** Lag = 6 *************** 0.0621 0.0201 -0.0891 0.0314 *************** Lag = 7 *************** 0.0160 -0.0283 0.0185 -0.0214 *************** Lag = 8 *************** 0.0038 0.0030 -0.0283 -0.0186 *************** Lag = 9 *************** -0.0537 0.0381 0.0603 -0.0795 *************** Lag = 10 *************** 0.0359 -0.0673 0.0734 0.0804 *************** Lag = 11 *************** 0.1452 -0.0332 0.0124 0.0782 *************** Lag = 12 *************** -0.0828 0.0136 -0.0093 0.1226 *************** Lag = 13 *************** 0.0960 -0.0435 0.0065 -0.0073 *************** Lag = 14 *************** 0.0406 0.0842 -0.0001 0.0614 *************** Lag = 15 *************** -0.0826 0.1118 0.0095 -0.0741 *************** Lag = 16 *************** 0.0160 0.0819 -0.0371 -0.0251 *************** Lag = 17 *************** 0.0626 0.0568 -0.0177 -0.0825 *************** Lag = 18 *************** -0.0551 0.0472 0.0432 -0.0226 *************** Lag = 19 *************** -0.0800 -0.1135 0.0956 -0.1256 *************** Lag = 20 *************** 0.0218 -0.0003 -0.0287 -0.0101 *************** Lag = 21 *************** 0.0100 -0.0391 0.0460 0.0066 *************** Lag = 22 *************** 0.0304 -0.0570 -0.0772 0.1005 *************** Lag = 23 *************** 0.0394 0.0673 -0.0861 0.0371 *************** Lag = 24 *************** -0.0026 0.0332 -0.0755 0.0084 Summaries or cross correlation matrices using +,-,., where + denotes a value greater that G/SQRT(NOBE) - denotes a value less than -G/SQRT(NOBE) . denotes a non-significant value based on the above criterion, where G = 2.000 . Behavior of values in (i,j)th position of cross correlation matrix over all outputted lags ...-......+. ............ ............ ............ ............ ...--......+ ............ ......-..... Cross Correlation Matrices in terms of +, -, . Note: Series i is lagged for each term P(i,j) Lags 1 through 6 . . . . . . - . . . . . . . . . . . . - . - . . Lags 7 through 12 . . . . . . . . + . . . . . . . . . . . . . . + Lags 13 through 18 . . . . . . . . . . . . . . . . . . . . . . . . Lags 19 through 24 . . . . . . . . . . . . . - . . . . . . . . . . B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 84 24 Forecasts, beginning at origin = 296 ---------------------------------------- T K Forecast Standard Error Actual Value (if available) 297 1 -.265543 0.189544 2 56.9728 0.245150 298 1 -.230933 0.420128 2 57.1803 0.465406 299 1 -.185203 0.638116 2 57.5041 0.678077 300 1 -.143693 0.809736 2 57.8342 0.865913 301 1 -.112695 0.927916 2 58.0473 1.06770 302 1 -.928317E-01 1.00076 2 58.1233 1.36082 303 1 -.819554E-01 1.04155 2 58.0930 1.75973 304 1 -.771307E-01 1.06261 2 58.0102 2.19519 305 1 -.757279E-01 1.07284 2 57.9198 2.58779 306 1 -.758514E-01 1.07765 2 57.8489 2.89548 307 1 -.763645E-01 1.07992 2 57.8068 3.11421 308 1 -.767249E-01 1.08105 2 57.7910 3.26175 309 1 -.767728E-01 1.08165 2 57.7940 3.36145 310 1 -.765479E-01 1.08200 2 57.8077 3.43289 311 1 -.761612E-01 1.08222 2 57.8259 3.48902 312 1 -.757230E-01 1.08236 2 57.8446 3.53722 313 1 -.753118E-01 1.08245 2 57.8622 3.58131 314 1 -.749692E-01 1.08251 2 57.8783 3.62317 315 1 -.747073E-01 1.08255 2 57.8931 3.66367 316 1 -.745195E-01 1.08257 2 57.9072 3.70324 317 1 -.743912E-01 1.08259 2 57.9211 3.74205 318 1 -.743057E-01 1.08260 2 57.9349 3.78019 319 1 -.742489E-01 1.08260 2 57.9490 3.81772 320 1 -.742099E-01 1.08260 2 57.9633 3.85468 -- 24 Forecasts starting at origin = 296 for series 1 ... 2 297 -0.26554 56.973 298 -0.23093 57.180 299 -0.18520 57.504 300 -0.14369 57.834 301 -0.11270 58.047 302 -0.92832E-01 58.123 303 -0.81955E-01 58.093 304 -0.77131E-01 58.010 305 -0.75728E-01 57.920 306 -0.75851E-01 57.849 307 -0.76364E-01 57.807 308 -0.76725E-01 57.791 309 -0.76773E-01 57.794 310 -0.76548E-01 57.808 311 -0.76161E-01 57.826 312 -0.75723E-01 57.845 313 -0.75312E-01 57.862 314 -0.74969E-01 57.878 315 -0.74707E-01 57.893 316 -0.74520E-01 57.907 317 -0.74391E-01 57.921 318 -0.74306E-01 57.935 319 -0.74249E-01 57.949 320 -0.74210E-01 57.963 -- -- 24 Standard Errors starting at origin = 296 for series 1 ... 2 297 0.18954 0.24515 298 0.42013 0.46541 299 0.63812 0.67808 300 0.80974 0.86591 301 0.92792 1.0677 302 1.0008 1.3608 303 1.0416 1.7597 304 1.0626 2.1952 305 1.0728 2.5878 306 1.0776 2.8955 307 1.0799 3.1142 308 1.0810 3.2617 309 1.0816 3.3615 310 1.0820 3.4329 311 1.0822 3.4890 312 1.0824 3.5372 313 1.0825 3.5813 314 1.0825 3.6232 315 1.0826 3.6637 316 1.0826 3.7032 317 1.0826 3.7421 318 1.0826 3.7802 319 1.0826 3.8177 320 1.0826 3.8547 -- 20 Forecasts, beginning at origin = 250 ---------------------------------------- T K Forecast Standard Error Actual Value (if available) 251 1 0.348269E-01 0.189544 0.185000 2 56.2461 0.245150 56.3000 252 1 0.307051 0.420128 0.662000 2 56.1916 0.465406 56.4000 253 1 0.418870 0.638116 0.709000 2 55.9653 0.678077 56.4000 254 1 0.413054 0.809736 0.605000 2 55.3855 0.865913 56.0000 255 1 0.341331 0.927916 0.501000 2 54.5583 1.06770 55.2000 256 1 0.246079 1.00076 0.603000 2 53.7393 1.36082 54.0000 257 1 0.154555 1.04155 0.943000 2 53.1386 1.75973 53.0000 258 1 0.801032E-01 1.06261 1.22300 2 52.8418 2.19519 52.0000 259 1 0.261542E-01 1.07284 1.24900 2 52.8195 2.58779 51.6000 260 1 -.949083E-02 1.07765 0.824000 2 52.9811 2.89548 51.6000 261 1 -.313085E-01 1.07992 0.102000 2 53.2259 3.11421 51.1000 262 1 -.439370E-01 1.08105 0.250000E-01 2 53.4762 3.26175 50.4000 263 1 -.511369E-01 1.08165 0.382000 2 53.6869 3.36145 50.0000 264 1 -.554966E-01 1.08200 0.922000 2 53.8424 3.43289 50.0000 265 1 -.585518E-01 1.08222 1.03200 2 53.9461 3.48902 52.0000 266 1 -.610688E-01 1.08236 0.866000 2 54.0104 3.53722 54.0000 267 1 -.633399E-01 1.08245 0.527000 2 54.0492 3.58131 55.1000 268 1 -.654160E-01 1.08251 0.930000E-01 2 54.0742 3.62317 54.5000 269 1 -.672601E-01 1.08255 -.458000 2 54.0932 3.66367 52.8000 270 1 -.688290E-01 1.08257 -.748000 2 54.1105 3.70324 51.4000 -- 20 Forecasts starting at origin = 250 for series 1 ... 2 251 0.34827E-01 56.246 252 0.30705 56.192 253 0.41887 55.965 254 0.41305 55.386 255 0.34133 54.558 256 0.24608 53.739 257 0.15456 53.139 258 0.80103E-01 52.842 259 0.26154E-01 52.820 260 -0.94908E-02 52.981 261 -0.31309E-01 53.226 262 -0.43937E-01 53.476 263 -0.51137E-01 53.687 264 -0.55497E-01 53.842 265 -0.58552E-01 53.946 266 -0.61069E-01 54.010 267 -0.63340E-01 54.049 268 -0.65416E-01 54.074 269 -0.67260E-01 54.093 270 -0.68829E-01 54.110 -- -- 20 Standard Errors starting at origin = 250 for series 1 ... 2 251 0.18954 0.24515 252 0.42013 0.46541 253 0.63812 0.67808 254 0.80974 0.86591 255 0.92792 1.0677 256 1.0008 1.3608 257 1.0416 1.7597 258 1.0626 2.1952 259 1.0728 2.5878 260 1.0776 2.8955 261 1.0799 3.1142 262 1.0810 3.2617 263 1.0816 3.3615 264 1.0820 3.4329 265 1.0822 3.4890 266 1.0824 3.5372 267 1.0825 3.5813 268 1.0825 3.6232 269 1.0826 3.6637 270 1.0826 3.7032 -- -- 20 Actual values starting at origin = 250 for series 1 ... 2 251 0.18500 56.300 252 0.66200 56.400 253 0.70900 56.400 254 0.60500 56.000 255 0.50100 55.200 256 0.60300 54.000 257 0.94300 53.000 258 1.2230 52.000 259 1.2490 51.600 260 0.82400 51.600 261 0.10200 51.100 262 0.25000E-01 50.400 263 0.38200 50.000 264 0.92200 50.000 265 1.0320 52.000 266 0.86600 54.000 267 0.52700 55.100 268 0.93000E-01 54.500 269 -0.45800 52.800 270 -0.74800 51.400 -- B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 85 Multivariate Time Series Modeling Option Selected Set up to run for 296 Observations Series # B34S Variable # Name 1 2 GASIN 2 3 GASOUT Of 6000000 space available 11743 used. Iterations terminated due to: Relative change in determinant of covariance matrix .LE. 0.100000E-02 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 86 Multivariate Time Series Estimation for: TEST RUN OF VAR SEARCH Series 1: VAR= B-J GASIN SERIES Series 2: VAR= B-J GASOUT SERIES Specified Model = ( 3, 0) Number of observations = 296 (Effective Number = NOBE = 293) ** Conditional Likelihood Method ** Forecasts Requested: 20 Forecasts, beginning at origin = 250 Final model summary with conditional likelihood parameter estimates Parameter Parameter Final Estimated Number Description Estimate Std. Error t Stat ---------- ----------------------------- ------------ ------------ ------------ 1 Constant( 1) 0.876549 0.422173 2.076 2 Constant( 2) 6.81028 0.559699 12.17 3 Reg Autoregressive ( 1, 1, 1) 1.93703 0.578235E-01 33.4990 4 Reg Autoregressive ( 1, 1, 2) -.552135E-01 0.426871E-01 -1.29345 5 Reg Autoregressive ( 1, 2, 1) 0.105619 0.766600E-01 1.37776 6 Reg Autoregressive ( 1, 2, 2) 1.61217 0.565928E-01 28.4872 7 Reg Autoregressive ( 2, 1, 1) -1.26446 0.113426 -11.1479 8 Reg Autoregressive ( 2, 1, 2) 0.613733E-01 0.650718E-01 0.943162 9 Reg Autoregressive ( 2, 2, 1) -.321518 0.150375 -2.13811 10 Reg Autoregressive ( 2, 2, 2) -.934120 0.862695E-01 -10.8279 11 Reg Autoregressive ( 3, 1, 1) 0.227811 0.796081E-01 2.86166 12 Reg Autoregressive ( 3, 1, 2) -.226606E-01 0.311442E-01 -.727602 13 Reg Autoregressive ( 3, 2, 1) -.195031 0.105541 -1.84792 14 Reg Autoregressive ( 3, 2, 2) 0.194313 0.412897E-01 4.70610 Error Covariance Matrix 1 2 1 0.350664E-01 2 -0.223192E-02 0.616340E-01 Error Correlation Matrix 1 2 1 1.00000 2 -0.480091E-01 1.00000 Note: Model as estimated is in the form AR(0)=MA(0)=I and SIGMA-N not a diagonal matrix. Model can be written in form AR(0) NE I and MA(0) = I where SIGMA-U is a diagonal matrix. The former case being model A and the latter being model C on page 223 of Granger and Newbold (1977). Diagonal elements of diagonal matrix SIGMA-U 0.350664E-01 0.614919E-01 AR(0) Matrix 1 2 1 1.00000 2 0.636484E-01 1.00000 Objective Function at final maximum likelihood parameter estimates = 586.00000 Correlation Matrix of the parameters ------------------------------------ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 1.0 2 . 1.0 3 . . 1.0 4 -.7 . . 1.0 5 . . . . 1.0 6 . -.7 . . . 1.0 7 . . -.9 . . . 1.0 8 .5 . . -.9 . . . 1.0 9 . . . . -.9 . . . 1.0 10 . .5 . . . -.9 . . . 1.0 11 -.6 . .7 . . . -.9 . . . 1.0 12 . . . .7 . . . -.9 . . . 1.0 13 . -.6 . . .7 . . . -.9 . . . 1.0 14 . . . . . .7 . . . -.9 . . . 1.0 Diagnostic checks on residuals: Summary Statistics on Residual Series Series Mean Standard Deviation Mean / (Se Mean ) Sum of Squares 1 0.19985360E-08 0.18726033 0.18268379E-06 10.274464 2 -0.37860176E-08 0.24826195 -0.26103953E-06 18.058760 Multivariate Q Statistic Portmanteau statistic for multivariate time series Orig-Q => Ljung Box (1978) LM-Q => Li and McLeod (1981) LB-Q => Hosking (1980, 1981) Code developed by Tsay (1990) Changes 2001 by H. H. Stokes Suggested # of Lags = 5 m Orig-Q LM-Q LB-Q d.f. 1 0.6345 0.6482 0.6367 0 2 19.2421 19.2831 19.3722 4 3 20.2367 20.3186 20.3771 8 4 26.8612 26.9977 27.0932 12 5 30.3720 30.5768 30.6650 16 6 40.4703 40.7570 40.9744 20 7 41.4609 41.8432 41.9893 24 8 43.9853 44.4768 44.5845 28 9 53.7301 54.3444 54.6381 32 10 54.7749 55.5257 55.7198 36 11 58.6459 59.5469 59.7419 40 12 64.5319 65.5967 65.8792 44 13 69.4740 70.7163 71.0507 48 14 70.6052 72.0386 72.2387 52 15 78.5391 80.1773 80.6007 56 16 79.5874 81.4440 81.7095 60 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 87 17 83.5731 85.6618 85.9407 64 18 84.6665 87.0010 87.1057 68 19 98.7708 101.3647 102.1881 72 20 101.0748 103.9417 104.6609 76 21 103.5151 106.6687 107.2895 80 22 109.3530 112.8070 113.6014 84 23 109.8990 113.6669 114.1939 88 24 110.5827 114.6782 114.9386 92 Multivariate Q Statistic for squared series *** m Orig-Q LM-Q LB-Q d.f. 1 80.2046 80.2182 80.4793 0 2 90.3686 90.4095 90.7131 4 3 101.8835 101.9654 102.3472 8 4 105.9154 106.0519 106.4348 12 5 108.1797 108.3845 108.7385 16 6 109.0299 109.3166 109.6065 20 7 109.4339 109.8162 110.0203 24 8 110.3566 110.8481 110.9690 28 9 111.5911 112.2054 112.2425 32 10 112.8581 113.6090 113.5543 36 11 121.3481 122.2491 122.3755 40 12 163.0225 164.0874 165.8296 44 13 174.6595 175.9018 178.0069 48 14 176.4690 177.9025 179.9072 52 15 177.8231 179.4614 181.3344 56 16 180.2315 182.0882 183.8819 60 17 182.1587 184.2474 185.9277 64 18 184.1228 186.4573 188.0204 68 19 185.9091 188.5030 189.9306 72 20 187.7785 190.6454 191.9369 76 21 188.9935 192.1471 193.2457 80 22 196.4965 199.9504 201.3578 84 23 200.5443 204.3123 205.7505 88 24 202.7282 206.8238 208.1292 92 Significance of Q statistics 1 0.7798 0.7803 0.7830 0 2 0.9993 0.9993 0.9993 4 3 0.9905 0.9910 0.9908 8 4 0.9919 0.9925 0.9923 12 5 0.9838 0.9852 0.9848 16 6 0.9956 0.9962 0.9960 20 7 0.9852 0.9871 0.9866 24 8 0.9721 0.9757 0.9751 28 9 0.9906 0.9924 0.9919 32 10 0.9767 0.9810 0.9802 36 11 0.9713 0.9769 0.9760 40 12 0.9766 0.9821 0.9810 44 13 0.9770 0.9831 0.9819 48 14 0.9561 0.9669 0.9657 52 15 0.9749 0.9827 0.9813 56 16 0.9538 0.9673 0.9658 60 17 0.9492 0.9649 0.9633 64 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 88 18 0.9167 0.9409 0.9400 68 19 0.9801 0.9888 0.9871 72 20 0.9711 0.9836 0.9816 76 21 0.9603 0.9774 0.9751 80 22 0.9670 0.9826 0.9803 84 23 0.9430 0.9683 0.9658 88 24 0.9092 0.9470 0.9452 92 Significance of Q statistics for squared series 1 1.0000 1.0000 1.0000 0 2 1.0000 1.0000 1.0000 4 3 1.0000 1.0000 1.0000 8 4 1.0000 1.0000 1.0000 12 5 1.0000 1.0000 1.0000 16 6 1.0000 1.0000 1.0000 20 7 1.0000 1.0000 1.0000 24 8 1.0000 1.0000 1.0000 28 9 1.0000 1.0000 1.0000 32 10 1.0000 1.0000 1.0000 36 11 1.0000 1.0000 1.0000 40 12 1.0000 1.0000 1.0000 44 13 1.0000 1.0000 1.0000 48 14 1.0000 1.0000 1.0000 52 15 1.0000 1.0000 1.0000 56 16 1.0000 1.0000 1.0000 60 17 1.0000 1.0000 1.0000 64 18 1.0000 1.0000 1.0000 68 19 1.0000 1.0000 1.0000 72 20 1.0000 1.0000 1.0000 76 21 1.0000 1.0000 1.0000 80 22 1.0000 1.0000 1.0000 84 23 1.0000 1.0000 1.0000 88 24 1.0000 1.0000 1.0000 92 Summaries or cross correlation matrices using +,-,., where + denotes a value greater that G/SQRT(NOBE) - denotes a value less than -G/SQRT(NOBE) . denotes a non-significant value based on the above criterion, where G = 2.000 . Behavior of values in (i,j)th position of cross correlation matrix over all outputted lags ...-........ ........+... ............ ......-..... ............ .+...+...... ............ ..-...-..... Cross Correlation Matrices in terms of +, -, . Note: Series i is lagged for each term P(i,j) Lags 1 through 6 . . . . . . - . . . . . . . . + . . . . . . . + Lags 7 through 12 . . . . . + . . . . . . . . . . . . . . . . . . Lags 13 through 18 . . . . . . . . . . . . . . . . . - . . . . . . Lags 19 through 24 . - . . . . . . . . . . . - . . . . . . . . . . B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 89 -- 20 Forecasts starting at origin = 250 for series 1 ... 2 251 0.46775E-01 56.105 252 0.33912 55.955 253 0.46012 55.668 254 0.43881 55.120 255 0.32716 54.378 256 0.17927 53.609 257 0.38443E-01 52.981 258 -0.68445E-01 52.596 259 -0.13102 52.476 260 -0.15191 52.575 261 -0.14173 52.812 262 -0.11407 53.096 263 -0.81593E-01 53.357 264 -0.53654E-01 53.551 265 -0.35411E-01 53.662 266 -0.28148E-01 53.697 267 -0.30303E-01 53.677 268 -0.38765E-01 53.627 269 -0.50064E-01 53.571 270 -0.61237E-01 53.525 -- B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 90 Multivariate Time Series Modeling Option Selected Set up to run for 296 Observations Series # B34S Variable # Name 1 2 GASIN 2 3 GASOUT Of 6000000 space available 8318 used. Iterations terminated due to: Relative change in determinant of covariance matrix .LE. 0.100000E-02 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 91 Multivariate Time Series Estimation for: TEST RUN OF VAR SEARCH Series 1: VAR= B-J GASIN SERIES Series 2: VAR= B-J GASOUT SERIES Specified Model = ( 3, 0) Number of observations = 296 (Effective Number = NOBE = 293) ** Conditional Likelihood Method ** Forecasts Requested: 20 Forecasts, beginning at origin = 250 Final model summary with conditional likelihood parameter estimates Parameter Parameter Final Estimated Number Description Estimate Std. Error t Stat ---------- ----------------------------- ------------ ------------ ------------ 1 Constant( 1) -.384038E-02 0.110535E-01 -0.3474 2 Constant( 2) 5.94518 0.380405 15.63 3 Reg Autoregressive ( 1, 1, 1) 1.98656 0.548685E-01 36.2059 *Fixed* Reg Autoregressive ( 1, 1, 2) 0.00000 *Fixed* Reg Autoregressive ( 1, 2, 1) 0.00000 4 Reg Autoregressive ( 1, 2, 2) 1.68911 0.502133E-01 33.6386 5 Reg Autoregressive ( 2, 1, 1) -1.38275 0.994565E-01 -13.9031 *Fixed* Reg Autoregressive ( 2, 1, 2) 0.00000 6 Reg Autoregressive ( 2, 2, 1) -.356299 0.222312E-01 -16.0270 7 Reg Autoregressive ( 2, 2, 2) -.992535 0.850912E-01 -11.6644 8 Reg Autoregressive ( 3, 1, 1) 0.340787 0.549121E-01 6.20605 *Fixed* Reg Autoregressive ( 3, 1, 2) 0.00000 *Fixed* Reg Autoregressive ( 3, 2, 1) 0.00000 9 Reg Autoregressive ( 3, 2, 2) 0.192021 0.424552E-01 4.52292 Error Covariance Matrix 1 2 1 0.356312E-01 2 -0.204899E-02 0.662143E-01 Error Correlation Matrix 1 2 1 1.00000 2 -0.421842E-01 1.00000 Note: Model as estimated is in the form AR(0)=MA(0)=I and SIGMA-N not a diagonal matrix. Model can be written in form AR(0) NE I and MA(0) = I where SIGMA-U is a diagonal matrix. The former case being model A and the latter being model C on page 223 of Granger and Newbold (1977). Diagonal elements of diagonal matrix SIGMA-U 0.356312E-01 0.660965E-01 AR(0) Matrix 1 2 1 1.00000 2 0.575056E-01 1.00000 Objective Function at final maximum likelihood parameter estimates = 586.00000 Correlation Matrix of the parameters ------------------------------------ 1 2 3 4 5 6 7 8 9 1 1.0 2 . 1.0 3 . . 1.0 4 . -.6 . 1.0 5 . . -.9 . 1.0 6 . -.6 . .6 . 1.0 7 . .5 . -.9 . -.5 1.0 8 . . .7 . -.9 . . 1.0 9 . -.5 . .8 . . -.9 . 1.0 Diagnostic checks on residuals: Summary Statistics on Residual Series Series Mean Standard Deviation Mean / (Se Mean ) Sum of Squares 1 0.21380611E-04 0.18876234 0.19388249E-02 10.439948 2 -0.70453741E-03 0.25732050 -0.46866604E-01 19.400800 Multivariate Q Statistic Portmanteau statistic for multivariate time series Orig-Q => Ljung Box (1978) LM-Q => Li and McLeod (1981) LB-Q => Hosking (1980, 1981) Code developed by Tsay (1990) Changes 2001 by H. H. Stokes Suggested # of Lags = 5 m Orig-Q LM-Q LB-Q d.f. 1 4.8299 4.8435 4.8464 0 2 28.7712 28.8121 28.9522 4 3 33.7119 33.7938 33.9441 8 4 41.4603 41.5969 41.7998 12 5 48.4627 48.6675 48.9237 16 6 62.0756 62.3623 62.8212 20 7 64.2688 64.6510 65.0681 24 8 65.7758 66.2673 66.6174 28 9 73.4466 74.0610 74.5313 32 10 74.7022 75.4530 75.8312 36 11 81.4605 82.3616 82.8532 40 12 87.5942 88.6590 89.2487 44 13 93.5058 94.7481 95.4349 48 14 95.7273 97.1607 97.7678 52 15 101.5280 103.1663 103.8816 56 16 103.0927 104.9493 105.5366 60 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 92 17 108.0009 110.0897 110.7472 64 18 108.8852 111.2197 111.6893 68 19 124.8680 127.4618 128.7804 72 20 126.1981 129.0650 130.2079 76 21 129.5582 132.7118 133.8275 80 22 135.1426 138.5965 139.8652 84 23 136.1612 139.9291 140.9706 88 24 137.1266 141.2222 142.0221 92 Multivariate Q Statistic for squared series *** m Orig-Q LM-Q LB-Q d.f. 1 79.9525 79.9661 80.2263 0 2 83.2121 83.2530 83.5083 4 3 96.6122 96.6941 97.0471 8 4 102.3661 102.5026 102.8805 12 5 104.5425 104.7473 105.0948 16 6 105.3979 105.6845 105.9680 20 7 105.8314 106.2137 106.4122 24 8 106.5635 107.0549 107.1648 28 9 107.9456 108.5599 108.5907 32 10 109.6385 110.3893 110.3434 36 11 119.0172 119.9182 120.0880 40 12 159.8483 160.9132 162.6627 44 13 173.7979 175.0402 177.2600 48 14 175.3661 176.7995 178.9069 52 15 176.7810 178.4192 180.3981 56 16 179.0019 180.8585 182.7473 60 17 180.3843 182.4731 184.2149 64 18 182.0270 184.3615 185.9651 68 19 183.6286 186.2225 187.6778 72 20 185.4445 188.3114 189.6267 76 21 186.4731 189.6267 190.7347 80 22 193.1475 196.6014 197.9509 84 23 196.7769 200.5448 201.8895 88 24 198.5374 202.6330 203.8071 92 Significance of Q statistics 1 0.9898 0.9899 0.9898 0 2 1.0000 1.0000 1.0000 4 3 1.0000 1.0000 1.0000 8 4 1.0000 1.0000 1.0000 12 5 1.0000 1.0000 1.0000 16 6 1.0000 1.0000 1.0000 20 7 1.0000 1.0000 1.0000 24 8 0.9999 0.9999 0.9999 28 9 1.0000 1.0000 1.0000 32 10 0.9998 0.9999 0.9999 36 11 0.9999 0.9999 0.9999 40 12 0.9999 0.9999 0.9999 44 13 0.9999 0.9999 0.9999 48 14 0.9998 0.9999 0.9999 52 15 0.9998 0.9999 0.9999 56 16 0.9995 0.9997 0.9997 60 17 0.9995 0.9997 0.9997 64 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 93 18 0.9988 0.9993 0.9992 68 19 0.9999 1.0000 0.9999 72 20 0.9997 0.9999 0.9999 76 21 0.9996 0.9998 0.9998 80 22 0.9997 0.9999 0.9998 84 23 0.9992 0.9997 0.9996 88 24 0.9984 0.9994 0.9992 92 Significance of Q statistics for squared series 1 1.0000 1.0000 1.0000 0 2 1.0000 1.0000 1.0000 4 3 1.0000 1.0000 1.0000 8 4 1.0000 1.0000 1.0000 12 5 1.0000 1.0000 1.0000 16 6 1.0000 1.0000 1.0000 20 7 1.0000 1.0000 1.0000 24 8 1.0000 1.0000 1.0000 28 9 1.0000 1.0000 1.0000 32 10 1.0000 1.0000 1.0000 36 11 1.0000 1.0000 1.0000 40 12 1.0000 1.0000 1.0000 44 13 1.0000 1.0000 1.0000 48 14 1.0000 1.0000 1.0000 52 15 1.0000 1.0000 1.0000 56 16 1.0000 1.0000 1.0000 60 17 1.0000 1.0000 1.0000 64 18 1.0000 1.0000 1.0000 68 19 1.0000 1.0000 1.0000 72 20 1.0000 1.0000 1.0000 76 21 1.0000 1.0000 1.0000 80 22 1.0000 1.0000 1.0000 84 23 1.0000 1.0000 1.0000 88 24 1.0000 1.0000 1.0000 92 Summaries or cross correlation matrices using +,-,., where + denotes a value greater that G/SQRT(NOBE) - denotes a value less than -G/SQRT(NOBE) . denotes a non-significant value based on the above criterion, where G = 2.000 . Behavior of values in (i,j)th position of cross correlation matrix over all outputted lags ...-......+. .+..-....... ............ ......-..... ............ .+...+...... ............ ......-..... Cross Correlation Matrices in terms of +, -, . Note: Series i is lagged for each term P(i,j) Lags 1 through 6 . . . + . . - . . - . . . . . + . . . . . . . + Lags 7 through 12 . . . . . . . . + . . . . . . . . . . . . . . . Lags 13 through 18 . . . . . . . . . . . . . . . . . . . . . . . . Lags 19 through 24 . - . . . . . . . . . . . - . . . . . . . . . . B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 94 -- 20 Forecasts starting at origin = 250 for series 1 ... 2 251 0.40057E-01 55.970 252 0.32339 55.592 253 0.44860 55.110 254 0.45381 54.486 255 0.38758 53.795 256 0.29149 53.152 257 0.19394 52.655 258 0.11046 52.356 259 0.46755E-01 52.256 260 0.23985E-02 52.317 261 -0.26084E-01 52.485 262 -0.43041E-01 52.705 263 -0.52459E-01 52.932 264 -0.57427E-01 53.135 265 -0.60053E-01 53.298 266 -0.61609E-01 53.417 267 -0.62762E-01 53.497 268 -0.63796E-01 53.545 269 -0.64787E-01 53.571 270 -0.65717E-01 53.582 -- B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 95 Multivariate Time Series Modeling Option Selected Set up to run for 296 Observations Series # B34S Variable # Name 1 2 GASIN 2 3 GASOUT Of 6000000 space available 20686 used. Iterations terminated due to: Relative change in determinant of covariance matrix .LE. 0.100000E-02 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 96 Multivariate Time Series Estimation for: TEST RUN OF VAR SEARCH Series 1: VAR= B-J GASIN SERIES Series 2: VAR= B-J GASOUT SERIES Specified Model = ( 6, 0) Number of observations = 296 (Effective Number = NOBE = 290) ** Conditional Likelihood Method ** Forecasts Requested: 20 Forecasts, beginning at origin = 250 Final model summary with conditional likelihood parameter estimates Parameter Parameter Final Estimated Number Description Estimate Std. Error t Stat ---------- ----------------------------- ------------ ------------ ------------ 1 Constant( 1) 0.769975 0.654330 1.177 2 Constant( 2) 3.82413 0.836079 4.574 3 Reg Autoregressive ( 1, 1, 1) 1.93132 0.581228E-01 33.2283 4 Reg Autoregressive ( 1, 1, 2) -.507540E-01 0.457461E-01 -1.10947 5 Reg Autoregressive ( 1, 2, 1) 0.631609E-01 0.742671E-01 0.850456 6 Reg Autoregressive ( 1, 2, 2) 1.54521 0.584526E-01 26.4353 7 Reg Autoregressive ( 2, 1, 1) -1.20446 0.126132 -9.54924 8 Reg Autoregressive ( 2, 1, 2) 0.998882E-01 0.843268E-01 1.18454 9 Reg Autoregressive ( 2, 2, 1) -.133456 0.161167 -.828064 10 Reg Autoregressive ( 2, 2, 2) -.592904 0.107750 -5.50261 11 Reg Autoregressive ( 3, 1, 1) 0.169695 0.144328 1.17576 12 Reg Autoregressive ( 3, 1, 2) -.795802E-01 0.880994E-01 -.903300 13 Reg Autoregressive ( 3, 2, 1) -.441240 0.184417 -2.39262 14 Reg Autoregressive ( 3, 2, 2) -.171084 0.112570 -1.51980 15 Reg Autoregressive ( 4, 1, 1) -.160198 0.145492 -1.10108 16 Reg Autoregressive ( 4, 1, 2) 0.268440E-01 0.876971E-01 0.306100 17 Reg Autoregressive ( 4, 2, 1) 0.152006 0.185904 0.817660 18 Reg Autoregressive ( 4, 2, 2) 0.132393 0.112056 1.18149 19 Reg Autoregressive ( 5, 1, 1) 0.380197 0.137233 2.77045 20 Reg Autoregressive ( 5, 1, 2) -.414423E-01 0.771239E-01 -.537348 21 Reg Autoregressive ( 5, 2, 1) -.120360 0.175351 -.686393 22 Reg Autoregressive ( 5, 2, 2) 0.568732E-01 0.985460E-01 0.577124 23 Reg Autoregressive ( 6, 1, 1) -.213661 0.839373E-01 -2.54548 24 Reg Autoregressive ( 6, 1, 2) 0.305300E-01 0.328070E-01 0.930596 25 Reg Autoregressive ( 6, 2, 1) 0.249304 0.107252 2.32447 26 Reg Autoregressive ( 6, 2, 2) -.420879E-01 0.419195E-01 -1.00402 Error Covariance Matrix 1 2 1 0.340853E-01 2 -0.229476E-02 0.556503E-01 Error Correlation Matrix 1 2 1 1.00000 2 -0.526890E-01 1.00000 Note: Model as estimated is in the form AR(0)=MA(0)=I and SIGMA-N not a diagonal matrix. Model can be written in form AR(0) NE I and MA(0) = I where SIGMA-U is a diagonal matrix. The former case being model A and the latter being model C on page 223 of Granger and Newbold (1977). Diagonal elements of diagonal matrix SIGMA-U 0.340853E-01 0.554958E-01 AR(0) Matrix 1 2 1 1.00000 2 0.673241E-01 1.00000 Objective Function at final maximum likelihood parameter estimates = 580.00000 Correlation Matrix of the parameters ------------------------------------ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 1 1.0 2 . 1.0 3 . . 1.0 4 . . . 1.0 5 . . . . 1.0 6 . . . . . 1.0 7 . . -.8 . . . 1.0 8 . . . -.8 . . . 1.0 9 . . . . -.8 . . . 1.0 10 . . . . . -.8 . . . 1.0 11 . . . . . . -.7 . . . 1.0 12 . . . . . . . -.6 . . . 1.0 13 . . . . . . . . -.7 . . . 1.0 14 . . . . . . . . . -.6 . . . 1.0 15 . . . . . . . . . . -.6 . . . 1.0 16 . . . . . . . . . . . -.6 . . . 1.0 17 . . . . . . . . . . . . -.6 . . . 1.0 18 . . . . . . . . . . . . . -.6 . . . 1.0 19 . . . . . . . . . . . . . . -.7 . . . 1.0 20 . . . . . . . . . . . . . . . -.7 . . . 1.0 21 . . . . . . . . . . . . . . . . -.7 . . . 1.0 22 . . . . . . . . . . . . . . . . . -.7 . . . 1.0 23 . . . . . . . . . . . . . . . . . . -.8 . . . 1.0 24 . . . . . . . . . . . . . . . . . . . -.9 . . . 25 . . . . . . . . . . . . . . . . . . . . -.8 . . 26 . . . . . . . . . . . . . . . . . . . . . -.9 . 24 25 26 24 1.0 25 . 1.0 26 . . 1.0 Diagnostic checks on residuals: Summary Statistics on Residual Series Series Mean Standard Deviation Mean / (Se Mean ) Sum of Squares 1 0.60802408E-10 0.18462209 0.56083631E-08 9.8847412 2 -0.90979879E-10 0.23590313 -0.65676599E-08 16.138583 Multivariate Q Statistic Portmanteau statistic for multivariate time series Orig-Q => Ljung Box (1978) LM-Q => Li and McLeod (1981) LB-Q => Hosking (1980, 1981) Code developed by Tsay (1990) Changes 2001 by H. H. Stokes Suggested # of Lags = 5 m Orig-Q LM-Q LB-Q d.f. 1 0.0311 0.0449 0.0312 0 2 0.1495 0.1909 0.1504 4 3 0.5289 0.6116 0.5337 8 4 0.7075 0.8454 0.7149 12 5 4.5605 4.7674 4.6355 16 6 7.5701 7.8598 7.7087 20 7 9.1287 9.5149 9.3058 24 8 10.1919 10.6884 10.3992 28 9 14.4388 15.0595 14.7822 32 10 17.1207 17.8793 17.5598 36 11 20.2583 21.1686 20.8210 40 12 28.0277 29.1036 28.9259 44 13 30.5430 31.7981 31.5592 48 14 32.1204 33.5686 33.2166 52 15 37.3797 39.0349 38.7628 56 16 39.3735 41.2494 40.8730 60 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 97 17 44.2648 46.3751 46.0689 64 18 45.0223 47.3809 46.8765 68 19 60.0699 62.6906 62.9792 72 20 61.8005 64.6971 64.8380 76 21 63.1425 66.3287 66.2847 80 22 69.3508 72.8405 73.0027 84 23 70.8227 74.6296 74.6013 88 24 72.9728 77.1107 76.9454 92 Multivariate Q Statistic for squared series *** m Orig-Q LM-Q LB-Q d.f. 1 75.1830 75.1968 75.4431 0 2 77.3240 77.3654 77.5991 4 3 88.7718 88.8546 89.1665 8 4 98.8961 99.0341 99.4324 12 5 101.2265 101.4334 101.8037 16 6 102.0365 102.3262 102.6308 20 7 102.5815 102.9677 103.1893 24 8 103.8667 104.3632 104.5109 28 9 105.0214 105.6421 105.7026 32 10 105.7339 106.4925 106.4405 36 11 111.7685 112.6788 112.7131 40 12 153.5387 154.6146 156.2863 44 13 168.3509 169.6060 171.7936 48 14 169.3821 170.8304 172.8772 52 15 170.8902 172.5453 174.4675 56 16 172.1778 174.0536 175.8303 60 17 173.2739 175.3843 176.9947 64 18 175.1825 177.5412 179.0296 68 19 177.0289 179.6496 181.0055 72 20 178.9562 181.8527 183.0755 76 21 180.1498 183.3360 184.3622 80 22 188.8024 192.2921 193.7252 84 23 192.0869 195.8938 197.2926 88 24 193.8321 197.9700 199.1952 92 Significance of Q statistics 1 0.3883 0.3886 0.4250 0 2 0.0027 0.0027 0.0043 4 3 0.0002 0.0002 0.0003 8 4 0.0000 0.0000 0.0000 12 5 0.0025 0.0027 0.0032 16 6 0.0056 0.0064 0.0072 20 7 0.0027 0.0031 0.0037 24 8 0.0008 0.0010 0.0013 28 9 0.0032 0.0040 0.0048 32 10 0.0032 0.0042 0.0050 36 11 0.0040 0.0053 0.0063 40 12 0.0291 0.0387 0.0409 44 13 0.0233 0.0322 0.0346 48 14 0.0137 0.0197 0.0221 52 15 0.0262 0.0384 0.0412 56 16 0.0182 0.0278 0.0308 60 17 0.0284 0.0443 0.0476 64 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 98 18 0.0143 0.0237 0.0270 68 19 0.1588 0.2327 0.2247 72 20 0.1194 0.1842 0.1808 76 21 0.0828 0.1356 0.1365 80 22 0.1247 0.2013 0.1975 84 23 0.0902 0.1549 0.1554 88 24 0.0717 0.1298 0.1327 92 Significance of Q statistics for squared series 1 1.0000 1.0000 1.0000 0 2 1.0000 1.0000 1.0000 4 3 1.0000 1.0000 1.0000 8 4 1.0000 1.0000 1.0000 12 5 1.0000 1.0000 1.0000 16 6 1.0000 1.0000 1.0000 20 7 1.0000 1.0000 1.0000 24 8 1.0000 1.0000 1.0000 28 9 1.0000 1.0000 1.0000 32 10 1.0000 1.0000 1.0000 36 11 1.0000 1.0000 1.0000 40 12 1.0000 1.0000 1.0000 44 13 1.0000 1.0000 1.0000 48 14 1.0000 1.0000 1.0000 52 15 1.0000 1.0000 1.0000 56 16 1.0000 1.0000 1.0000 60 17 1.0000 1.0000 1.0000 64 18 1.0000 1.0000 1.0000 68 19 1.0000 1.0000 1.0000 72 20 1.0000 1.0000 1.0000 76 21 1.0000 1.0000 1.0000 80 22 1.0000 1.0000 1.0000 84 23 1.0000 1.0000 1.0000 88 24 1.0000 1.0000 1.0000 92 Summaries or cross correlation matrices using +,-,., where + denotes a value greater that G/SQRT(NOBE) - denotes a value less than -G/SQRT(NOBE) . denotes a non-significant value based on the above criterion, where G = 2.000 . Behavior of values in (i,j)th position of cross correlation matrix over all outputted lags ...........- ............ ............ ............ ............ ............ ............ ......-..... Cross Correlation Matrices in terms of +, -, . Note: Series i is lagged for each term P(i,j) Lags 1 through 6 . . . . . . . . . . . . . . . . . . . . . . . . Lags 7 through 12 . . . . . . . . . . - . . . . . . . . . . . . . Lags 13 through 18 . . . . . . . . . . . . . . . . . . . . . . . . Lags 19 through 24 . . . . . . . . . . . . . - . . . . . . . . . . B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 99 -- 20 Forecasts starting at origin = 250 for series 1 ... 2 251 0.67038E-01 56.229 252 0.36366 56.133 253 0.46301 55.873 254 0.40844 55.268 255 0.31028 54.390 256 0.21964 53.507 257 0.14883 52.858 258 0.93772E-01 52.544 259 0.46182E-01 52.518 260 0.13205E-01 52.652 261 0.32730E-02 52.834 262 0.14753E-01 53.002 263 0.36614E-01 53.134 264 0.52936E-01 53.228 265 0.52881E-01 53.283 266 0.35409E-01 53.300 267 0.68181E-02 53.287 268 -0.24040E-01 53.265 269 -0.50453E-01 53.255 270 -0.69565E-01 53.272 -- B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 100 Multivariate Time Series Modeling Option Selected Set up to run for 296 Observations Series # B34S Variable # Name 1 2 GASIN 2 3 GASOUT Of 6000000 space available 8990 used. Iterations terminated due to: Relative change in determinant of covariance matrix .LE. 0.100000E-02 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 101 Multivariate Time Series Estimation for: TEST RUN OF VAR SEARCH Series 1: VAR= B-J GASIN SERIES Series 2: VAR= B-J GASOUT SERIES Specified Model = ( 6, 0) Number of observations = 296 (Effective Number = NOBE = 290) ** Conditional Likelihood Method ** Forecasts Requested: 20 Forecasts, beginning at origin = 250 Final model summary with conditional likelihood parameter estimates Parameter Parameter Final Estimated Number Description Estimate Std. Error t Stat ---------- ----------------------------- ------------ ------------ ------------ 1 Constant( 1) -.395631E-02 0.110102E-01 -0.3593 2 Constant( 2) 4.26036 0.854058 4.988 3 Reg Autoregressive ( 1, 1, 1) 1.89486 0.449366E-01 42.1675 *Fixed* Reg Autoregressive ( 1, 1, 2) 0.00000 *Fixed* Reg Autoregressive ( 1, 2, 1) 0.00000 4 Reg Autoregressive ( 1, 2, 2) 1.44187 0.327376E-01 44.0432 5 Reg Autoregressive ( 2, 1, 1) -1.07647 0.568112E-01 -18.9482 *Fixed* Reg Autoregressive ( 2, 1, 2) 0.00000 *Fixed* Reg Autoregressive ( 2, 2, 1) 0.00000 6 Reg Autoregressive ( 2, 2, 2) -.521628 0.256114E-01 -20.3670 *Fixed* Reg Autoregressive ( 3, 1, 1) 0.00000 *Fixed* Reg Autoregressive ( 3, 1, 2) 0.00000 7 Reg Autoregressive ( 3, 2, 1) -.509098 0.257620E-01 -19.7616 *Fixed* Reg Autoregressive ( 3, 2, 2) 0.00000 *Fixed* Reg Autoregressive ( 4, 1, 1) 0.00000 *Fixed* Reg Autoregressive ( 4, 1, 2) 0.00000 *Fixed* Reg Autoregressive ( 4, 2, 1) 0.00000 *Fixed* Reg Autoregressive ( 4, 2, 2) 0.00000 8 Reg Autoregressive ( 5, 1, 1) 0.244103 0.568282E-01 4.29545 *Fixed* Reg Autoregressive ( 5, 1, 2) 0.00000 *Fixed* Reg Autoregressive ( 5, 2, 1) 0.00000 *Fixed* Reg Autoregressive ( 5, 2, 2) 0.00000 9 Reg Autoregressive ( 6, 1, 1) -.114646 0.449638E-01 -2.54975 *Fixed* Reg Autoregressive ( 6, 1, 2) 0.00000 10 Reg Autoregressive ( 6, 2, 1) 0.269226 0.440043E-01 6.11818 *Fixed* Reg Autoregressive ( 6, 2, 2) 0.00000 Error Covariance Matrix 1 2 1 0.349947E-01 2 -0.276053E-02 0.594018E-01 Error Correlation Matrix 1 2 1 1.00000 2 -0.605469E-01 1.00000 Note: Model as estimated is in the form AR(0)=MA(0)=I and SIGMA-N not a diagonal matrix. Model can be written in form AR(0) NE I and MA(0) = I where SIGMA-U is a diagonal matrix. The former case being model A and the latter being model C on page 223 of Granger and Newbold (1977). Diagonal elements of diagonal matrix SIGMA-U 0.349947E-01 0.591840E-01 AR(0) Matrix 1 2 1 1.00000 2 0.788843E-01 1.00000 Objective Function at final maximum likelihood parameter estimates = 580.00000 Correlation Matrix of the parameters ------------------------------------ 1 2 3 4 5 6 7 8 9 10 1 1.0 2 . 1.0 3 . . 1.0 4 . -.6 . 1.0 5 . . -.9 . 1.0 6 . . . -.8 . 1.0 7 . . . .7 . -.6 1.0 8 . . .5 . -.7 . . 1.0 9 . . . . .5 . . -.9 1.0 10 . -.8 . . . . . . . 1.0 Diagnostic checks on residuals: Summary Statistics on Residual Series Series Mean Standard Deviation Mean / (Se Mean ) Sum of Squares 1 0.54638588E-05 0.18706872 0.49739027E-03 10.148465 2 -0.12387628E-03 0.24372483 -0.86554045E-02 17.226524 Multivariate Q Statistic Portmanteau statistic for multivariate time series Orig-Q => Ljung Box (1978) LM-Q => Li and McLeod (1981) LB-Q => Hosking (1980, 1981) Code developed by Tsay (1990) Changes 2001 by H. H. Stokes Suggested # of Lags = 5 m Orig-Q LM-Q LB-Q d.f. 1 6.0927 6.1064 6.1137 0 2 9.2307 9.2721 9.2735 4 3 11.8308 11.9135 11.9008 8 4 16.4259 16.5638 16.5602 12 5 19.2295 19.4364 19.4130 16 6 25.1751 25.4647 25.4842 20 7 25.9898 26.3760 26.3190 24 8 28.6543 29.1509 29.0592 28 9 35.8071 36.4278 36.4410 32 10 38.2686 39.0272 38.9904 36 11 44.2648 45.1752 45.2231 40 12 49.7111 50.7870 50.9045 44 13 57.4686 58.7237 59.0260 48 14 58.9637 60.4119 60.5969 52 15 64.0980 65.7532 66.0113 56 16 65.1184 66.9942 67.0913 60 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 102 17 70.3892 72.4996 72.6903 64 18 71.7338 74.0924 74.1239 68 19 87.5426 90.1632 91.0410 72 20 89.2471 92.1436 92.8718 76 21 91.1985 94.3847 94.9755 80 22 96.8996 100.3892 101.1446 84 23 98.6011 102.4080 102.9928 88 24 99.2384 103.3763 103.6875 92 Multivariate Q Statistic for squared series *** m Orig-Q LM-Q LB-Q d.f. 1 85.6710 85.6848 85.9675 0 2 96.5020 96.5434 96.8737 4 3 113.9847 114.0674 114.5391 8 4 139.4363 139.5742 140.3467 12 5 146.3529 146.5598 147.3846 16 6 147.9973 148.2870 149.0638 20 7 148.5664 148.9526 149.6469 24 8 149.7038 150.2003 150.8166 28 9 150.7872 151.4079 151.9347 32 10 151.7209 152.4795 152.9017 36 11 155.7666 156.6769 157.1069 40 12 196.1601 197.2359 199.2440 44 13 211.6848 212.9400 215.4973 48 14 212.7194 214.1677 216.5844 52 15 214.2863 215.9414 218.2368 56 16 215.8753 217.7511 219.9185 60 17 217.3919 219.5022 221.5296 64 18 219.6741 222.0327 223.9628 68 19 222.0582 224.6789 226.5141 72 20 223.9418 226.8383 228.5372 76 21 226.2312 229.4174 231.0054 80 22 235.2456 238.7353 240.7598 84 23 240.7719 244.5788 246.7621 88 24 243.0896 247.2276 249.2890 92 Significance of Q statistics 1 0.9953 0.9953 0.9953 0 2 0.9444 0.9454 0.9454 4 3 0.8411 0.8443 0.8449 8 4 0.8275 0.8331 0.8332 12 5 0.7431 0.7522 0.7533 16 6 0.8052 0.8165 0.8158 20 7 0.6463 0.6628 0.6656 24 8 0.5698 0.5905 0.5951 28 9 0.7057 0.7304 0.7299 32 10 0.6331 0.6632 0.6647 36 11 0.7036 0.7370 0.7354 40 12 0.7437 0.7796 0.7763 44 13 0.8356 0.8678 0.8619 48 14 0.7640 0.8065 0.8020 52 15 0.7862 0.8307 0.8251 56 16 0.6967 0.7529 0.7503 60 17 0.7276 0.7865 0.7819 64 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 103 18 0.6449 0.7147 0.7139 68 19 0.8975 0.9357 0.9275 72 20 0.8580 0.9086 0.8998 76 21 0.8158 0.8789 0.8703 80 22 0.8413 0.9020 0.8928 84 23 0.7937 0.8690 0.8603 88 24 0.7154 0.8097 0.8038 92 Significance of Q statistics for squared series 1 1.0000 1.0000 1.0000 0 2 1.0000 1.0000 1.0000 4 3 1.0000 1.0000 1.0000 8 4 1.0000 1.0000 1.0000 12 5 1.0000 1.0000 1.0000 16 6 1.0000 1.0000 1.0000 20 7 1.0000 1.0000 1.0000 24 8 1.0000 1.0000 1.0000 28 9 1.0000 1.0000 1.0000 32 10 1.0000 1.0000 1.0000 36 11 1.0000 1.0000 1.0000 40 12 1.0000 1.0000 1.0000 44 13 1.0000 1.0000 1.0000 48 14 1.0000 1.0000 1.0000 52 15 1.0000 1.0000 1.0000 56 16 1.0000 1.0000 1.0000 60 17 1.0000 1.0000 1.0000 64 18 1.0000 1.0000 1.0000 68 19 1.0000 1.0000 1.0000 72 20 1.0000 1.0000 1.0000 76 21 1.0000 1.0000 1.0000 80 22 1.0000 1.0000 1.0000 84 23 1.0000 1.0000 1.0000 88 24 1.0000 1.0000 1.0000 92 Summaries or cross correlation matrices using +,-,., where + denotes a value greater that G/SQRT(NOBE) - denotes a value less than -G/SQRT(NOBE) . denotes a non-significant value based on the above criterion, where G = 2.000 . Behavior of values in (i,j)th position of cross correlation matrix over all outputted lags ..........+. ............ ............ -.....-..... ............ +........... ............ ......-..... Cross Correlation Matrices in terms of +, -, . Note: Series i is lagged for each term P(i,j) Lags 1 through 6 . . . . . . . . . . . . . + . . . . . . . . . . Lags 7 through 12 . . . . . . . . + . . . . . . . . . . . . . . . Lags 13 through 18 . - . . . . . . . . . . . . . . . . . . . . . . Lags 19 through 24 . - . . . . . . . . . . . - . . . . . . . . . . B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 104 -- 20 Forecasts starting at origin = 250 for series 1 ... 2 251 0.70408E-01 56.206 252 0.39848 56.094 253 0.52123 55.741 254 0.46967 55.034 255 0.32892 54.096 256 0.17620 53.181 257 0.65038E-01 52.502 258 0.11161E-01 52.161 259 0.20715E-02 52.133 260 0.14399E-01 52.314 261 0.26399E-01 52.579 262 0.26241E-01 52.830 263 0.12617E-01 53.018 264 -0.90693E-02 53.137 265 -0.31446E-01 53.208 266 -0.48987E-01 53.259 267 -0.59550E-01 53.310 268 -0.63991E-01 53.368 269 -0.64768E-01 53.430 270 -0.64434E-01 53.489 -- B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 105 Multivariate Time Series Modeling Option Selected Set up to run for 296 Observations Series # B34S Variable # Name 1 1 TIME 2 2 GASIN 3 3 GASOUT 4 4 CONSTANT MTSM Option Selected B34S variable X- 1 TIME Loaded on unit 11 B34S variable X- 2 GASIN Loaded on unit 11 B34S variable X- 3 GASOUT Loaded on unit 11 B34S variable X- 4 CONSTANT Loaded on unit 11 NOTE: ALL DATA LOADED IN UNFORMATED FORM MULTIPLE TIME SERIES MANIPULATOR Edition 8302 DATE 15/ 7/04 AT TIME 14:46: 5 Copyright (c) 1983 by John Geweke. All rights reserved. Program Modified Feb 1997 By Houston H. Stokes Storage Available in Real*8 = 6000000 Observations per year: 4 Maximum data range -- First observation (GIVE YEAR AND PERIOD) : 1900 1 Last observation (GIVE YEAR AND PERIOD) : 1973 4 Number of columns: 8 5996414 REAL*8 WORDS AVAILABLE FOR WORKSPACE. > SCAN UNFORMATED/FORMATED/FREE: UNFORMAT FILE UNIT # (ENTER 11 IF UNFORMATED FROM B34S): 11 Series Name Range Obs/Yr Mean Minimum Maximum 1 TIME 1900 1 1973 4 4 0.14850E+03 0.10000E+01 0.29600E+03 2 GASIN 1900 1 1973 4 4 -0.56834E-01 -0.27160E+01 0.28340E+01 3 GASOUT 1900 1 1973 4 4 0.53509E+02 0.45600E+02 0.60500E+02 4 CONSTANT 1900 1 1973 4 4 0.10000E+01 0.10000E+01 0.10000E+01 > READ UNFORMATED/FORMATED/FREE: UNFORMAT FILE UNIT # (ENTER 11 IF UNFORMATED FROM B34S): 11 Read from series number: 1 To column number: 1 Series TIME read from UNIT 11 Read from series number: 2 To column number: 2 Series GASIN read from UNIT 11 Read from series number: 3 To column number: 3 Series GASOUT read from UNIT 11 Read from series number: 4 To column number: 4 Series CONSTANT read from UNIT 11 Read from series number: > INFO 4 observations per year Maximum data range 1900 1 to 1973 4 ( 296 observations) Current range 1900 1 to 1973 4 ( 296 observations) 8 columns available for manipulations Variable Mean Stan. dev. Maximum Minimum #non-0 1 TIME 1.48500E+02 8.55921E+01 2.96000E+02 1.00000E+00 296 2 GASIN -5.68345E-02 1.07277E+00 2.83400E+00 -2.71600E+00 292 3 GASOUT 5.35091E+01 3.20212E+00 6.05000E+01 4.56000E+01 296 4 CONSTANT 1.00000E+00 0.00000E+00 1.00000E+00 1.00000E+00 296 > VAR ))Variables in autoregression: 2 3 ))Dummy variables -- NONE/CONSTANT/SEASONALS/USER: CONS ))Range of variables -- First observation (GIVE YEAR AND PERIOD) : 1900 1 Last observation (GIVE YEAR AND PERIOD) : 1973 4 ))Number of lags: 6 >> ESTI Estimation time 0.0000000 seconds >> COEF Equation 2 GASIN LAG 1 2 3 4 2 GASIN 1.93036E+00 -1.20856E+00 1.81816E-01 -1.35104E-01 3 GASOUT 1.33770E-03 9.31934E-03 -2.00587E-02 8.05871E-04 LAG 5 6 2 GASIN 3.55706E-01 -2.02320E-01 3 GASOUT -1.88518E-02 1.86976E-02 Equation 3 GASOUT LAG 1 2 3 4 2 GASIN 2.70203E-02 -6.77006E-03 -5.98449E-01 3.44618E-02 3 GASOUT 1.27395E+00 -2.79406E-01 -1.86669E-01 -5.98349E-03 LAG 5 6 2 GASIN -3.53191E-02 1.72608E-01 3 GASOUT 1.00323E-01 -2.91720E-02 >> VARM Equation Innovation variance Standard deviation 2 GASIN 3.42197E-02 1.84986E-01 3 GASOUT 9.52170E-02 3.08572E-01 Log[Det(Upsilon)] = -5.74104E+00 Scaled by T/2: -8.49673E+02 >> FEED Measures of feedback Variables in X vector: 2 Variables in Y vector: 3 X vector 2 GASIN Y vector 3 GASOUT Computation time 0.0000000 seconds F(X.Y) F(Y to X) F(X to Y) 0.014 ( 1.4%) 0.005 ( 0.5%) 0.668 (48.7%) PERIOD/FREQ: Frequencies: Frequency Periodicity f(Y to X) f(X to Y) 1.000pi 2.00 0.002 ( 0.2%) 0.009 ( 0.9%) 0.900pi 2.22 0.002 ( 0.2%) 0.010 ( 1.0%) 0.850pi 2.35 0.001 ( 0.1%) 0.012 ( 1.2%) 0.800pi 2.50 0.001 ( 0.1%) 0.012 ( 1.2%) 0.700pi 2.86 0.000 ( 0.0%) 0.010 ( 1.0%) 0.600pi 3.33 0.000 ( 0.0%) 0.010 ( 1.0%) 0.500pi 4.00 0.001 ( 0.1%) 0.027 ( 2.7%) 0.400pi 5.00 0.003 ( 0.3%) 0.119 (11.2%) 0.300pi 6.67 0.008 ( 0.8%) 0.696 (50.1%) 0.200pi 10.0 0.015 ( 1.5%) 1.899 (85.0%) 0.100pi 20.0 0.015 ( 1.4%) 3.174 (95.8%) 0.000pi 0.00 0.013 ( 1.3%) 1.805 (83.6%) Number of replications: 4 Replication 1 One replication time 0.0000000 seconds Replication 2 Replication 3 Replication 4 TOTAL TIME REQ. time 0.20028830E-01 seconds Estimate Mean 25.00% 75.00% Adjusted 25.000% 75.000% F(Y TO X) 0.01 0.03 0.01 0.05 0.00 0.00 0.01 F(X TO Y) 0.67 0.55 0.49 0.61 0.81 0.59 0.74 F(X.Y) 0.01 0.10 0.03 0.17 0.00 0.00 0.02 F(Y TO X) PERIOD Estimate Mean 25.00% 75.00% Adjusted 25.000% 75.000% 2.000 0.002 0.030 0.000 0.059 0.000 0.000 0.000 2.222 0.002 0.023 0.002 0.043 0.000 0.000 0.000 2.353 0.001 0.017 0.004 0.030 0.000 0.000 0.000 2.500 0.001 0.013 0.006 0.020 0.000 0.000 0.000 2.857 0.000 0.011 0.008 0.014 0.000 0.000 0.000 3.333 0.000 0.016 0.005 0.027 0.000 0.000 0.000 4.000 0.001 0.024 0.004 0.045 0.000 0.000 0.000 5.000 0.003 0.034 0.006 0.063 0.000 0.000 0.000 6.667 0.008 0.048 0.009 0.087 0.001 0.000 0.002 10.000 0.015 0.060 0.021 0.099 0.004 0.001 0.006 20.000 0.015 0.043 0.018 0.067 0.005 0.002 0.008 0.000 0.013 0.027 0.001 0.053 0.006 0.000 0.012 F(X TO Y) PERIOD Estimate Mean 25.00% 75.00% Adjusted 25.000% 75.000% 2.000 0.009 0.004 0.001 0.007 0.023 0.003 0.042 2.222 0.010 0.007 0.004 0.010 0.016 0.009 0.023 2.353 0.012 0.010 0.007 0.013 0.013 0.010 0.017 2.500 0.012 0.014 0.008 0.020 0.011 0.006 0.016 2.857 0.010 0.020 0.012 0.027 0.005 0.003 0.007 3.333 0.010 0.021 0.012 0.031 0.005 0.003 0.007 4.000 0.027 0.037 0.016 0.058 0.020 0.009 0.031 5.000 0.119 0.125 0.078 0.173 0.113 0.070 0.155 6.667 0.696 0.535 0.466 0.603 0.905 0.789 1.021 10.000 1.899 1.892 1.429 2.354 1.907 1.440 2.373 20.000 3.174 2.211 1.329 3.092 4.558 2.740 6.375 0.000 1.805 1.442 0.678 2.205 2.259 1.063 3.456 >> TABL Write table on UNIT: Table Number (UP TO 16 CHARACTERS): B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 BOX-TIAO STEP PAGE 106 TABLE TEST OF PROGRAM ESTIMATED MEASURES OF LINEAR Feedback QUARTERLY DATA 1900: 1 - 1973: 4 6 lags 296 observations Dummy variables: CONSTANT X vector: GASIN Y vector: GASOUT Estimate Adjusted Estimate 25.0% 75.0% F(Y to X) 0.005 ( 0.5%) 0.001 ( 0.1%) 0.000 0.001 F(X to Y) 0.668 (48.7%) 0.812 (55.6%) 0.719 0.904 F(X.Y) 0.014 ( 1.4%) 0.002 ( 0.2%) 0.001 0.004 f(Y to X) PERIOD ESTIMATE ADJUSTED ESTIMATE 25.0 % 75.0 % 2.000 0.002 ( 0.2%) 0.000 ( 0.0%) 0.000 0.000 2.222 0.002 ( 0.2%) 0.000 ( 0.0%) 0.000 0.000 2.353 0.001 ( 0.1%) 0.000 ( 0.0%) 0.000 0.000 2.500 0.001 ( 0.1%) 0.000 ( 0.0%) 0.000 0.000 2.857 0.000 ( 0.0%) 0.000 ( 0.0%) 0.000 0.000 3.333 0.000 ( 0.0%) 0.000 ( 0.0%) 0.000 0.000 4.000 0.001 ( 0.1%) 0.000 ( 0.0%) 0.000 0.000 5.000 0.003 ( 0.3%) 0.000 ( 0.0%) 0.000 0.000 6.667 0.008 ( 0.8%) 0.001 ( 0.1%) 0.000 0.002 10.000 0.015 ( 1.5%) 0.004 ( 0.4%) 0.001 0.006 20.000 0.015 ( 1.4%) 0.005 ( 0.5%) 0.002 0.008 Infinite 0.013 ( 1.3%) 0.006 ( 0.6%) 0.000 0.012 f(X to Y) PERIOD ESTIMATE ADJUSTED ESTIMATE 25.0 % 75.0 % 2.000 0.009 ( 0.9%) 0.023 ( 2.2%) 0.003 0.042 2.222 0.010 ( 1.0%) 0.016 ( 1.6%) 0.009 0.023 2.353 0.012 ( 1.2%) 0.013 ( 1.3%) 0.010 0.017 2.500 0.012 ( 1.2%) 0.011 ( 1.1%) 0.006 0.016 2.857 0.010 ( 1.0%) 0.005 ( 0.5%) 0.003 0.007 3.333 0.010 ( 1.0%) 0.005 ( 0.5%) 0.003 0.007 4.000 0.027 ( 2.7%) 0.020 ( 2.0%) 0.009 0.031 5.000 0.119 (11.2%) 0.113 (10.7%) 0.070 0.155 6.667 0.696 (50.1%) 0.905 (59.5%) 0.789 1.021 10.000 1.899 (85.0%) 1.907 (85.1%) 1.440 2.373 20.000 3.174 (95.8%) 4.558 (99.0%) 2.740 6.375 Infinite 1.805 (83.6%) 2.259 (89.6%) 1.063 3.456 4 replications >> TERM > TERM B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 STAT. PROC. STEP PAGE 107 Obs PERIOD FREQ SIN_1 SIN_2 COS_1 COS_2 P_1 P_2 S_1 S_2 1 296.0 0.3378E-02 0.4798 -1.714 0.1931 -0.2243 39.60 442.4 2.976 33.99 2 148.0 0.6757E-02 0.3560 -1.482 0.3565 -0.7423 37.56 406.7 2.675 30.88 3 98.67 0.1014E-01 -0.4462E-01 0.6334 -0.5042 1.783 37.92 529.8 2.235 26.01 4 74.00 0.1351E-01 -0.1421 0.6519 -0.2708 0.6703 13.84 129.4 1.714 19.35 5 59.20 0.1689E-01 -0.9377E-01 0.5667 -0.2222 0.4589 8.612 78.69 1.299 13.83 6 49.33 0.2027E-01 -0.6245E-01 -0.1568 0.2150 -0.3118 7.418 18.02 1.190 11.03 7 42.29 0.2365E-01 0.3529 -1.063 0.1057 0.7739 20.08 255.9 1.227 10.46 8 37.00 0.2703E-01 -0.2504 0.4674 -0.2797E-01 -0.3030 9.395 45.92 1.278 10.20 9 32.89 0.3041E-01 -0.3567 -0.4580 0.3711 -1.249 39.21 262.0 1.308 10.13 10 29.60 0.3378E-01 0.1291 0.5578E-01 -0.1646 0.7187 6.479 76.91 1.049 8.601 11 26.91 0.3716E-01 -0.1486 -0.3376 0.1131 -0.4302 5.165 44.26 0.8214 7.051 12 24.67 0.4054E-01 0.3193E-02 -0.2289E-01 -0.6891E-01 0.9868E-01 0.7043 1.519 0.6559 6.359 13 22.77 0.4392E-01 0.1735 -0.9361 0.2199 0.3890 11.61 152.1 0.5668 6.014 14 21.14 0.4730E-01 0.1826 -0.8758 0.2172 0.3462 11.92 131.3 0.5671 5.550 15 19.73 0.5068E-01 0.6261E-01 0.8874E-01 -0.1209 0.1638 2.745 5.137 0.5458 4.477 16 18.50 0.5405E-01 0.1643 0.2742 -0.1507 0.3253 7.355 26.79 0.5440 3.741 17 17.41 0.5743E-01 0.7021E-01 -0.2818 0.9312E-01 0.2096 2.013 18.26 0.4795 2.919 18 16.44 0.6081E-01 -0.2711 0.4794E-01 -0.1195 -0.6516 12.99 63.18 0.5033 2.845 19 15.58 0.6419E-01 0.9543E-01 -0.2331 0.1405 0.4178 4.271 33.87 0.4622 2.880 20 14.80 0.6757E-01 0.1108E-01 -0.4056 0.9569E-01 0.2647 1.373 34.72 0.3981 2.643 21 14.10 0.7095E-01 -0.5102E-01 0.2422 -0.2574 -0.4199 10.19 34.78 0.4056 2.405 22 13.45 0.7432E-01 -0.6070E-02 -0.3126 0.8152E-01 0.1288 0.9889 16.91 0.3545 2.121 23 12.87 0.7770E-01 0.8882E-01 -0.8514E-01 0.1528E-01 0.2173 1.202 8.063 0.3834 2.207 24 12.33 0.8108E-01 -0.6353E-01 0.1641 -0.2489 -0.5095 9.764 42.41 0.4592 2.436 25 11.84 0.8446E-01 -0.6266E-01 0.1842E-01 -0.2016 -0.5336 6.595 42.18 0.4519 2.445 26 11.38 0.8784E-01 0.1244 0.4029 -0.1371 -0.3746 5.072 44.78 0.4363 2.232 27 10.96 0.9122E-01 -0.1261 -0.2429 0.1878 0.1310 7.577 11.27 0.3766 1.659 28 10.57 0.9459E-01 0.7276E-01 0.1863 -0.6586E-01 -0.5671E-01 1.425 5.615 0.2564 1.042 29 10.21 0.9797E-01 -0.7566E-01 -0.1554 0.5779E-01 0.1007 1.342 5.072 0.1770 0.6215 30 9.867 0.1014 0.3848E-01 0.4538E-01 -0.2020E-01 0.6868E-02 0.2795 0.3118 0.1213 0.4066 31 9.548 0.1047 0.1100 0.1857 0.2119E-02 0.6038E-01 1.792 5.645 0.9122E-01 0.4173 32 9.250 0.1081 -0.8815E-01 -0.2289 -0.3095E-01 -0.5963E-01 1.292 8.278 0.8530E-01 0.4302 33 8.970 0.1115 -0.6512E-01 -0.2054 -0.3968E-01 -0.1437 0.8606 9.300 0.8654E-01 0.4339 34 8.706 0.1149 -0.8999E-02 -0.6225E-01 0.6456E-01 0.6460E-01 0.6288 1.191 0.8751E-01 0.3735 35 8.457 0.1182 0.4304E-01 -0.1184E-01 0.6325E-01 0.5566E-01 0.8663 0.4793 0.8479E-01 0.3037 36 8.222 0.1216 0.1303 0.2045 -0.2427E-01 -0.1395 2.599 9.069 0.8274E-01 0.2585 37 8.000 0.1250 -0.1981E-02 -0.8518E-02 -0.4682E-01 -0.6563E-01 0.3251 0.6482 0.6805E-01 0.1779 38 7.789 0.1284 -0.1171E-02 -0.1834E-01 0.3996E-01 0.3119E-01 0.2366 0.1938 0.5485E-01 0.1505 39 7.590 0.1318 0.4124E-03 0.4063E-01 0.2228E-01 -0.2612E-02 0.7352E-01 0.2453 0.4527E-01 0.1356 40 7.400 0.1351 -0.5830E-01 0.2978E-01 0.7638E-01 0.1332 1.367 2.758 0.4053E-01 0.1322 41 7.220 0.1385 -0.1621E-01 -0.3604E-01 0.1831E-01 0.1292 0.8854E-01 2.663 0.3730E-01 0.1560 42 7.048 0.1419 -0.3355E-02 -0.1076 -0.6207E-01 -0.1499E-01 0.5718 1.746 0.3565E-01 0.1578 43 6.884 0.1453 0.6101E-02 -0.1162 -0.4106E-01 -0.4435E-01 0.2550 2.289 0.3296E-01 0.1507 44 6.727 0.1486 0.4746E-01 -0.6025E-01 -0.2654E-01 -0.9716E-01 0.4376 1.934 0.2851E-01 0.1225 45 6.578 0.1520 -0.2491E-01 -0.1553E-01 0.2265E-01 -0.3873E-01 0.1678 0.2576 0.2734E-01 0.8944E-01 46 6.435 0.1554 0.1374E-01 0.1003 0.6736E-01 -0.1115E-01 0.6994 1.509 0.2572E-01 0.6877E-01 47 6.298 0.1588 0.1470E-01 0.1159E-01 -0.1864E-01 -0.1872E-01 0.8341E-01 0.7176E-01 0.2050E-01 0.4272E-01 48 6.167 0.1622 0.6298E-02 -0.2800E-02 -0.3294E-01 -0.3227E-01 0.1665 0.1553 0.1719E-01 0.3317E-01 49 6.041 0.1655 -0.2609E-01 -0.1299E-01 -0.1938E-01 0.4581E-01 0.1563 0.3356 0.1527E-01 0.3851E-01 50 5.920 0.1689 0.1755E-01 -0.3453E-01 -0.2002E-01 -0.9690E-02 0.1049 0.1903 0.1350E-01 0.4309E-01 51 5.804 0.1723 -0.8304E-02 -0.8465E-01 -0.4381E-01 0.2718E-01 0.2942 1.170 0.1463E-01 0.5540E-01 52 5.692 0.1757 0.3457E-01 -0.8801E-01 -0.1042E-02 -0.3907E-01 0.1770 1.372 0.1414E-01 0.5720E-01 53 5.585 0.1791 -0.3704E-02 -0.1125E-01 0.3387E-01 -0.4026E-01 0.1719 0.2586 0.1400E-01 0.4803E-01 54 5.481 0.1824 -0.1904E-01 -0.4899E-01 -0.1715E-01 -0.2225E-01 0.9715E-01 0.4285 0.1317E-01 0.3825E-01 55 5.382 0.1858 -0.1627E-01 0.1627E-01 0.3039E-01 -0.2785E-01 0.1758 0.1540 0.1191E-01 0.2525E-01 56 5.286 0.1892 -0.4781E-02 0.5069E-01 0.4162E-01 0.3134E-02 0.2597 0.3818 0.1055E-01 0.1677E-01 57 5.193 0.1926 0.1224E-01 -0.1470E-01 -0.1362E-01 -0.1399E-01 0.4959E-01 0.6093E-01 0.7550E-02 0.1173E-01 58 5.103 0.1959 -0.1271E-02 -0.1910E-02 -0.2441E-02 -0.1134E-01 0.1121E-02 0.1957E-01 0.4982E-02 0.7832E-02 59 5.017 0.1993 0.8297E-02 -0.5465E-02 -0.1344E-01 0.1656E-01 0.3691E-01 0.4501E-01 0.3066E-02 0.6078E-02 60 4.933 0.2027 0.9513E-02 -0.2328E-01 -0.2844E-02 -0.5351E-02 0.1459E-01 0.8447E-01 0.1703E-02 0.5209E-02 61 4.852 0.2061 -0.8764E-02 -0.2471E-01 -0.3619E-02 -0.3493E-02 0.1331E-01 0.9219E-01 0.1520E-02 0.5961E-02 62 4.774 0.2095 -0.1217E-02 -0.1501E-01 0.1560E-01 -0.7615E-02 0.3622E-01 0.4192E-01 0.1503E-02 0.6301E-02 63 4.698 0.2128 0.7884E-02 -0.1055E-01 -0.3033E-03 -0.2567E-01 0.9212E-02 0.1140 0.1215E-02 0.6420E-02 64 4.625 0.2162 0.6423E-02 -0.1527E-01 -0.1934E-02 -0.2305E-01 0.6659E-02 0.1132 0.1244E-02 0.6001E-02 65 4.554 0.2196 0.5553E-02 -0.1063E-02 -0.6248E-02 -0.1648E-01 0.1034E-01 0.4038E-01 0.1371E-02 0.4983E-02 66 4.485 0.2230 -0.3606E-02 -0.9039E-02 -0.1010E-01 -0.7330E-02 0.1702E-01 0.2004E-01 0.1607E-02 0.4726E-02 67 4.418 0.2264 -0.1363E-01 -0.1938E-01 -0.1089E-01 0.1136E-01 0.4505E-01 0.7471E-01 0.1952E-02 0.4767E-02 68 4.353 0.2297 0.1039E-01 -0.9051E-02 -0.4061E-02 0.7965E-02 0.1842E-01 0.2151E-01 0.1898E-02 0.5040E-02 69 4.290 0.2331 0.7734E-02 -0.2642E-01 0.1183E-01 -0.1605E-01 0.2958E-01 0.1415 0.1712E-02 0.5821E-02 70 4.229 0.2365 0.1146E-01 -0.1862E-01 -0.8583E-03 0.6756E-02 0.1955E-01 0.5805E-01 0.1329E-02 0.5914E-02 71 4.169 0.2399 0.1911E-02 -0.2356E-01 0.4142E-03 0.4101E-03 0.5661E-03 0.8217E-01 0.8423E-03 0.5619E-02 72 4.111 0.2432 -0.3654E-02 -0.9954E-02 0.3403E-02 -0.1084E-01 0.3690E-02 0.3206E-01 0.5899E-03 0.4980E-02 73 4.055 0.2466 -0.5526E-02 -0.2644E-01 -0.5729E-02 0.2223E-02 0.9378E-02 0.1042 0.3939E-03 0.4491E-02 74 4.000 0.2500 0.2027E-03 -0.2027E-02 -0.2669E-02 -0.1081E-01 0.1060E-02 0.1791E-01 0.2868E-03 0.3842E-02 75 3.947 0.2534 -0.4549E-02 -0.7903E-02 -0.1049E-02 -0.8801E-02 0.3225E-02 0.2071E-01 0.3558E-03 0.3473E-02 76 3.895 0.2568 -0.1094E-02 -0.2073E-01 0.9316E-03 -0.7738E-02 0.3057E-03 0.7249E-01 0.4710E-03 0.3931E-02 77 3.844 0.2601 0.1197E-02 -0.4981E-02 0.6802E-02 -0.1454E-01 0.7060E-02 0.3496E-01 0.6074E-03 0.4288E-02 78 3.795 0.2635 -0.1386E-03 0.7327E-02 0.1102E-01 -0.1328E-01 0.1797E-01 0.3404E-01 0.7274E-03 0.4902E-02 79 3.747 0.2669 0.9173E-02 -0.2220E-01 0.4300E-02 -0.1883E-01 0.1519E-01 0.1254 0.7480E-03 0.5572E-02 80 3.700 0.2703 0.2632E-02 0.1951E-03 -0.9421E-03 -0.2502E-01 0.1156E-02 0.9263E-01 0.6850E-03 0.5322E-02 81 3.654 0.2736 0.2422E-03 -0.4810E-02 -0.3132E-02 -0.9761E-02 0.1460E-02 0.1753E-01 0.6611E-03 0.5021E-02 82 3.610 0.2770 -0.9629E-02 -0.2024E-01 0.2822E-02 0.1932E-02 0.1490E-01 0.6120E-01 0.6973E-03 0.4730E-02 83 3.566 0.2804 -0.7523E-02 -0.1182E-01 -0.3648E-02 -0.1291E-01 0.1034E-01 0.4532E-01 0.8553E-03 0.4269E-02 84 3.524 0.2838 -0.6325E-02 0.1523E-01 -0.5167E-02 -0.2146E-01 0.9872E-02 0.1025 0.1076E-02 0.4018E-02 85 3.482 0.2872 0.7237E-02 -0.2084E-02 -0.1130E-02 -0.3053E-02 0.7940E-02 0.2022E-02 0.1415E-02 0.3489E-02 86 3.442 0.2905 0.1260E-01 -0.7487E-02 0.9300E-02 -0.1763E-01 0.3630E-01 0.5430E-01 0.1774E-02 0.3518E-02 87 3.402 0.2939 0.5106E-02 -0.6428E-02 -0.9822E-02 0.2858E-02 0.1814E-01 0.7324E-02 0.1847E-02 0.3452E-02 88 3.364 0.2973 -0.1429E-01 -0.1936E-01 -0.9034E-02 0.2689E-02 0.4230E-01 0.5657E-01 0.1908E-02 0.3617E-02 89 3.326 0.3007 -0.3983E-02 -0.3923E-02 0.1046E-01 -0.2552E-01 0.1854E-01 0.9870E-01 0.1662E-02 0.3884E-02 90 3.289 0.3041 0.1206E-02 0.8697E-02 -0.8155E-04 -0.1070E-01 0.2164E-03 0.2815E-01 0.1301E-02 0.3355E-02 91 3.253 0.3074 0.5297E-02 -0.9110E-02 0.1139E-01 -0.4935E-02 0.2334E-01 0.1589E-01 0.1132E-02 0.2891E-02 92 3.217 0.3108 0.5599E-02 -0.6424E-02 0.7627E-02 -0.1304E-01 0.1325E-01 0.3126E-01 0.8222E-03 0.2361E-02 93 3.183 0.3142 -0.2655E-02 0.1231E-02 -0.5734E-02 -0.1538E-01 0.5909E-02 0.3526E-01 0.6230E-03 0.1864E-02 94 3.149 0.3176 0.4118E-02 -0.9830E-02 -0.8153E-03 -0.2106E-02 0.2608E-02 0.1496E-01 0.4690E-03 0.1769E-02 95 3.116 0.3209 -0.1210E-02 -0.7456E-02 -0.1082E-02 -0.4552E-02 0.3899E-03 0.1129E-01 0.3301E-03 0.1814E-02 96 3.083 0.3243 -0.6085E-02 0.9001E-02 0.2456E-02 0.1923E-02 0.6373E-02 0.1254E-01 0.3138E-03 0.2009E-02 97 3.052 0.3277 0.3986E-02 -0.1885E-01 -0.4951E-03 0.8546E-03 0.2388E-02 0.5271E-01 0.3155E-03 0.2258E-02 98 3.020 0.3311 -0.4487E-02 -0.1290E-01 0.5838E-02 -0.5913E-02 0.8023E-02 0.2978E-01 0.3725E-03 0.2515E-02 99 2.990 0.3345 -0.3677E-02 0.6970E-02 0.7855E-03 -0.1419E-01 0.2093E-02 0.3699E-01 0.4194E-03 0.2724E-02 100 2.960 0.3378 0.3944E-02 -0.4236E-02 0.2344E-02 -0.3733E-02 0.3115E-02 0.4718E-02 0.4886E-03 0.2652E-02 101 2.931 0.3412 -0.4210E-02 -0.1682E-01 0.7059E-02 -0.1416E-01 0.9998E-02 0.7156E-01 0.6105E-03 0.2712E-02 102 2.902 0.3446 0.8513E-02 -0.8779E-02 0.2116E-02 -0.1264E-01 0.1139E-01 0.3505E-01 0.6830E-03 0.2495E-02 103 2.874 0.3480 0.2769E-02 -0.3380E-02 -0.6952E-02 -0.5597E-02 0.8287E-02 0.6327E-02 0.6900E-03 0.2179E-02 104 2.846 0.3514 -0.8188E-02 -0.1179E-01 0.1919E-02 -0.4315E-02 0.1047E-01 0.2333E-01 0.7067E-03 0.2798E-02 105 2.819 0.3547 -0.5261E-02 -0.1416E-01 0.4900E-02 -0.5820E-02 0.7650E-02 0.3467E-01 0.7430E-03 0.3738E-02 106 2.792 0.3581 -0.3277E-02 -0.1052E-01 -0.2387E-03 -0.5324E-02 0.1598E-02 0.2056E-01 0.7831E-03 0.4746E-02 107 2.766 0.3615 0.7977E-02 -0.1456E-01 0.6887E-02 -0.2988E-01 0.1644E-01 0.1636 0.9011E-03 0.5758E-02 108 2.741 0.3649 0.1008E-01 -0.1563E-01 -0.6739E-02 -0.2180E-01 0.2176E-01 0.1065 0.9524E-03 0.5240E-02 109 2.716 0.3682 -0.1790E-03 0.1061E-02 -0.6390E-02 -0.8679E-02 0.6049E-02 0.1131E-01 0.9039E-03 0.3865E-02 110 2.691 0.3716 -0.6512E-02 -0.1468E-02 -0.2847E-02 -0.6756E-02 0.7476E-02 0.7075E-02 0.8842E-03 0.2762E-02 111 2.667 0.3750 -0.8549E-02 -0.5815E-02 0.1566E-02 -0.7342E-02 0.1118E-01 0.1298E-01 0.8023E-03 0.1789E-02 112 2.643 0.3784 0.5942E-03 -0.7054E-02 0.9351E-02 -0.8326E-02 0.1299E-01 0.1762E-01 0.7050E-03 0.1667E-02 113 2.619 0.3818 0.5235E-02 -0.1191E-01 0.6463E-02 -0.1202E-01 0.1024E-01 0.4238E-01 0.6259E-03 0.2078E-02 114 2.596 0.3851 -0.1476E-02 0.2215E-02 -0.1871E-02 -0.1137E-01 0.8407E-03 0.1987E-01 0.5022E-03 0.2428E-02 115 2.574 0.3885 0.2949E-02 -0.9708E-02 -0.3236E-02 -0.1147E-01 0.2836E-02 0.3342E-01 0.4841E-03 0.2715E-02 116 2.552 0.3919 0.9031E-03 -0.5807E-02 -0.7239E-02 -0.1446E-01 0.7877E-02 0.3592E-01 0.5042E-03 0.2980E-02 117 2.530 0.3953 -0.6073E-02 0.1301E-01 0.1976E-03 -0.1564E-01 0.5464E-02 0.6127E-01 0.5163E-03 0.3005E-02 118 2.508 0.3986 0.2764E-02 0.9739E-02 0.9830E-02 -0.6308E-02 0.1543E-01 0.1993E-01 0.5416E-03 0.2639E-02 119 2.487 0.4020 -0.6354E-03 -0.7429E-03 0.3781E-02 -0.1826E-01 0.2175E-02 0.4941E-01 0.4239E-03 0.2374E-02 120 2.467 0.4054 0.2625E-02 -0.1001E-02 0.1011E-02 -0.6265E-02 0.1171E-02 0.5957E-02 0.3188E-03 0.1886E-02 121 2.446 0.4088 -0.4399E-03 0.2013E-02 -0.4720E-02 -0.2605E-02 0.3326E-02 0.1604E-02 0.2608E-03 0.1608E-02 122 2.426 0.4122 -0.2732E-02 -0.9929E-02 0.1028E-02 -0.1319E-01 0.1261E-02 0.4035E-01 0.2119E-03 0.1782E-02 123 2.407 0.4155 0.4930E-02 -0.4011E-02 0.1779E-02 -0.1106E-01 0.4066E-02 0.2047E-01 0.2353E-03 0.2191E-02 124 2.387 0.4189 0.1053E-02 -0.2691E-02 -0.5042E-02 -0.1081E-01 0.3926E-02 0.1835E-01 0.2382E-03 0.2683E-02 125 2.368 0.4223 -0.3032E-02 -0.6877E-02 0.3348E-02 -0.1316E-01 0.3019E-02 0.3261E-01 0.2204E-03 0.3177E-02 126 2.349 0.4257 0.2785E-02 -0.4426E-02 -0.1803E-02 -0.2665E-01 0.1629E-02 0.1080 0.2320E-03 0.3430E-02 127 2.331 0.4291 -0.2089E-02 -0.2490E-02 0.2836E-02 -0.7095E-02 0.1836E-02 0.8368E-02 0.2458E-03 0.2828E-02 128 2.312 0.4324 -0.1253E-02 -0.2763E-02 0.3925E-02 -0.1427E-01 0.2513E-02 0.3125E-01 0.2637E-03 0.2427E-02 129 2.295 0.4358 0.7183E-02 0.1002E-01 -0.2589E-02 0.1086E-03 0.8628E-02 0.1487E-01 0.3044E-03 0.2026E-02 130 2.277 0.4392 0.1172E-02 -0.5145E-02 -0.3882E-02 -0.9604E-03 0.2434E-02 0.4055E-02 0.3003E-03 0.1665E-02 131 2.260 0.4426 -0.3247E-03 -0.5466E-02 -0.1660E-02 -0.1470E-01 0.4235E-03 0.3642E-01 0.3157E-03 0.1812E-02 132 2.242 0.4459 -0.4619E-02 0.5263E-02 -0.4141E-02 -0.1651E-01 0.5695E-02 0.4446E-01 0.3626E-03 0.1841E-02 133 2.226 0.4493 -0.4200E-02 -0.3902E-02 0.4206E-02 -0.4213E-02 0.5229E-02 0.4881E-02 0.3799E-03 0.1669E-02 134 2.209 0.4527 0.7879E-04 0.2473E-02 0.6954E-02 -0.3023E-02 0.7158E-02 0.2258E-02 0.4108E-03 0.1605E-02 135 2.193 0.4561 0.4567E-02 -0.1014E-01 0.3920E-02 -0.1318E-01 0.5361E-02 0.4092E-01 0.4012E-03 0.1594E-02 136 2.176 0.4595 0.4384E-02 0.6495E-02 0.6354E-03 -0.8552E-02 0.2905E-02 0.1707E-01 0.3443E-03 0.1382E-02 137 2.161 0.4628 -0.1379E-02 0.1345E-03 -0.5381E-02 -0.1063E-01 0.4567E-02 0.1673E-01 0.3004E-03 0.1397E-02 138 2.145 0.4662 -0.4676E-02 -0.8280E-03 -0.1863E-02 -0.8637E-02 0.3749E-02 0.1114E-01 0.2560E-03 0.1326E-02 139 2.129 0.4696 -0.2299E-02 0.3979E-02 -0.1012E-03 -0.4151E-02 0.7835E-03 0.4893E-02 0.2482E-03 0.1169E-02 140 2.114 0.4730 -0.8754E-03 -0.1295E-01 0.4204E-02 -0.8511E-02 0.2729E-02 0.3553E-01 0.2741E-03 0.1448E-02 141 2.099 0.4764 0.3913E-02 0.2306E-03 0.3214E-02 -0.8599E-02 0.3795E-02 0.1095E-01 0.2890E-03 0.1601E-02 142 2.085 0.4797 0.7189E-02 -0.1592E-02 0.6023E-03 -0.4215E-02 0.7702E-02 0.3005E-02 0.2906E-03 0.1795E-02 143 2.070 0.4831 -0.1600E-02 -0.7746E-02 -0.4195E-02 -0.1792E-01 0.2983E-02 0.5640E-01 0.2596E-03 0.2722E-02 144 2.056 0.4865 -0.1277E-02 0.1146E-01 0.8484E-03 -0.7936E-02 0.3478E-03 0.2875E-01 0.2100E-03 0.3194E-02 145 2.041 0.4899 -0.1216E-02 -0.4212E-02 0.9022E-03 -0.8494E-02 0.3395E-03 0.1330E-01 0.1774E-03 0.3637E-02 146 2.027 0.4932 -0.5533E-02 0.2172E-02 -0.2000E-02 -0.3095E-01 0.5124E-02 0.1425 0.1674E-03 0.4084E-02 147 2.014 0.4966 -0.2916E-02 0.8966E-02 0.1011E-02 -0.5409E-02 0.1410E-02 0.1623E-01 0.1517E-03 0.3208E-02 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 STAT. PROC. STEP PAGE 108 Obs PERIOD FREQ RP_1 IP_1 CS_1 QS_1 A_1 K_1 PH_1 1 296.0 0.3378E-02 -128.2 -33.07 -9.691 -2.641 10.04 0.9974 -2.876 2 148.0 0.6757E-02 -117.2 -39.08 -8.722 -2.475 9.067 0.9952 -2.865 3 98.67 0.1014E-01 -137.2 -35.49 -7.268 -2.123 7.571 0.9862 -2.857 4 74.00 0.1351E-01 -40.57 -12.04 -5.301 -1.867 5.620 0.9525 -2.803 5 59.20 0.1689E-01 -22.96 -12.27 -3.648 -1.722 4.034 0.9058 -2.701 6 49.33 0.2027E-01 -8.471 -7.870 -2.626 -2.071 3.344 0.8515 -2.474 7 42.29 0.2365E-01 -43.41 -57.05 -2.184 -2.612 3.405 0.9030 -2.267 8 37.00 0.2703E-01 -16.07 -13.16 -1.991 -2.837 3.466 0.9216 -2.183 9 32.89 0.3041E-01 -44.43 -91.10 -1.846 -2.990 3.514 0.9317 -2.124 10 29.60 0.3378E-01 -16.45 -15.09 -1.429 -2.499 2.879 0.9186 -2.090 11 26.91 0.3716E-01 0.2236 -15.12 -0.9536 -2.084 2.292 0.9066 -2.000 12 24.67 0.4054E-01 -1.017 0.1868 -0.7065 -1.817 1.950 0.9113 -1.942 13 22.77 0.4392E-01 -11.38 -40.45 -0.5322 -1.688 1.770 0.9188 -1.876 14 21.14 0.4730E-01 -12.53 -37.51 -0.4658 -1.639 1.704 0.9226 -1.848 15 19.73 0.5068E-01 -2.110 -3.106 -0.3087 -1.427 1.460 0.8722 -1.784 16 18.50 0.5405E-01 -0.5905 -14.02 -0.1028 -1.312 1.316 0.8510 -1.649 17 17.41 0.5743E-01 -0.3994E-01 -6.062 0.1193 -1.088 1.094 0.8554 -1.462 18 16.44 0.6081E-01 9.601 -26.99 0.3557 -1.066 1.124 0.8817 -1.249 19 15.58 0.6419E-01 5.397 -10.75 0.4434 -0.9803 1.076 0.8698 -1.146 20 14.80 0.6757E-01 3.084 -6.178 0.4637 -0.8184 0.9407 0.8410 -1.055 21 14.10 0.7095E-01 14.17 -12.40 0.5361 -0.7187 0.8967 0.8244 -0.9299 22 13.45 0.7432E-01 1.835 -3.655 0.5457 -0.5532 0.7771 0.8031 -0.7922 23 12.87 0.7770E-01 -0.6276 -3.049 0.6595 -0.4920 0.8228 0.8003 -0.6409 24 12.33 0.8108E-01 17.22 -10.84 0.8470 -0.4753 0.9712 0.8432 -0.5114 25 11.84 0.8446E-01 15.75 -5.497 0.8913 -0.3875 0.9719 0.8550 -0.4101 26 11.38 0.8784E-01 15.02 -1.282 0.8623 -0.3078 0.9156 0.8610 -0.3428 27 10.96 0.9122E-01 8.177 -4.308 0.6943 -0.2343 0.7327 0.8595 -0.3254 28 10.57 0.9459E-01 2.559 -1.206 0.4569 -0.1377 0.4772 0.8525 -0.2927 29 10.21 0.9797E-01 2.601 -0.2014 0.2960 -0.8169E-01 0.3071 0.8571 -0.2693 30 9.867 0.1014 0.2379 -0.1748 0.2015 -0.5190E-01 0.2081 0.8779 -0.2521 31 9.548 0.1047 3.043 -0.9250 0.1829 -0.2928E-01 0.1852 0.9012 -0.1588 32 9.250 0.1081 3.259 0.2703 0.1769 -0.2120E-01 0.1781 0.8645 -0.1193 33 8.970 0.1115 2.823 -0.1786 0.1732 -0.1209E-01 0.1737 0.8031 -0.6965E-01 34 8.706 0.1149 0.7001 -0.5087 0.1567 -0.1997E-02 0.1568 0.7518 -0.1274E-01 35 8.457 0.1182 0.4456 -0.4654 0.1354 0.1177E-01 0.1359 0.7172 0.8671E-01 36 8.222 0.1216 4.444 1.955 0.1247 0.2623E-01 0.1275 0.7596 0.2073 37 8.000 0.1250 0.4573 0.3978E-01 0.9227E-01 0.2999E-01 0.9702E-01 0.7774 0.3142 38 7.789 0.1284 0.1877 -0.1030 0.7148E-01 0.3352E-01 0.7895E-01 0.7553 0.4384 39 7.590 0.1318 -0.6136E-02 0.1341 0.5326E-01 0.4042E-01 0.6686E-01 0.7280 0.6491 40 7.400 0.1351 1.249 1.486 0.3813E-01 0.4738E-01 0.6082E-01 0.6905 0.8931 41 7.220 0.1385 0.4367 0.2124 0.3248E-01 0.5385E-01 0.6289E-01 0.6796 1.028 42 7.048 0.1419 0.1911 0.9807 0.2439E-01 0.5744E-01 0.6240E-01 0.6922 1.169 43 6.884 0.1453 0.1646 0.7461 0.1580E-01 0.5584E-01 0.5804E-01 0.6780 1.295 44 6.727 0.1486 -0.4160E-01 0.9191 0.5924E-02 0.4754E-01 0.4791E-01 0.6573 1.447 45 6.578 0.1520 -0.7258E-01 -0.1948 0.3443E-02 0.3771E-01 0.3786E-01 0.5862 1.480 46 6.435 0.1554 0.9288E-01 1.023 0.3451E-02 0.3193E-01 0.3212E-01 0.5832 1.463 47 6.298 0.1588 0.7687E-01 0.8758E-02 0.3184E-02 0.2149E-01 0.2172E-01 0.5388 1.424 48 6.167 0.1622 0.1547 0.4373E-01 0.2611E-02 0.1757E-01 0.1776E-01 0.5533 1.423 49 6.041 0.1655 -0.8122E-01 0.2142 -0.1918E-02 0.1884E-01 0.1894E-01 0.6098 1.672 50 5.920 0.1689 -0.6098E-01 0.1275 -0.6972E-02 0.1663E-01 0.1803E-01 0.5592 1.968 51 5.804 0.1723 -0.7216E-01 0.5822 -0.9991E-02 0.1854E-01 0.2106E-01 0.5472 2.065 52 5.692 0.1757 -0.4442 0.2134 -0.1273E-01 0.1474E-01 0.1947E-01 0.4689 2.283 53 5.585 0.1791 -0.1957 -0.7847E-01 -0.1036E-01 0.1059E-01 0.1482E-01 0.3265 2.345 54 5.481 0.1824 0.1945 0.6166E-01 -0.6439E-02 0.8567E-02 0.1072E-01 0.2279 2.215 55 5.382 0.1858 -0.1644 0.6112E-02 -0.4735E-02 0.6554E-02 0.8085E-02 0.2173 2.196 56 5.286 0.1892 -0.1657E-01 0.3145 -0.1951E-02 0.7329E-02 0.7584E-02 0.3252 1.831 57 5.193 0.1926 0.1579E-02 0.5495E-01 -0.1364E-02 0.6123E-02 0.6273E-02 0.4443 1.790 58 5.103 0.1959 0.4456E-02 -0.1443E-02 -0.1597E-02 0.4024E-02 0.4329E-02 0.4803 1.949 59 5.017 0.1993 -0.3965E-01 -0.9466E-02 -0.9810E-03 0.2067E-02 0.2288E-02 0.2808 2.014 60 4.933 0.2027 -0.3053E-01 0.1733E-01 -0.8439E-03 0.3855E-03 0.9278E-03 0.9702E-01 2.713 61 4.852 0.2061 0.3392E-01 0.8707E-02 -0.5251E-03 0.2265E-03 0.5718E-03 0.3608E-01 2.734 62 4.774 0.2095 -0.1487E-01 -0.3601E-01 -0.4643E-03 0.3264E-03 0.5676E-03 0.3402E-01 2.529 63 4.698 0.2128 -0.1116E-01 0.3042E-01 -0.1550E-03 0.8252E-03 0.8396E-03 0.9034E-01 1.756 64 4.625 0.2162 -0.7918E-02 0.2628E-01 0.1716E-03 0.1244E-02 0.1255E-02 0.2111 1.434 65 4.554 0.2196 0.1437E-01 0.1453E-01 0.3320E-03 0.1453E-02 0.1490E-02 0.3252 1.346 66 4.485 0.2230 0.1578E-01 0.9600E-02 0.2280E-03 0.1422E-02 0.1440E-02 0.2731 1.412 67 4.418 0.2264 0.2079E-01 0.5416E-01 -0.2682E-03 0.1072E-02 0.1105E-02 0.1311 1.816 68 4.353 0.2297 -0.1871E-01 -0.6808E-02 -0.1060E-02 0.3259E-03 0.1109E-02 0.1285 2.843 69 4.290 0.2331 -0.5835E-01 -0.2790E-01 -0.1705E-02 -0.2755E-03 0.1727E-02 0.2994 -2.981 70 4.229 0.2365 -0.3243E-01 -0.9094E-02 -0.1600E-02 -0.4065E-03 0.1651E-02 0.3468 -2.893 71 4.169 0.2399 -0.6640E-02 -0.1560E-02 -0.1073E-02 -0.3937E-03 0.1143E-02 0.2762 -2.790 72 4.111 0.2432 -0.7800E-04 -0.1088E-01 -0.3438E-03 -0.1194E-03 0.3640E-03 0.4509E-01 -2.807 73 4.055 0.2466 0.1974E-01 0.2424E-01 0.3049E-03 0.2087E-03 0.3695E-03 0.7719E-01 0.6003 74 4.000 0.2500 0.4209E-02 0.1125E-02 0.3898E-03 0.1449E-03 0.4159E-03 0.1570 0.3559 75 3.947 0.2534 0.6687E-02 -0.4698E-02 0.1632E-03 0.8276E-04 0.1830E-03 0.2708E-01 0.4694 76 3.895 0.2568 0.2291E-02 -0.4112E-02 -0.3725E-03 0.1165E-03 0.3903E-03 0.8227E-01 2.839 77 3.844 0.2601 -0.1552E-01 -0.2439E-02 -0.9137E-03 0.1853E-03 0.9323E-03 0.3337 2.941 78 3.795 0.2635 -0.2181E-01 0.1168E-01 -0.1181E-02 0.4118E-03 0.1250E-02 0.4385 2.806 79 3.747 0.2669 -0.4212E-01 0.1144E-01 -0.1062E-02 0.4994E-03 0.1174E-02 0.3306 2.702 80 3.700 0.2703 0.3564E-02 0.9717E-02 -0.3916E-03 0.4100E-03 0.5670E-03 0.8819E-01 2.333 81 3.654 0.2736 0.4352E-02 0.2579E-02 0.2658E-03 0.4579E-04 0.2697E-03 0.2191E-01 0.1706 82 3.610 0.2770 0.2966E-01 -0.5700E-02 0.7941E-03 -0.3383E-03 0.8631E-03 0.2259 -0.4027 83 3.566 0.2804 0.2012E-01 -0.7989E-02 0.7288E-03 -0.4953E-03 0.8812E-03 0.2127 -0.5969 84 3.524 0.2838 0.2162E-02 -0.3174E-01 0.2091E-03 -0.4802E-03 0.5237E-03 0.6344E-01 -1.160 85 3.482 0.2872 -0.1721E-02 0.3618E-02 -0.1286E-03 0.5600E-04 0.1403E-03 0.3986E-02 2.731 86 3.442 0.2905 -0.3823E-01 0.2258E-01 -0.6125E-03 0.4640E-03 0.7684E-03 0.9461E-01 2.493 87 3.402 0.2939 -0.9012E-02 0.7183E-02 -0.5603E-03 0.6280E-03 0.8416E-03 0.1111 2.299 88 3.364 0.2973 0.3736E-01 0.3158E-01 -0.3953E-03 0.6237E-03 0.7384E-03 0.7904E-01 2.136 89 3.326 0.3007 -0.3720E-01 -0.2112E-01 -0.6907E-03 0.1652E-03 0.7102E-03 0.7812E-01 2.907 90 3.289 0.3041 0.1682E-02 0.1806E-02 -0.5622E-03 -0.1006E-03 0.5711E-03 0.7471E-01 -2.964 91 3.253 0.3074 -0.1546E-01 -0.1148E-01 -0.6691E-03 -0.2598E-03 0.7178E-03 0.1575 -2.771 92 3.217 0.3108 -0.2004E-01 0.3551E-02 -0.6568E-03 -0.2671E-03 0.7090E-03 0.2590 -2.755 93 3.183 0.3142 0.1257E-01 -0.7091E-02 -0.2962E-03 -0.1278E-03 0.3226E-03 0.8963E-01 -2.734 94 3.149 0.3176 -0.5736E-02 0.2470E-02 -0.3013E-03 -0.1868E-04 0.3018E-03 0.1098 -3.080 95 3.116 0.3209 0.2064E-02 0.3785E-03 -0.2237E-03 -0.5107E-07 0.2237E-03 0.8363E-01 -3.141 96 3.083 0.3243 -0.7408E-02 0.5003E-02 -0.2707E-03 -0.7669E-04 0.2814E-03 0.1256 -2.866 97 3.052 0.3277 -0.1118E-01 0.8773E-03 -0.3624E-03 -0.1819E-03 0.4055E-03 0.2308 -2.676 98 3.020 0.3311 0.3454E-02 -0.1507E-01 -0.3017E-03 -0.4624E-03 0.5521E-03 0.3254 -2.149 99 2.990 0.3345 -0.5443E-02 -0.6913E-02 -0.3787E-03 -0.5152E-03 0.6394E-03 0.3580 -2.205 100 2.960 0.3378 -0.3768E-02 0.7088E-03 -0.3695E-03 -0.4687E-03 0.5968E-03 0.2749 -2.238 101 2.931 0.3412 -0.4315E-02 -0.2640E-01 -0.2946E-03 -0.4469E-03 0.5353E-03 0.1731 -2.154 102 2.902 0.3446 -0.1502E-01 0.1318E-01 -0.1987E-03 -0.2319E-03 0.3054E-03 0.5472E-01 -2.279 103 2.874 0.3480 0.4373E-02 0.5771E-02 0.9012E-04 -0.2338E-03 0.2506E-03 0.4175E-01 -1.203 104 2.846 0.3514 0.1306E-01 -0.8576E-02 0.7137E-04 -0.2259E-03 0.2369E-03 0.2838E-01 -1.265 105 2.819 0.3547 0.6802E-02 -0.1480E-01 -0.1039E-03 0.1102E-03 0.1514E-03 0.8255E-02 2.327 106 2.792 0.3581 0.5288E-02 -0.2211E-02 -0.3276E-03 0.4560E-03 0.5615E-03 0.8482E-01 2.194 107 2.766 0.3615 -0.4765E-01 0.2043E-01 -0.6574E-03 0.8600E-03 0.1082E-02 0.2258 2.223 108 2.741 0.3649 -0.1573E-02 0.4811E-01 -0.4633E-03 0.1037E-02 0.1135E-02 0.2583 1.991 109 2.716 0.3682 0.8180E-02 -0.1234E-02 -0.2490E-03 0.6470E-03 0.6932E-03 0.1375 1.938 110 2.691 0.3716 0.4262E-02 -0.5893E-02 -0.1853E-03 0.1857E-03 0.2623E-03 0.2818E-01 2.355 111 2.667 0.3750 0.5656E-02 -0.1064E-01 -0.1244E-03 -0.2434E-03 0.2733E-03 0.5205E-01 -2.043 112 2.643 0.3784 -0.1214E-01 -0.9031E-02 -0.3506E-03 -0.4170E-03 0.5448E-03 0.2525 -2.270 113 2.619 0.3818 -0.2073E-01 -0.2080E-02 -0.3906E-03 -0.2209E-03 0.4488E-03 0.1548 -2.627 114 2.596 0.3851 0.2666E-02 -0.3099E-02 -0.2442E-03 -0.7828E-04 0.2565E-03 0.5394E-01 -2.831 115 2.574 0.3885 0.1255E-02 0.9655E-02 -0.1290E-03 0.1491E-03 0.1972E-03 0.2958E-01 2.284 116 2.552 0.3919 0.1471E-01 0.8154E-02 -0.4855E-04 0.2170E-03 0.2224E-03 0.3292E-01 1.791 117 2.530 0.3953 -0.1215E-01 -0.1368E-01 -0.1815E-03 0.1702E-03 0.2488E-03 0.3991E-01 2.388 118 2.508 0.3986 -0.5192E-02 0.1675E-01 -0.2882E-03 0.2413E-03 0.3759E-03 0.9886E-01 2.444 119 2.487 0.4020 -0.1015E-01 -0.2132E-02 -0.3200E-03 0.9634E-04 0.3342E-03 0.1110 2.849 120 2.467 0.4054 -0.1327E-02 0.2284E-02 -0.2737E-03 0.5547E-04 0.2793E-03 0.1297 2.942 121 2.446 0.4088 0.1689E-02 -0.1575E-02 -0.1030E-03 0.5080E-04 0.1149E-03 0.3145E-01 2.683 122 2.426 0.4122 0.2008E-02 -0.6846E-02 -0.2663E-04 -0.5254E-04 0.5890E-04 0.9187E-02 -2.040 123 2.407 0.4155 -0.5837E-02 0.7012E-02 0.3024E-04 0.5603E-04 0.6367E-04 0.7865E-02 1.076 124 2.387 0.4189 0.7643E-02 0.3692E-02 0.8373E-04 0.6814E-04 0.1080E-03 0.1823E-01 0.6831 125 2.368 0.4223 -0.3433E-02 -0.9310E-02 0.1593E-04 0.3373E-04 0.3731E-04 0.1987E-02 1.130 126 2.349 0.4257 0.5287E-02 0.1217E-01 0.4345E-04 0.6443E-04 0.7771E-04 0.7589E-02 0.9774 127 2.331 0.4291 -0.2208E-02 -0.3238E-02 0.2669E-04 -0.4440E-04 0.5181E-04 0.3860E-02 -1.030 128 2.312 0.4324 -0.7775E-02 -0.4251E-02 0.2213E-04 -0.8298E-04 0.8588E-04 0.1153E-01 -1.310 129 2.295 0.4358 0.1061E-01 -0.3956E-02 0.1654E-03 -0.1331E-03 0.2123E-03 0.7306E-01 -0.6777 130 2.277 0.4392 -0.3403E-03 0.3123E-02 0.1850E-03 -0.2153E-03 0.2838E-03 0.1612 -0.8609 131 2.260 0.4426 0.3875E-02 0.6365E-03 0.2190E-03 -0.2552E-03 0.3362E-03 0.1977 -0.8616 132 2.242 0.4459 0.6523E-02 -0.1451E-01 0.1313E-03 -0.3025E-03 0.3297E-03 0.1629 -1.161 133 2.226 0.4493 -0.1966E-03 -0.5048E-02 -0.4298E-04 -0.1959E-03 0.2006E-03 0.6347E-01 -1.787 134 2.209 0.4527 -0.3083E-02 0.2581E-02 -0.1205E-03 -0.7015E-04 0.1395E-03 0.2951E-01 -2.615 135 2.193 0.4561 -0.1450E-01 0.3021E-02 -0.1544E-03 0.1689E-04 0.1553E-03 0.3774E-01 3.033 136 2.176 0.4595 0.3410E-02 0.6160E-02 -0.3124E-04 0.6972E-04 0.7640E-04 0.1227E-01 1.992 137 2.161 0.4628 0.8440E-02 -0.2276E-02 0.7248E-04 -0.5646E-04 0.9187E-04 0.2010E-01 -0.6618 138 2.145 0.4662 0.2955E-02 -0.5749E-02 0.7158E-04 -0.1598E-03 0.1751E-03 0.9034E-01 -1.150 139 2.129 0.4696 -0.1291E-02 -0.1472E-02 0.1567E-04 -0.1715E-03 0.1722E-03 0.1022 -1.480 140 2.114 0.4730 -0.3618E-02 -0.9159E-02 -0.3505E-04 -0.1507E-03 0.1548E-03 0.6036E-01 -1.799 141 2.099 0.4764 -0.3956E-02 0.5090E-02 -0.4855E-04 -0.8532E-05 0.4929E-04 0.5252E-02 -2.968 142 2.085 0.4797 -0.2070E-02 0.4343E-02 0.1742E-04 0.6132E-04 0.6375E-04 0.7794E-02 1.294 143 2.070 0.4831 0.1296E-01 0.5648E-03 0.1554E-03 -0.6988E-04 0.1704E-03 0.4107E-01 -0.4226 144 2.056 0.4865 -0.3161E-02 -0.6095E-04 0.1348E-03 -0.2190E-03 0.2571E-03 0.9857E-01 -1.019 145 2.041 0.4899 -0.3758E-03 -0.2092E-02 0.1043E-03 -0.4179E-03 0.4308E-03 0.2875 -1.326 146 2.027 0.4932 0.7384E-02 -0.2599E-01 0.3469E-04 -0.5757E-03 0.5768E-03 0.4867 -1.511 147 2.014 0.4966 -0.4679E-02 -0.9933E-03 -0.1420E-03 -0.4583E-03 0.4798E-03 0.4731 -1.871 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 STAT. PROC. STEP PAGE 109 P_1 39.596 *. * . * *.. * * * * * * * * * * * * * * * * * * * * * * . * * * * * * * . * . * * * * * . . * . * . * . . . * . . * * . . * . * * . . * . . * . * * * . . * . . . .* *.*.*.*.*.*..*.*.*.*.*.*.*.*.*.*..*.*.*.*.*.*.*.*.*..*.*.*.*.*.*.*.*.*... 0.21635E-03 ***************************************************************************************************** 0.33784E-02 0.49662 FREQ B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 STAT. PROC. STEP PAGE 110 P_2 529.75 * . * * * * * * * * *. * * *. * * * * * * * * * * * * * . * . * * * * * * * * * . * * . * . * * * * . . * * . * . . . * *. .. * . * . . . . * . . . *..*.*.*.*.*.*.*.*.*..*.*.*.*.*.*.*.*.*.*..*.*.*.*.*.*.*.*.*..*.*.*.*.*.*.*.*.*... 0.16039E-02 ***************************************************************************************************** 0.33784E-02 0.49662 FREQ B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 STAT. PROC. STEP PAGE 111 S_1 2.9758 *. * * * * *. * * * * * * * * . * * * * * * * * . * * * * * * * . .. * . * . * * . * * * * . * * * . * * * ... * . . .* * ... . * . * . * * . * ..*.*. * *.*.*.*.*.*.*..*.*.*.*.*.*.*.*.*.*..*.*.*.*.*.*.*.*.*..*.*.*.*.*.*.*.*.*... 0.15168E-03 ***************************************************************************************************** 0.33784E-02 0.49662 FREQ B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 STAT. PROC. STEP PAGE 112 S_2 33.987 *. * * * * *. * * * * * * * . * * * * * * * * * * . * * * * * * * * . * * * * .. * .. * * . * * . * . * . * . * . * . * ... * ..*.* * . * . * ...*.*.*.*.*.*.*.*.*..*.*.*.*.*.*.*.*.*.*..*.*.*.*.*.*.*.*.*..*.*.*.*.*.*.*.*.*... 0.11690E-02 ***************************************************************************************************** 0.33784E-02 0.49662 FREQ B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 STAT. PROC. STEP PAGE 113 A_1 10.044 *. * * * * *. * * * * * * * * . * * * * * * * * * . * * * * * * * * . * * . * .* * * . * * * . * * . * * * . * . * ... * ....* * . . * . * .. * .*.*.*.*.*.*.*.*.*..*.*.*.*.*.*.*.*.*.*..*.*.*.*.*.*.*.*.*..*.*.*.*.*.*.*.*.*... 0.37306E-04 ***************************************************************************************************** 0.33784E-02 0.49662 FREQ B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 STAT. PROC. STEP PAGE 114 K_1 0.99744 *. *.. * * . * ... * * . . .. . * . . * .. . ... . * . . . .. . * . * * . * . * . . * . * . . * * .*. * . * * * . * .. * . . * . . * * * . .. * . * . . * * * * . * . .. * . . . . * . . * . . . . * . . . * . . . . * . . . * . * . * . . . .. * .. . . . * . . . * . . . . .. . . .. . * . . . ... . . * . . . . . * .. . * . *. . * . * . . . *.*.. .. .. 0.19871E-02 ***************************************************************************************************** 0.33784E-02 0.49662 FREQ B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 STAT. PROC. STEP PAGE 115 PH_1 3.0327 * . * . . . * . . . . * * . . . * . * . . * .. . . . . .. * .. * * . . * . .. .. . * * . . * . . * * *.* . . * . . . * . * . . . * . . * * . . * . * . . * . . * . . * . *---------------------..----------------------------------------------------------------------------- * .. * ..*. * . . . * . . * . . . * . .. * . * . . . * .. . . . . * . . . * . . * . * . * *. . . . * .. * .. . . * . ..* * . . . * . * . . * . .. . **.. .. . . . * * . . * * -3.1414 ***************************************************************************************************** 0.33784E-02 0.49662 FREQ B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 STAT. PROC. STEP PAGE 116 Polynomial Division Order of Numerator 0 Order of Denominator 1 # of terms in answer 12 Numerator Coefficients Lag Coef. 0 1.0000000 Denominator Coefficients Lag Coef. 0 1.0000000 1 -0.50000000 IRF Coefficients Lag Coef. Sum 0 1.0000000 1.0000000 1 0.50000000 1.5000000 2 0.25000000 1.7500000 3 0.12500000 1.8750000 4 0.62500000E-01 1.9375000 5 0.31250000E-01 1.9687500 6 0.15625000E-01 1.9843750 7 0.78125000E-02 1.9921875 8 0.39062500E-02 1.9960938 9 0.19531250E-02 1.9980469 10 0.97656250E-03 1.9990234 11 0.48828125E-03 1.9995117 # Real Root Complex Root Sqrt(real**2 + imag**2) 1 -2.0000000 0.0000000 2.0000000 2 1.7320508 1.0000000 2.0000000 3 1.7320508 -1.0000000 2.0000000 4 -1.0000000 1.7320508 2.0000000 5 -1.0000000 -1.7320508 2.0000000 6 -1.7320508 -1.0000000 2.0000000 7 -1.7320508 1.0000000 2.0000000 8 1.0000000 1.7320508 2.0000000 9 1.0000000 -1.7320508 2.0000000 10 0.20666052E-22 2.0000000 2.0000000 11 0.20666052E-22 -2.0000000 2.0000000 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 STAT. PROC. STEP PAGE 117 Polynomial Division Order of Numerator 3 Order of Denominator 1 # of terms in answer 40 Numerator Coefficients Lag Coef. 0 1.0000000 1 -0.40000000 2 0.0000000 3 -0.30000000 Denominator Coefficients Lag Coef. 0 1.0000000 1 -0.50000000 IRF Coefficients Lag Coef. Sum 0 1.0000000 1.0000000 1 0.10000000 1.1000000 2 0.50000000E-01 1.1500000 3 -0.27500000 0.87500000 4 -0.13750000 0.73750000 5 -0.68750000E-01 0.66875000 6 -0.34375000E-01 0.63437500 7 -0.17187500E-01 0.61718750 8 -0.85937500E-02 0.60859375 9 -0.42968750E-02 0.60429688 10 -0.21484375E-02 0.60214844 11 -0.10742188E-02 0.60107422 12 -0.53710938E-03 0.60053711 13 -0.26855469E-03 0.60026855 14 -0.13427734E-03 0.60013428 15 -0.67138672E-04 0.60006714 16 -0.33569336E-04 0.60003357 17 -0.16784668E-04 0.60001678 18 -0.83923340E-05 0.60000839 19 -0.41961670E-05 0.60000420 20 -0.20980835E-05 0.60000210 21 -0.10490417E-05 0.60000105 22 -0.52452087E-06 0.60000052 23 -0.26226044E-06 0.60000026 24 -0.13113022E-06 0.60000013 25 -0.65565109E-07 0.60000007 26 -0.32782555E-07 0.60000003 27 -0.16391277E-07 0.60000002 28 -0.81956387E-08 0.60000001 29 -0.40978193E-08 0.60000000 30 -0.20489097E-08 0.60000000 31 -0.10244548E-08 0.60000000 32 -0.51222742E-09 0.60000000 33 -0.25611371E-09 0.60000000 34 -0.12805685E-09 0.60000000 35 -0.64028427E-10 0.60000000 36 -0.32014214E-10 0.60000000 37 -0.16007107E-10 0.60000000 38 -0.80035534E-11 0.60000000 39 -0.40017767E-11 0.60000000 # Real Root Complex Root Sqrt(real**2 + imag**2) 1 -2.0270202 -0.16767368 2.0339433 2 -2.0270202 0.16767368 2.0339433 3 1.2009428 0.0000000 1.2009428 4 -0.55869842 1.8710246 1.9526589 5 -0.55869842 -1.8710246 1.9526589 6 1.9726091 0.34357946 2.0023071 7 1.9726091 -0.34357946 2.0023071 8 -1.4739596 1.3598006 2.0053964 9 -1.4739596 -1.3598006 2.0053964 10 1.3368414 1.5128439 2.0188714 11 1.3368414 -1.5128439 2.0188714 12 -1.9694713 0.49795910 2.0314479 13 -1.9694713 -0.49795910 2.0314479 14 0.44701438 1.9577780 2.0081624 15 0.44701438 -1.9577780 2.0081624 16 1.8903803 0.67577400 2.0075378 17 1.8903803 -0.67577400 2.0075378 18 -0.60062641 1.5533997 1.6654737 19 -0.60062641 -1.5533997 1.6654737 20 -1.8559303 0.81316219 2.0262552 21 -1.8559303 -0.81316219 2.0262552 22 -0.90884792 1.7359314 1.9594546 23 -0.90884792 -1.7359314 1.9594546 24 -0.22161577 1.9666199 1.9790673 25 -0.22161577 -1.9666199 1.9790673 26 1.7544288 0.98690692 2.0129594 27 1.7544288 -0.98690692 2.0129594 28 0.76784445 1.8628932 2.0149333 29 0.76784445 -1.8628932 2.0149333 30 -1.6893926 1.1035520 2.0178885 31 -1.6893926 -1.1035520 2.0178885 32 1.0674094 1.7129565 2.0183119 33 1.0674094 -1.7129565 2.0183119 34 0.11425680 1.9936496 1.9969210 35 0.11425680 -1.9936496 1.9969210 36 1.5681318 1.2685118 2.0169679 37 1.5681318 -1.2685118 2.0169679 38 -1.2138253 1.5729916 1.9868756 39 -1.2138253 -1.5729916 1.9868756 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 STAT. PROC. STEP PAGE 118 Polynomial Solver Input Order Input Coefficient 0 1.0000000 1 -3.0000000 2 4.0000000 3 -2.0000000 Root # Real Root Imag. Root 1 1.0000000 0.0000000 2 0.50000000 0.50000000 3 0.50000000 -0.50000000 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 KFILTER STEP PAGE 119 KF CONTROL CARD READ IOPT NSERIE IBEGIN IEND IUNIT ICON IB34S(I),I=1... 0 2 0 0 0 0 2 3 SET UP TO RUN FOR 296 OBSERVATIONS SERIES # B34S VARIABLE # NAME 1 2 GASIN 2 3 GASOUT THESE ROUTINES WERE OBTAINED FROM MASANAO AOKI AND WERE CONVERTED BY HOUSTON H. STOKES FOR FURTHER DETAIL SEE 'STATE SPACE MODELING OF TIME SERIES' BY AOKI, SPRINGER(1987) ******************** VERSION DATE 1 JANUARY 1987 ******************** ******************** AOKI1 OPTION SELECTED ******************** STATE SPACE PROGRAM AOKI1. WRITTEN BY MASANAO AOKI. MODIFIED FOR B34S BY HOUSTON H. STOKES JANUARY 1988. MODEL ESTIMATED. Y(T) = C * X(T) + E(T) X(T+1) = A * X(T) + B * E(T) E(E(T)E(T)') = DELTA E(X(T)X(T)') = PI FOR THIS PROBLEM K (NUMBER OF LAGS ON HANKEL MATRIX) = 8 NSTAR (DIMENSION OF STATE VECTOR) = 5 MXITER (MAXIMUM NUMBER OF ITERATIONS) = 500 EPS (STEP SIZE) = 0.50000000E-01 P (NUMBER OF SERIES) = 2 IOLDD (= 0 IF WANT EISPACK) = 0 DIFFERENCING OPERATOR - NEW(T)= OLD(T) - OLD(T-DIF) 0 0 LOG OPERATOR - IF LOG NE 1, NEW = LOG(OLD) 0 0 AOKI1 PROGRAM REQUIRES 22765 REAL*4 WORDS OF SPACE. 12000000 WAS AVAILABLE SERIES # MEAN 1 -0.56834459E-01 2 53.509122 SERIES 1 SLOPE= -0.38228485E-02 INTERCEPT= 0.51085854 SERIES 2 SLOPE= 0.15004026E-01 INTERCEPT= 51.281024 Means of Series used -0.568345E-01 53.5091 Sums of Squares 340.450 850540. SUM (X(T) - XBAR)**2 339.494 3024.81 SERIES 1 SLOPE= -0.76147219E-03 INTERCEPT= 0.11307862 SERIES 2 SLOPE= 0.29886479E-02 INTERCEPT= -0.44381421 Variances 1.146937901650383 -1.658526509998173 -1.658526509998173 10.21893706628927 1 LAG 1.0924 -1.3470 -2.0487 9.9201 SINGULAR VALUES 42.932 4.3061 1.5686 0.47783 0.12362 0.46122E-01 0.25228E-01 0.69604E-02 0.42498E-02 0.30743E-02 0.23122E-02 0.18644E-02 0.15934E-02 0.94173E-03 0.37753E-03 0.10066E-03 1.0D+00/DSQRT(N)= 5.812381937190964E-02 100 * SUMEI / SUMEIG 100 * SUMSI / SUMSIN THISS REMA DROP 1 98.860263 86.729675 1.0000000 0.15300789 1.0000000 2 99.854812 95.428688 0.10030031 0.52707584E-01 9.9700590 3 99.986781 98.597480 0.36536414E-01 0.16171170E-01 2.7452149 4 99.999027 99.562760 0.11129755E-01 0.50414142E-02 3.2827689 5 99.999847 99.812481 0.28793032E-02 0.21621110E-02 3.8654336 6 99.999961 99.905654 0.10742893E-02 0.10878216E-02 2.6801934 7 99.999995 99.956618 0.58762908E-03 0.50019255E-03 1.8281760 8 99.999998 99.970680 0.16212503E-03 0.33806752E-03 3.6245425 9 99.999999 99.979265 0.98988110E-04 0.23907940E-03 1.6378233 10 99.999999 99.985475 0.71607154E-04 0.16747225E-03 1.3823774 11 100.00000 99.990146 0.53857559E-04 0.11361469E-03 1.3295655 12 100.00000 99.993913 0.43426086E-04 0.70188606E-04 1.2402121 13 100.00000 99.997132 0.37115144E-04 0.33073462E-04 1.1700368 14 100.00000 99.999034 0.21935109E-04 0.11138353E-04 1.6920429 15 100.00000 99.999797 0.87936953E-05 0.23446577E-05 2.4944131 16 100.00000 100.00000 0.23446577E-05 0.0000000 3.7505241 SUM EIGENVALUES (SUMEIG) = 1864.4435 SUM SQRT(ABS(EIGENVAL)) (SUMSIN) = 49.501433 SUMSI(I) = SUM(S(I)), SUMEI(I) = SUM(SQRT(ABS(S(I)))) THISS(I) = SQRT(ABS(S(I)) /SQRT(ABS(S(I-1))) REMA = (SUMSIN - SUMSI) / SQRT(S(I-1)) DROP = SQRT(S(I)) / SQRT(S(I-1)) SINGULAR VALUES OF H = SQRT(EIGENVALUES OF H'H) Eigenvalues of A: ( 0.89552084 , 0.0000000 ) R = 0.89552084 THETA = 0.0000000 ( 0.73020120 , 0.33157203 ) R = 0.80195624 THETA = 0.42624424 ( 0.73020120 , -0.33157203 ) R = 0.80195624 THETA = -0.42624424 ( 0.88546807 , 0.40304941 ) R = 0.97288361 THETA = 0.42715518 ( 0.88546807 , -0.40304941 ) R = 0.97288361 THETA = -0.42715518 m matrix. 1 2 1 -1.16603 3.02651 2 1.38955 0.369718 3 -0.146956 -0.505962 4 -0.318382 0.234847E-01 5 -0.119215 0.420601E-01 c matrix. 1 2 3 4 5 1 -0.483775 0.353517 0.381781E-01 -0.177862 0.987818E-01 2 3.21275 1.26089 0.517491 -0.588180E-01 0.256398E-01 Pi Matrix - Deviation= 0.27658630 DELTA MATRIX 1 2 1 0.276870E-01 -0.669374E-01 2 -0.669374E-01 0.782411 Pi Matrix - Deviation= 0.26604395 Pi Matrix 1 2 3 4 5 1 1.38085 -1.00625 -0.133357E-01 0.215017 0.101811 2 -1.00625 2.91851 -1.25845 -1.09383 -0.718226 3 -0.133357E-01 -1.25845 1.59776 1.10849 0.877830 4 0.215017 -1.09383 1.10849 0.948480 0.724101 5 0.101811 -0.718226 0.877830 0.724101 0.892022 DELTA INVERSE 1 2 1 45.5366 3.89579 2 3.89579 1.61140 B * DELTA MATRIX 1 2 1 -0.570957E-01 0.199737 2 0.979015E-01 0.312804E-01 3 -0.160058 0.607823E-01 4 -0.129192 0.115685 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 5 KFILTER STEP PAGE 120 5 -0.141136 0.106090 B MATRIX 1 2 1 -1.82181 0.994225E-01 2 4.57997 0.431809 3 -7.05170 -0.525607 4 -5.43227 -0.316889 5 -6.01355 -0.378883 PREDICT. MULTIPLIER 1 2 3 4 5 1 -0.310901 0.404761 -0.411568E-02 -0.310407 0.175158 2 0.844077 -1.48595 -0.848271 0.829523 -0.478175 3 -1.68174 3.46496 1.26243 -1.08094 0.633125 4 -1.63140 2.46143 0.162887 -0.969639E-01 0.728991 5 -1.68726 2.62297 0.431956 -1.62669 1.55405 EIGENVALUES OF PRED: ( -0.49284211 , 0.0000000 ) R = 0.49284211 THETA = 3.1415927 ( -0.18739788 , 0.57480521 ) R = 0.60458167 THETA = 1.8859503 ( -0.18739788 , -0.57480521 ) R = 0.60458167 THETA = -1.8859503 ( 0.89514998 , 0.38294387 ) R = 0.97362185 THETA = 0.40423866 ( 0.89514998 , -0.38294387 ) R = 0.97362185 THETA = -0.40423866 N= 296 SUMS OF SQUARES BEFORE 339.5 3025. SUM AFTER 17.42 352.0 PERCENTAGE REDUCTION 94.87 PERCENTAGE REDUCTION 88.36 SUM AFTER UPDATE 17.42 352.0 PERCENTAGE REDUCTION 94.87 PERCENTAGE REDUCTION 88.36 PREDICTED VALUES (OUT OF SAMPLE) 296 -0.3728 56.19 297 -0.5081 55.08 298 -0.5699 54.42 299 -0.5517 54.19 300 -0.4673 54.26 301 -0.3436 54.51 302 -0.2121 54.80 303 -0.1006 55.02 304 -0.2911E-01 55.12 305 -0.6275E-02 55.06 306 -0.2970E-01 54.87 307 -0.8784E-01 54.59 308 -0.1634 54.26 309 -0.2374 53.95 310 -0.2928 53.70 311 -0.3179 53.55 312 -0.3076 53.49 313 -0.2643 53.54 314 -0.1963 53.65 315 -0.1162 53.80 316 -0.3831E-01 53.95 317 0.2434E-01 54.06 318 0.6210E-01 54.11 RESIDUALS FOR SERIES 1 MEAN = -0.29166749E-04 VARIANCE = 0.59035684E-01 AUTOCORRELATIONS 1-12 -0.558 0.174 0.140 -0.140 0.002 0.054 -0.027 0.030 -0.051 -0.031 0.148 -0.198 13-24 0.112 0.048 -0.092 0.016 0.065 -0.051 -0.044 0.065 -0.020 -0.016 0.037 -0.013 25-36 0.003 -0.044 0.077 -0.044 -0.013 0.019 0.019 -0.035 0.068 -0.032 0.061 -0.044 37-48 0.005 0.047 -0.085 0.031 0.019 -0.052 0.023 0.034 -0.041 0.038 -0.049 0.070 RESIDUALS FOR SERIES 2 MEAN = 0.56561075E-02 VARIANCE = 1.1931025 AUTOCORRELATIONS 1-12 -0.503 0.020 0.235 -0.118 -0.017 0.068 -0.014 0.015 -0.078 0.019 0.157 -0.222 13-24 0.098 0.074 -0.142 -0.007 0.109 -0.065 -0.072 0.066 -0.027 -0.021 0.029 -0.008 25-36 0.009 -0.027 0.076 -0.030 -0.031 0.028 0.003 -0.053 0.064 -0.039 0.052 -0.039 37-48 0.002 0.064 -0.071 0.046 0.018 -0.068 0.035 0.038 -0.037 0.025 -0.023 0.067 AUTOCOVARIANCES OF ERROR TERMS 0 0.58795E-01 -0.15722 -0.15722 1.1869 1 -0.32796E-01 0.32324E-01 0.23781 -0.59922 2 0.10261E-01 0.41860E-01 -0.15597 0.19841E-01 3 0.82060E-02 -0.38341E-01 0.63704E-02 0.27729 4 -0.82387E-02 -0.44293E-02 0.57643E-01 -0.14288 5 0.19866E-03 0.94256E-02 -0.30705E-01 -0.26105E-01 6 0.31418E-02 -0.44496E-02 -0.43411E-02 0.79143E-01 7 -0.15420E-02 0.10034E-01 0.14905E-01 -0.18656E-01 8 0.17728E-02 -0.17346E-01 -0.10146E-01 0.13452E-01 9 -0.30251E-02 0.30480E-02 0.58359E-02 -0.94769E-01 10 -0.18216E-02 0.37570E-01 -0.88517E-02 0.25046E-01 11 0.87506E-02 -0.56207E-01 -0.17566E-02 0.18386 12 -0.11730E-01 0.30471E-01 0.40839E-01 -0.26464 13 0.65943E-02 0.15083E-01 -0.57979E-01 0.11754 14 0.28968E-02 -0.30124E-01 0.22762E-01 0.89125E-01 15 -0.54069E-02 0.21593E-02 0.18392E-01 -0.16818 16 0.94362E-03 0.20918E-01 -0.26598E-01 -0.77400E-02 17 0.38193E-02 -0.11091E-01 0.41348E-02 0.12946 18 -0.30105E-02 -0.10651E-01 0.27290E-01 -0.77618E-01 19 -0.26084E-02 0.16245E-01 -0.15556E-01 -0.85807E-01 20 0.37884E-02 -0.93880E-02 -0.13992E-01 0.80956E-01 21 -0.11394E-02 -0.75229E-02 0.21196E-01 -0.31688E-01 22 -0.97749E-03 0.45273E-02 -0.67597E-02 -0.25189E-01 23 0.21618E-02 -0.24471E-02 -0.96486E-02 0.33625E-01 B34S KALMAN FILTER OPTION ENDING B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 DATA STEP Weighted Data fron Glass(1954) PAGE 121 Variable Label # Cases Mean Std. Dev. Variance Maximum Minimum FATHER 1 Father 25 3.00000 1.44338 2.08333 5.00000 1.00000 SON 2 Son 25 3.00000 1.44338 2.08333 5.00000 1.00000 COUNT 3 Count or weight 25 140.000 171.013 29245.3 714.000 3.00000 INCOME 4 Mean income 25 688.920 144.818 20972.2 875.000 361.000 CONSTANT 5 25 1.00000 0.00000 0.00000 1.00000 1.00000 Number of observations in data file 25 Current missing variable code 1.000000000000000E+31 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 DATA STEP Expanded data PAGE 122 Variable Label # Cases Mean Std. Dev. Variance Maximum Minimum FATHER 1 Father 3500 3.70086 1.09479 1.19857 5.00000 1.00000 SON 2 Son 3500 3.78914 1.09956 1.20903 5.00000 1.00000 INCOME 3 Mean income 3500 792.514 105.097 11045.4 875.000 361.000 CONSTANT 4 3500 1.00000 0.00000 0.00000 1.00000 1.00000 Number of observations in data file 3500 Current missing variable code 1.000000000000000E+31 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 DESCRIBE STEP Expanded data PAGE 123 Describe Command. Version 1 July 1997 Series FATHER Label: Father Number of observations 3500 Number of nonmissing observations 3500 Mean of series 3.700857142857143 Median of series 4.000000000000000 Standard deviation of series 1.094792348067734 Variance of series 1.198570285387662 Skewness of series -0.7088879825803317 Kurtosis of series -0.3031812993004968 C6 -4.493141804761946 Coefficient of Variation 3.087726425372000 Maximum of Series 5.000000000000000 Minimum of Series 1.000000000000000 1st Quartile 3.000000000000000 3rd Quartile 4.000000000000000 Maximim - Minimum 4.000000000000000 Q3 - Q1 1.000000000000000 Series SON Label: Son Number of observations 3500 Number of nonmissing observations 3500 Mean of series 3.789142857142857 Median of series 4.000000000000000 Standard deviation of series 1.099557892470596 Variance of series 1.209027558894378 Skewness of series -0.7537614935292055 Kurtosis of series -0.3041035878027154 C6 -4.923089481434747 Coefficient of Variation 3.134041758823036 Maximum of Series 5.000000000000000 Minimum of Series 1.000000000000000 1st Quartile 3.000000000000000 3rd Quartile 5.000000000000000 Maximim - Minimum 4.000000000000000 Q3 - Q1 2.000000000000000 Series INCOME Label: Mean income Number of observations 3500 Number of nonmissing observations 3500 Mean of series 792.5142857142857 Median of series 852.0000000000000 Standard deviation of series 105.0973123630533 Variance of series 11045.44506593721 Skewness of series -1.930126537829592 Kurtosis of series 3.886878596931728 C6 -19.43099926551731 Coefficient of Variation 7.175032612839678E-02 Maximum of Series 875.0000000000000 Minimum of Series 361.0000000000000 1st Quartile 762.0000000000000 3rd Quartile 852.0000000000000 Maximim - Minimum 514.0000000000000 Q3 - Q1 90.00000000000000 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 FREQ STEP Expanded data PAGE 124 FREQ Command. Version 1 August 1997 Series FATHER Label: Father Class Value Count Percentage Cumulative % 1 1.0000000 129.00000 0.36857143E-01 0.36857143E-01 2 2.0000000 495.00000 0.14142857 0.17828571 3 3.0000000 518.00000 0.14800000 0.32628571 4 4.0000000 1510.0000 0.43142857 0.75771429 5 5.0000000 848.00000 0.24228571 1.0000000 Frequency--- - 1532 * * 1501 * I * 1470 * I * 1439 * I * 1408 * I * 1377 * I * 1346 * I * 1315 * I * 1284 * I * 1253 * I * 1222 * I * 1191 * I * 1160 * I * 1129 * I * 1098 * I * 1067 * I * 1036 * I * 1005 * I * 974 * I * 943 * I * 912 * I * 881 * I * 850 * I * 819 * II * 788 * II * 757 * II * 726 * II * 695 * II * 664 * II * 633 * II * 602 * II * 571 * II * 540 * II * 509 * III * 478 * IIII * 447 * IIII * 416 * IIII * 385 * IIII * 354 * IIII * 323 * IIII * 292 * IIII * 261 * IIII * 230 * IIII * 199 * IIII * 168 * IIII * 137 * IIII * 106 *IIIII * 75 *IIIII * 44 *IIIII * 13 *IIIII * ------------ - Class 5 Class -- - - - - - - - - - - - - - - - 5 *IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII * * * 4 *IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII * * * 3 *IIIIIIIIIIIIIIIIIII * * * 2 *IIIIIIIIIIIIIIIIIII * * * 1 *IIII * ----------------- Frequency 5 10 15 20 25 30 35 40 45 50 55 One frequency unit is equal to 26 count unit(s) Series SON Label: Son Class Value Count Percentage Cumulative % 1 1.0000000 106.00000 0.30285714E-01 0.30285714E-01 2 2.0000000 489.00000 0.13971429 0.17000000 3 3.0000000 459.00000 0.13114286 0.30114286 4 4.0000000 1429.0000 0.40828571 0.70942857 5 5.0000000 1017.0000 0.29057143 1.0000000 Frequency--- - 1437 * * 1408 * I * 1379 * I * 1350 * I * 1321 * I * 1292 * I * 1263 * I * 1234 * I * 1205 * I * 1176 * I * 1147 * I * 1118 * I * 1089 * I * 1060 * I * 1031 * I * 1002 * II * 973 * II * 944 * II * 915 * II * 886 * II * 857 * II * 828 * II * 799 * II * 770 * II * 741 * II * 712 * II * 683 * II * 654 * II * 625 * II * 596 * II * 567 * II * 538 * II * 509 * II * 480 * I II * 451 * IIII * 422 * IIII * 393 * IIII * 364 * IIII * 335 * IIII * 306 * IIII * 277 * IIII * 248 * IIII * 219 * IIII * 190 * IIII * 161 * IIII * 132 * IIII * 103 *IIIII * 74 *IIIII * 45 *IIIII * 16 *IIIII * ------------ - Class 5 Class -- - - - - - - - - - - - - - - - 5 *IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII * * * 4 *IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII * * * 3 *IIIIIIIIIIIIIIIIIII * * * 2 *IIIIIIIIIIIIIIIIIIII * * * 1 *IIII * ----------------- Frequency 5 10 15 20 25 30 35 40 45 50 55 One frequency unit is equal to 24 count unit(s) Series INCOME Label: Mean income Class Value Count Percentage Cumulative % 1 361.00000 50.000000 0.14285714E-01 0.14285714E-01 2 431.00000 28.000000 0.80000000E-02 0.22285714E-01 3 492.00000 11.000000 0.31428571E-02 0.25428571E-01 4 496.00000 14.000000 0.40000000E-02 0.29428571E-01 5 512.00000 45.000000 0.12857143E-01 0.42285714E-01 6 582.00000 3.0000000 0.85714286E-03 0.43142857E-01 7 631.00000 174.00000 0.49714286E-01 0.92857143E-01 8 634.00000 8.0000000 0.22857143E-02 0.95142857E-01 9 652.00000 84.000000 0.24000000E-01 0.11914286 10 670.00000 78.000000 0.22285714E-01 0.14142857 11 683.00000 150.00000 0.42857143E-01 0.18428571 12 684.00000 18.000000 0.51428571E-02 0.18942857 13 696.00000 42.000000 0.12000000E-01 0.20142857 14 718.00000 8.0000000 0.22857143E-02 0.20371429 15 732.00000 110.00000 0.31428571E-01 0.23514286 16 762.00000 72.000000 0.20571429E-01 0.25571429 17 763.00000 185.00000 0.52857143E-01 0.30857143 18 793.00000 154.00000 0.44000000E-01 0.35257143 19 815.00000 55.000000 0.15714286E-01 0.36828571 20 831.00000 223.00000 0.63714286E-01 0.43200000 21 842.00000 96.000000 0.27428571E-01 0.45942857 22 852.00000 1161.0000 0.33171429 0.79114286 23 864.00000 320.00000 0.91428571E-01 0.88257143 24 875.00000 411.00000 0.11742857 1.0000000 Frequency--- - - - - - - 1170 * * 1146 * I * 1122 * I * 1098 * I * 1074 * I * 1050 * I * 1026 * I * 1002 * I * 978 * I * 954 * I * 930 * I * 906 * I * 882 * I * 858 * I * 834 * I * 810 * I * 786 * I * 762 * I * 738 * I * 714 * I * 690 * I * 666 * I * 642 * I * 618 * I * 594 * I * 570 * I * 546 * I * 522 * I * 498 * I * 474 * I * 450 * I * 426 * I * 402 * I I * 378 * I I * 354 * I I * 330 * I I * 306 * III * 282 * III * 258 * III * 234 * III * 210 * I III * 186 * I III * 162 * I I I III * 138 * I I II I III * 114 * I I II I III * 90 * I I I II IIIII * 66 * I III IIII IIIII * 42 *I I I III I IIIIIIIIII * 18 *II I I IIIII IIIIIIIIII * ------------ - - - - - - Class 5 10 15 20 Class -- - - - - - - - - - - - - - - - 24 *IIIIIIIIIIIIIIIIIIII * * * 23 *IIIIIIIIIIIIIIII * * * 22 *IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII * * * 21 *IIII * * * 20 *IIIIIIIIIII * * * 19 *II * * * 18 *IIIIIII * * * 17 *IIIIIIIII * * * 16 *III * * * 15 *IIIII * * * 14 * * * * 13 *II * * * 12 * * * * 11 *IIIIIII * * * 10 *III * * * 9 *IIII * * * 8 * * * * 7 *IIIIIIII * * * 6 * * * * 5 *II * * * 4 * * * * 3 * * * * 2 *I * * * 1 *II * ----------------- Frequency 5 10 15 20 25 30 35 40 45 50 55 One frequency unit is equal to 20 count unit(s) Cross Tabulations of: Series FATHER Label: Father Series SON Label: Son Chi-Squared statistic for table 1176.527790738906 Degrees of Freedom 16.00000000000000 Exact Mean 16.00457273506716 Exact Standard Deviation 5.658752249111912 Exact Probability of 2x2 0.000000000000000E+00 Tochers Probability of 2x2 0.000000000000000E+00 Rows are 5 classes of FATHER Cols are 5 classes of SON Bottom row is column totals Right hand column is row totals Actual counts 1 2 3 4 5 6 1 50.00000 45.00000 8.00000 18.00000 8.00000 129.00000 2 28.00000 174.00000 84.00000 154.00000 55.00000 495.00000 3 11.00000 78.00000 110.00000 223.00000 96.00000 518.00000 4 14.00000 150.00000 185.00000 714.00000 447.00000 1510.00000 5 3.00000 42.00000 72.00000 320.00000 411.00000 848.00000 6 106.00000 489.00000 459.00000 1429.00000 1017.00000 3500.00000 Expected counts 1 2 3 4 5 6 1 3.90686 18.02314 16.91743 52.66886 37.48371 129.00000 2 14.99143 69.15857 64.91571 202.10143 143.83286 495.00000 3 15.68800 72.37200 67.93200 211.49200 150.51600 518.00000 4 45.73143 210.96857 198.02571 616.51143 438.76286 1510.00000 5 25.68229 118.47771 111.20914 346.22629 246.40457 848.00000 6 106.00000 489.00000 459.00000 1429.00000 1017.00000 3500.00000 Chi-Square Value 1 2 3 4 5 6 1 543.80740 40.37869 4.70051 22.82050 23.19112 634.89822 2 11.28798 158.93511 5.61051 11.44845 54.86421 242.14625 3 1.40090 0.43766 26.05130 0.62619 19.74537 48.26142 4 22.01732 17.61953 0.85680 15.41581 0.15464 56.06410 5 20.03272 49.36659 13.82402 1.98661 109.94786 195.15780 6 598.54632 266.73757 51.04313 52.29756 207.90321 1176.52779 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 DATA STEP Data from prior step PAGE 125 Variable Label # Cases Mean Std. Dev. Variance Maximum Minimum FATHER 1 Father 3500 3.49543 0.778925 0.606724 4.00000 2.00000 SON 2 Son 3500 3.52886 0.767682 0.589336 4.00000 2.00000 INCOME 3 Mean income 3500 792.514 105.097 11045.4 875.000 361.000 CONSTANT 4 3500 1.00000 0.00000 0.00000 1.00000 1.00000 Number of observations in data file 3500 Current missing variable code 1.000000000000000E+31 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 FREQ STEP Data from prior step PAGE 126 FREQ Command. Version 1 August 1997 Series FATHER Label: Father Class Value Count Percentage Cumulative % 1 2.0000000 624.00000 0.17828571 0.17828571 2 3.0000000 518.00000 0.14800000 0.32628571 3 4.0000000 2358.0000 0.67371429 1.0000000 Series SON Label: Son Class Value Count Percentage Cumulative % 1 2.0000000 595.00000 0.17000000 0.17000000 2 3.0000000 459.00000 0.13114286 0.30114286 3 4.0000000 2446.0000 0.69885714 1.0000000 Series INCOME Label: Mean income Class Value Count Percentage Cumulative % 1 361.00000 50.000000 0.14285714E-01 0.14285714E-01 2 431.00000 28.000000 0.80000000E-02 0.22285714E-01 3 492.00000 11.000000 0.31428571E-02 0.25428571E-01 4 496.00000 14.000000 0.40000000E-02 0.29428571E-01 5 512.00000 45.000000 0.12857143E-01 0.42285714E-01 6 582.00000 3.0000000 0.85714286E-03 0.43142857E-01 7 631.00000 174.00000 0.49714286E-01 0.92857143E-01 8 634.00000 8.0000000 0.22857143E-02 0.95142857E-01 9 652.00000 84.000000 0.24000000E-01 0.11914286 10 670.00000 78.000000 0.22285714E-01 0.14142857 11 683.00000 150.00000 0.42857143E-01 0.18428571 12 684.00000 18.000000 0.51428571E-02 0.18942857 13 696.00000 42.000000 0.12000000E-01 0.20142857 14 718.00000 8.0000000 0.22857143E-02 0.20371429 15 732.00000 110.00000 0.31428571E-01 0.23514286 16 762.00000 72.000000 0.20571429E-01 0.25571429 17 763.00000 185.00000 0.52857143E-01 0.30857143 18 793.00000 154.00000 0.44000000E-01 0.35257143 19 815.00000 55.000000 0.15714286E-01 0.36828571 20 831.00000 223.00000 0.63714286E-01 0.43200000 21 842.00000 96.000000 0.27428571E-01 0.45942857 22 852.00000 1161.0000 0.33171429 0.79114286 23 864.00000 320.00000 0.91428571E-01 0.88257143 24 875.00000 411.00000 0.11742857 1.0000000 Cross Tabulations of: Series FATHER Label: Father Series SON Label: Son Chi-Squared statistic for table 605.5791843481634 Degrees of Freedom 4.000000000000000 Exact Mean 4.001143183766790 Exact Standard Deviation 2.827298641708804 Exact Probability of 2x2 0.000000000000000E+00 Tochers Probability of 2x2 0.000000000000000E+00 Rows are 3 classes of FATHER Cols are 3 classes of SON Bottom row is column totals Right hand column is row totals Actual counts 1 2 3 4 1 297.00000 92.00000 235.00000 624.00000 2 89.00000 110.00000 319.00000 518.00000 3 209.00000 257.00000 1892.00000 2358.00000 4 595.00000 459.00000 2446.00000 3500.00000 Expected counts 1 2 3 4 1 106.08000 81.83314 436.08686 624.00000 2 88.06000 67.93200 362.00800 518.00000 3 400.86000 309.23486 1647.90514 2358.00000 4 595.00000 459.00000 2446.00000 3500.00000 Chi-Square Value 1 2 3 4 1 343.61281 1.26312 92.72447 437.60040 2 0.01003 26.05130 5.10952 31.17085 3 91.82822 8.82333 36.15639 136.80793 4 435.45106 36.13774 133.99038 605.57918 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 LPMAX STEP Data from prior step PAGE 127 LPMAX Command. Version 1 September 1997 Real*8 space available 6000000 Real*8 space used 93 Number of activities (X) 2 Number of constraints (m1+m2) 4 Number of inquality constraints (m1) 4 Number of equality constraints (m2) 0 Constraint Matrix (A) 1 2 1 1.00000 0.00000 2 0.00000 1.00000 3 1.00000 1.00000 4 -1.00000 -1.00000 Constraint vector (B) 1.00000 1.00000 1.50000 -0.500000 Cost vector (C) 1.00000 3.00000 Objective function maximized at 3.500000000000000 Primal values 0.500000 1.00000 Dual values 0.00000 2.00000 1.00000 0.00000 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 LPMAX STEP Data from prior step PAGE 128 LPMAX Command. Version 1 September 1997 Real*8 space available 6000000 Real*8 space used 85 Number of activities (X) 4 Number of constraints (m1+m2) 3 Number of inquality constraints (m1) 3 Number of equality constraints (m2) 0 Constraint Matrix (A) 1 2 3 4 1 1.50000 1.00000 2.40000 1.00000 2 1.00000 5.00000 1.00000 3.50000 3 1.50000 3.00000 3.50000 1.00000 Constraint vector (B) 2000.00 8000.00 5000.00 Cost vector (C) 5.24000 7.30000 8.34000 4.18000 Objective function maximized at 12737.05882352941 Primal values 294.118 1500.00 0.00000 58.8235 Dual values 1.95353 0.242353 1.37824 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 LPMAX STEP Data from prior step PAGE 129 LPMAX Command. Version 1 September 1997 Real*8 space available 6000000 Real*8 space used 54 Number of activities (X) 2 Number of constraints (m1+m2) 2 Number of inquality constraints (m1) 2 Number of equality constraints (m2) 0 Constraint Matrix (A) 1 2 1 3.00000 5.00000 2 5.00000 2.00000 Constraint vector (B) 15.0000 10.0000 Cost vector (C) 5.00000 3.00000 Objective function maximized at 12.36842105263158 Primal values 1.05263 2.36842 Dual values 0.263158 0.842105 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 LPMAX STEP Data from prior step PAGE 130 LPMAX Command. Version 1 September 1997 Real*8 space available 6000000 Real*8 space used 85 Number of activities (X) 4 Number of constraints (m1+m2) 3 Number of inquality constraints (m1) 3 Number of equality constraints (m2) 0 Constraint Matrix (A) 1 2 3 4 1 1.00000 3.00000 2.00000 5.00000 2 -2.00000 -16.0000 -1.00000 -1.00000 3 3.00000 -1.00000 -5.00000 10.0000 Constraint vector (B) 20.0000 -4.00000 -10.0000 Cost vector (C) 2.00000 1.00000 4.00000 5.00000 Objective function maximized at 40.00000000000000 Primal values 7.27273 0.00000 6.36364 0.00000 Dual values 2.00000 0.00000 0.555112E-16 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 LPMAX STEP Data from prior step PAGE 131 LPMAX Command. Version 1 September 1997 Real*8 space available 6000000 Real*8 space used 93 Number of activities (X) 2 Number of constraints (m1+m2) 4 Number of inquality constraints (m1) 4 Number of equality constraints (m2) 0 Constraint Matrix (A) 1 2 1 1.00000 0.00000 2 0.00000 1.00000 3 1.00000 1.00000 4 -1.00000 -1.00000 Constraint vector (B) 1.00000 1.00000 1.50000 -0.500000 Cost vector (C) 1.00000 3.00000 Objective function maximized at 3.500000000000000 Primal values 0.500000 1.00000 Dual values 0.00000 2.00000 1.00000 0.00000 Simulation for: A( 2 , 1 ) Number of steps 10 Begin value 0.000000000000000E+00 End value 3.500000000000000 Results saved in formated DMF on unit 60 DMF name set as ASIM File rewound. Changing A( 2 1 ) = 0.000000000000000E+00 Objective function maximized at 3.500000000000000 Primal values 0.500000 1.00000 Dual values 0.00000 2.00000 1.00000 0.00000 Changing A( 2 1 ) = 0.3500000000000000 Objective function maximized at 3.000000000000000 Primal values 0.00000 1.00000 Dual values B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 LPMAX STEP Data from prior step PAGE 132 0.00000 3.00000 0.00000 0.00000 Changing A( 2 1 ) = 0.7000000000000000 Objective function maximized at 3.000000000000000 Primal values 0.00000 1.00000 Dual values 0.00000 3.00000 0.00000 0.00000 Changing A( 2 1 ) = 1.050000000000000 Objective function maximized at 3.000000000000000 Primal values 0.00000 1.00000 Dual values 0.00000 3.00000 0.00000 0.00000 Changing A( 2 1 ) = 1.400000000000000 Objective function maximized at 3.000000000000000 Primal values 0.00000 1.00000 Dual values 0.00000 3.00000 0.00000 0.00000 Changing A( 2 1 ) = 1.750000000000000 Objective function maximized at 3.000000000000000 Primal values 0.00000 1.00000 Dual values 0.00000 3.00000 0.00000 0.00000 Changing A( 2 1 ) = 2.100000000000000 Objective function maximized at 3.000000000000000 Primal values 0.00000 1.00000 Dual values 0.00000 3.00000 0.00000 0.00000 Changing A( 2 1 ) = 2.450000000000000 Objective function maximized at 3.000000000000000 Primal values 0.00000 1.00000 Dual values 0.00000 3.00000 0.00000 0.00000 Changing A( 2 1 ) = 2.800000000000000 Objective function maximized at 2.999999999999999 Primal values 0.00000 1.00000 Dual values B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 LPMAX STEP Data from prior step PAGE 133 0.00000 3.00000 0.00000 0.00000 Changing A( 2 1 ) = 3.150000000000000 Objective function maximized at 3.000000000000000 Primal values 0.00000 1.00000 Dual values 0.00000 3.00000 0.00000 0.00000 Changing A( 2 1 ) = 3.500000000000000 Objective function maximized at 3.000000000000000 Primal values 0.00000 1.00000 Dual values 0.00000 3.00000 0.00000 0.444089E-15 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 LPMAX STEP Data from prior step PAGE 134 LPMAX Command. Version 1 September 1997 Real*8 space available 6000000 Real*8 space used 93 Number of activities (X) 2 Number of constraints (m1+m2) 4 Number of inquality constraints (m1) 4 Number of equality constraints (m2) 0 Constraint Matrix (A) 1 2 1 1.00000 0.00000 2 0.00000 1.00000 3 1.00000 1.00000 4 -1.00000 -1.00000 Constraint vector (B) 1.00000 1.00000 1.50000 -0.500000 Cost vector (C) 1.00000 3.00000 Objective function maximized at 3.500000000000000 Primal values 0.500000 1.00000 Dual values 0.00000 2.00000 1.00000 0.00000 Simulation for: B( 2 ) Number of steps 10 Begin value 0.5000000000000000 End value 7.500000000000000 Results saved in formated DMF on unit 60 DMF name set as BSIM File not rewound. Changing B( 2 ) = 0.5000000000000000 Objective function maximized at 2.500000000000000 Primal values 1.00000 0.500000 Dual values 1.00000 3.00000 0.00000 0.00000 Changing B( 2 ) = 1.200000000000000 Objective function maximized at 3.900000000000000 Primal values 0.300000 1.20000 Dual values B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 LPMAX STEP Data from prior step PAGE 135 0.00000 2.00000 1.00000 0.00000 Changing B( 2 ) = 1.900000000000000 Objective function maximized at 4.500000000000000 Primal values 0.00000 1.50000 Dual values 0.00000 0.00000 3.00000 0.00000 Changing B( 2 ) = 2.600000000000000 Objective function maximized at 4.500000000000000 Primal values 0.00000 1.50000 Dual values 0.00000 0.00000 3.00000 0.00000 Changing B( 2 ) = 3.300000000000000 Objective function maximized at 4.500000000000000 Primal values 0.00000 1.50000 Dual values 0.00000 0.00000 3.00000 0.00000 Changing B( 2 ) = 4.000000000000000 Objective function maximized at 4.500000000000000 Primal values 0.00000 1.50000 Dual values 0.00000 0.00000 3.00000 0.00000 Changing B( 2 ) = 4.699999999999999 Objective function maximized at 4.500000000000000 Primal values 0.00000 1.50000 Dual values 0.00000 0.00000 3.00000 0.00000 Changing B( 2 ) = 5.399999999999999 Objective function maximized at 4.500000000000000 Primal values 0.00000 1.50000 Dual values 0.00000 0.00000 3.00000 0.00000 Changing B( 2 ) = 6.100000000000000 Objective function maximized at 4.500000000000000 Primal values 0.00000 1.50000 Dual values B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 LPMAX STEP Data from prior step PAGE 136 0.00000 0.00000 3.00000 0.00000 Changing B( 2 ) = 6.800000000000000 Objective function maximized at 4.500000000000000 Primal values 0.00000 1.50000 Dual values 0.00000 0.00000 3.00000 0.00000 Changing B( 2 ) = 7.500000000000000 Objective function maximized at 4.500000000000000 Primal values 0.00000 1.50000 Dual values 0.00000 0.00000 3.00000 0.00000 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 LPMAX STEP Data from prior step PAGE 137 LPMAX Command. Version 1 September 1997 Real*8 space available 6000000 Real*8 space used 93 Number of activities (X) 2 Number of constraints (m1+m2) 4 Number of inquality constraints (m1) 4 Number of equality constraints (m2) 0 Constraint Matrix (A) 1 2 1 1.00000 0.00000 2 0.00000 1.00000 3 1.00000 1.00000 4 -1.00000 -1.00000 Constraint vector (B) 1.00000 1.00000 1.50000 -0.500000 Cost vector (C) 1.00000 3.00000 Objective function maximized at 3.500000000000000 Primal values 0.500000 1.00000 Dual values 0.00000 2.00000 1.00000 0.00000 Simulation for: C( 2 ) Number of steps 10 Begin value 0.5000000000000000 End value 1.500000000000000 Results saved in formated DMF on unit 60 DMF name set as CSIM File not rewound. Changing C( 2 ) = 0.5000000000000000 Objective function maximized at 1.250000000000000 Primal values 1.00000 0.500000 Dual values 0.500000 0.00000 0.500000 0.00000 Changing C( 2 ) = 0.6000000000000000 Objective function maximized at 1.300000000000000 Primal values 1.00000 0.500000 Dual values B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 LPMAX STEP Data from prior step PAGE 138 0.400000 0.00000 0.600000 0.00000 Changing C( 2 ) = 0.7000000000000000 Objective function maximized at 1.350000000000000 Primal values 1.00000 0.500000 Dual values 0.300000 0.00000 0.700000 0.00000 Changing C( 2 ) = 0.8000000000000000 Objective function maximized at 1.400000000000000 Primal values 1.00000 0.500000 Dual values 0.200000 0.00000 0.800000 0.00000 Changing C( 2 ) = 0.9000000000000000 Objective function maximized at 1.450000000000000 Primal values 1.00000 0.500000 Dual values 0.100000 0.00000 0.900000 0.00000 Changing C( 2 ) = 1.000000000000000 Objective function maximized at 1.500000000000000 Primal values 1.00000 0.500000 Dual values 0.00000 0.00000 1.00000 0.00000 Changing C( 2 ) = 1.100000000000000 Objective function maximized at 1.600000000000000 Primal values 0.500000 1.00000 Dual values 0.00000 0.100000 1.00000 0.00000 Changing C( 2 ) = 1.200000000000000 Objective function maximized at 1.700000000000000 Primal values 0.500000 1.00000 Dual values 0.00000 0.200000 1.00000 0.00000 Changing C( 2 ) = 1.300000000000000 Objective function maximized at 1.800000000000000 Primal values 0.500000 1.00000 Dual values B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 LPMAX STEP Data from prior step PAGE 139 0.00000 0.300000 1.00000 0.00000 Changing C( 2 ) = 1.400000000000000 Objective function maximized at 1.900000000000000 Primal values 0.500000 1.00000 Dual values 0.00000 0.400000 1.00000 0.00000 Changing C( 2 ) = 1.500000000000000 Objective function maximized at 2.000000000000000 Primal values 0.500000 1.00000 Dual values 0.00000 0.500000 1.00000 0.00000 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 DATA STEP MARS TEST DATA PAGE 140 Variable Label # Cases Mean Std. Dev. Variance Maximum Minimum X1 1 INPUT SERIES # 1 FROM FRIEDMAN 50 0.482860 0.285296 0.813936E-01 0.969000 0.160000E-01 X2 2 INPUT SERIES # 2 FROM FRIEDMAN 50 0.488140 0.284521 0.809520E-01 0.963000 0.120000E-01 X3 3 INPUT SERIES # 3 FROM FRIEDMAN 50 0.484320 0.290867 0.846033E-01 0.968000 0.800000E-02 X4 4 INPUT SERIES # 4 FROM FRIEDMAN 50 0.482980 0.292618 0.856253E-01 0.980000 0.300000E-02 X5 5 INPUT SERIES # 5 FROM FRIEDMAN 50 0.453760 0.279433 0.780826E-01 0.934000 0.800000E-02 Y 6 OUTPUT SERIES FROM FRIEDMAN 50 14.2065 4.79856 23.0262 24.7480 3.92500 CONSTANT 7 50 1.00000 0.00000 0.00000 1.00000 1.00000 Number of observations in data file 50 Current missing variable code 1.000000000000000E+31 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 REGRESSION STEP MARS TEST DATA PAGE 141 ******************************************************************** Problem Number 8 Subproblem Number 1 F to enter 9.999999776482582E-03 F to remove 4.999999888241291E-03 Tolerance (1.-R**2) for including a variable 1.000000000000000E-05 Maximum Number of Variables Allowed 6 Internal Number of dependent variable 6 Dependent Variable Y Standard Error of Y 4.798558968384292 Degrees of Freedom 49 ............. Step Number 6 Analysis of Variance for reduction in SS due to variable entering Variable Entering 3 Source DF SS MS F F Sig. Multiple R 0.821544 Due Regression 5 761.52 152.30 18.271 1.000000 Std Error of Y.X 2.88714 Dev. from Reg. 44 366.77 8.3356 R Square 0.674934 Total 49 1128.3 23.026 Multiple Regression Equation Variable Coefficient Std. Error T Val. T Sig. P. Cor. Elasticity Partial Cor. for Var. not in equation Y = Variable Coefficient F for selection X1 X- 1 7.073248 1.454214 4.864 0.99998 0.5913 0.2404 X2 X- 2 7.863029 1.459978 5.386 1.00000 0.6303 0.2702 X3 X- 3 -0.3064989 1.430539 -0.2143 0.16866 -0.0323 -0.1045E-01 X4 X- 4 9.610696 1.426141 6.739 1.00000 0.7127 0.3267 X5 X- 5 4.695815 1.494747 3.142 0.99700 0.4280 0.1500 CONSTANT X- 7 0.3287290 1.803096 0.1823 0.14383 Adjusted R Square 0.6379948084639820 -2 * ln(Maximum of Likelihood Function) 241.5289142370375 Akaike Information Criterion (AIC) 255.5289142370375 Scwartz Information Criterion (SIC) 268.9130752750345 Akaike (1970) Finite Prediction Error 9.335863510209180 Generalized Cross Validation 9.472264113442757 Hannan & Quinn (1979) HQ 10.17643069434118 Shibata (1981) 9.095798448518087 Rice (1984) 9.651738591381671 Residual Variance 8.335592419829625 Order of entrance (or deletion) of the variables = 7 4 2 1 5 3 Estimate of Computational Error in Coefficients 1 2 3 4 5 6 0.773341E-14 -0.137818E-13 -0.193878E-14 -0.260162E-13 0.121673E-13 0.507358E-13 Covariance Matrix of Regression Coefficients Row 1 Variable X- 1 X1 2.1147374 Row 2 Variable X- 2 X2 0.12102404 2.1315368 Row 3 Variable X- 3 X3 0.93172245E-01 0.12573447 2.0464430 Row 4 Variable X- 4 X4 0.17355752 0.16755902 0.10359916 2.0338795 Row 5 Variable X- 5 X5 0.90581013E-01 0.13480772 0.23534844 0.22271207 2.2342687 Row 6 Variable X- 7 CONSTANT -1.2502508 -1.3019198 -1.2543265 -1.2991523 -1.3449142 3.2511553 Program terminated. All variables put in. Residual Statistics for Original data Von Neumann Ratio 1 ... 1.80695 Durbin-Watson TEST..... 1.77081 Von Neumann Ratio 2 ... 1.80695 For D. F. 44 t(.9999)= 4.2783, t(.999)= 3.5258, t(.99)= 2.6923, t(.95)= 2.0154, t(.90)= 1.6802, t(.80)= 1.3011 Skewness test (Alpha 3) = -.288095 , Peakedness test (Alpha 4)= 2.42569 Normality Test -- Extended grid cell size = 5.00 t Stat Infin 1.680 1.301 1.049 0.850 0.680 0.528 0.388 0.255 0.126 Cell No. 5 3 5 2 5 7 10 4 5 4 Interval 1.000 0.900 0.800 0.700 0.600 0.500 0.400 0.300 0.200 0.100 Act Per 1.000 0.900 0.840 0.740 0.700 0.600 0.460 0.260 0.180 0.080 Normality Test -- Small sample grid cell size = 10.00 Cell No. 8 7 12 14 9 Interval 1.000 0.800 0.600 0.400 0.200 Act Per 1.000 0.840 0.700 0.460 0.180 Extended grid normality test - Prob of rejecting normality assumption Chi= 8.800 Chi Prob= 0.6406 F(8, 44)= 1.10000 F Prob =0.618433 Small sample normality test - Large grid Chi= 3.400 Chi Prob= 0.6660 F(3, 44)= 1.13333 F Prob =0.653978 Autocorrelation function of residuals 1 2 3 4 0.106385 -0.378202 -0.268837 -0.232714E-01 F( 17, 17) = 1.213 1/F = 0.8241 Heteroskedasticity at 0.6528 level Sum of squared residuals 366.7660664725008 Mean squared residual 7.335321329450015 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 142 Multivariate Adaptive Regression Splines (MARS) Program developed by Jerome Friedman Basic reference: Multivariate Adaptive Regression Splines Annals of Statistics, 1991, Vol. 19, No. 1, pp. 1-141 Program Modified by H. H. Stokes March 2002 Real*8 storage available : 5999699 Real*8 Storage used : 6693 Exogenous Variables Var # Name Mean Variance Max Min 1 X1 0.48286000 0.81393592E-01 0.96900000 0.16000000E-01 2 X2 0.48814000 0.80952000E-01 0.96300000 0.12000000E-01 3 X3 0.48432000 0.84603324E-01 0.96800000 0.80000000E-02 4 X4 0.48298000 0.85625326E-01 0.98000000 0.30000000E-02 5 X5 0.45376000 0.78082594E-01 0.93400000 0.80000000E-02 Endogenous Variable Name Mean Variance Max Min Y 14.206480 23.026168 24.748000 3.9250000 MARS Modeling, Version 3.5 (6/16/91) - Revised (1/3/02) Input parameters (see doc.): N P NK MS MI DF IL FV IC 50 5 15 0 2 3.000 0 0.000 0 Predictor variable flags: 1 2 3 4 5 1 1 1 1 1 Ordinal Response: MIN N/4 N/2 3N/4 MAX 3.925 10.04 14.10 17.20 24.75 Number of ordinal predictor variables. 5 VAR MIN N/4 N/2 3N/4 MAX 1 0.1600E-01 0.2190 0.4690 0.7190 0.9690 2 0.1200E-01 0.2220 0.4810 0.7410 0.9630 3 0.8000E-02 0.2080 0.4800 0.7280 0.9680 4 0.3000E-02 0.2040 0.4690 0.7350 0.9800 5 0.8000E-02 0.1980 0.4550 0.6610 0.9340 Forward stepwise knot placement: BASFN(S) GCV #INDBSFNS #EFPRMS Variable Knot Parent 0 23.50 0.0 1.0 1 20.96 1.0 5.0 4. 0.3000E-02 0. 3 2 17.98 3.0 10.0 2. 0.4810 0. 5 4 13.97 5.0 15.0 1. 0.5620 0. B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 143 7 6 12.22 7.0 20.0 3. 0.5680 0. 9 8 9.847 9.0 25.0 5. 0.3640 0. 11 10 9.411 11.0 30.0 2. 0.5930 5. 13 12 11.84 13.0 35.0 2. 0.5560 4. 15 14 18.43 14.0 39.0 3. 0.3680 0. Final model after backward stepwise elimination: BSFN: 0 1 2 3 4 5 Coef: 10.19 9.952 0.000 -21.78 0.000 -17.46 BSFN: 6 7 8 9 10 11 Coef: 0.000 12.49 3.625 -7.040 0.000 26.02 BSFN: 12 13 14 15 Coef: -39.59 0.000 10.79 0.000 Piecewise Linear GCV = 5.025 # Effective Parameters= 25.43 Number of Basis for ANOVA decomposition 9 Fun. Std. Dev. -GCV #BSFNS #EFPRMS Variable(s) 1 2.883 31.07 1 2.7 4 2 3.374 24.87 1 2.7 2 3 3.259 21.84 1 2.7 1 4 1.522 9.677 2 5.4 3 5 1.346 7.938 2 5.4 5 6 1.769 6.586 2 5.4 1 2 Number of basic functions for Piecewise cubic fit 9 Generalized Cross Validation Criteria 4.553407145134045 GCV removing each variable 1 2 3 4 5 16.7088 18.9849 9.67688 31.0695 7.93815 Relative variable importance 1 2 3 4 5 66.9783 73.2123 42.2627 100.000 33.4446 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 144 Analysis of MARS Forecasts by observation. Linear approximation method used. Obs # Var # Basis # Total Effect ( )+ Coef. used 1 4 1 1.3932927 0.14000000 9.9520908 1 2 3 -3.2239642 0.14800000 -21.783542 1 1 5 -1.0822281 0.62000000E-01 -17.455291 1 3 7 4.5973114 0.36800000 12.492694 1 5 8 0.0000000 0.0000000 3.6250167 1 5 9 -1.9218138 0.27300000 -7.0396110 1 2 11 0.41948796 0.16120000E-01 26.022826 1 2 12 0.0000000 0.0000000 -39.591336 1 3 14 0.0000000 0.0000000 10.793116 2 4 1 2.8164417 0.28300000 9.9520908 2 2 3 0.0000000 0.0000000 -21.783542 2 1 5 -5.4460509 0.31200000 -17.455291 2 3 7 2.0987726 0.16800000 12.492694 2 5 8 0.0000000 0.0000000 3.6250167 2 5 9 -1.2812092 0.18200000 -7.0396110 2 2 11 0.0000000 0.0000000 26.022826 2 2 12 0.0000000 0.0000000 -39.591336 2 3 14 0.34537970 0.32000000E-01 10.793116 3 4 1 4.2395907 0.42600000 9.9520908 3 2 3 -8.0599104 0.37000000 -21.783542 3 1 5 0.0000000 0.0000000 -17.455291 3 3 7 0.0000000 0.0000000 12.492694 3 5 8 0.0000000 0.0000000 3.6250167 3 5 9 -0.64060461 0.91000000E-01 -7.0396110 3 2 11 0.0000000 0.0000000 26.022826 3 2 12 0.0000000 0.0000000 -39.591336 3 3 14 2.5040028 0.23200000 10.793116 4 4 1 5.6527876 0.56800000 9.9520908 4 2 3 -0.80599104 0.37000000E-01 -21.783542 4 1 5 -7.6279623 0.43700000 -17.455291 4 3 7 0.0000000 0.0000000 12.492694 4 5 8 0.0000000 0.0000000 3.6250167 4 5 9 0.0000000 0.0000000 -7.0396110 4 2 11 1.6944243 0.65113000E-01 26.022826 4 2 12 0.0000000 0.0000000 -39.591336 4 3 14 4.6626259 0.43200000 10.793116 5 4 1 7.0759365 0.71100000 9.9520908 5 2 3 0.0000000 0.0000000 -21.783542 5 1 5 0.0000000 0.0000000 -17.455291 5 3 7 6.5961424 0.52800000 12.492694 5 5 8 0.32987652 0.91000000E-01 3.6250167 5 5 9 0.0000000 0.0000000 -7.0396110 5 2 11 0.0000000 0.0000000 26.022826 5 2 12 -0.55372443 0.13986000E-01 -39.591336 5 3 14 0.0000000 0.0000000 10.793116 6 4 1 8.4990855 0.85400000 9.9520908 6 2 3 -5.6419373 0.25900000 -21.783542 6 1 5 -3.2641395 0.18700000 -17.455291 6 3 7 4.0976036 0.32800000 12.492694 6 5 8 0.65612802 0.18100000 3.6250167 6 5 9 0.0000000 0.0000000 -7.0396110 6 2 11 1.8053856 0.69377000E-01 26.022826 6 2 12 0.0000000 0.0000000 -39.591336 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 145 6 3 14 0.0000000 0.0000000 10.793116 7 4 1 0.16918554 0.17000000E-01 9.9520908 7 2 3 0.0000000 0.0000000 -21.783542 7 1 5 0.0000000 0.0000000 -17.455291 7 3 7 1.5990648 0.12800000 12.492694 7 5 8 0.98600454 0.27200000 3.6250167 7 5 9 0.0000000 0.0000000 -7.0396110 7 2 11 0.0000000 0.0000000 26.022826 7 2 12 0.0000000 0.0000000 -39.591336 7 3 14 0.77710432 0.72000000E-01 10.793116 8 4 1 1.5923345 0.16000000 9.9520908 8 2 3 0.0000000 0.0000000 -21.783542 8 1 5 -8.7276457 0.50000000 -17.455291 8 3 7 0.0000000 0.0000000 12.492694 8 5 8 1.3158811 0.36300000 3.6250167 8 5 9 0.0000000 0.0000000 -7.0396110 8 2 11 0.0000000 0.0000000 26.022826 8 2 12 0.0000000 0.0000000 -39.591336 8 3 14 2.9357274 0.27200000 10.793116 9 4 1 3.0154835 0.30300000 9.9520908 9 2 3 -9.6718925 0.44400000 -21.783542 9 1 5 0.0000000 0.0000000 -17.455291 9 3 7 0.0000000 0.0000000 12.492694 9 5 8 1.6457576 0.45400000 3.6250167 9 5 9 0.0000000 0.0000000 -7.0396110 9 2 11 0.0000000 0.0000000 26.022826 9 2 12 0.0000000 0.0000000 -39.591336 9 3 14 5.0943506 0.47200000 10.793116 10 4 1 4.4386325 0.44600000 9.9520908 10 2 3 -2.4179731 0.11100000 -21.783542 10 1 5 -4.3638228 0.25000000 -17.455291 10 3 7 6.0964347 0.48800000 12.492694 10 5 8 1.9756341 0.54500000 3.6250167 10 5 9 0.0000000 0.0000000 -7.0396110 10 2 11 1.4507726 0.55750000E-01 26.022826 10 2 12 0.0000000 0.0000000 -39.591336 10 3 14 0.0000000 0.0000000 10.793116 11 4 1 5.8617815 0.58900000 9.9520908 11 2 3 0.0000000 0.0000000 -21.783542 11 1 5 0.0000000 0.0000000 -17.455291 11 3 7 3.5978959 0.28800000 12.492694 11 5 8 0.0000000 0.0000000 3.6250167 11 5 9 -2.5061015 0.35600000 -7.0396110 11 2 11 0.0000000 0.0000000 26.022826 11 2 12 -1.4648794 0.37000000E-01 -39.591336 11 3 14 0.0000000 0.0000000 10.793116 12 4 1 7.2849304 0.73200000 9.9520908 12 2 3 -7.2539194 0.33300000 -21.783542 12 1 5 -6.5282790 0.37400000 -17.455291 12 3 7 1.0993571 0.88000000E-01 12.492694 12 5 8 0.0000000 0.0000000 3.6250167 12 5 9 -1.8654969 0.26500000 -7.0396110 12 2 11 4.3309789 0.16643000 26.022826 12 2 12 0.0000000 0.0000000 -39.591336 12 3 14 1.2088289 0.11200000 10.793116 13 4 1 8.7080794 0.87500000 9.9520908 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 146 13 2 3 0.0000000 0.0000000 -21.783542 13 1 5 0.0000000 0.0000000 -17.455291 13 3 7 0.0000000 0.0000000 12.492694 13 5 8 0.0000000 0.0000000 3.6250167 13 5 9 -1.2248923 0.17400000 -7.0396110 13 2 11 0.0000000 0.0000000 26.022826 13 2 12 0.0000000 0.0000000 -39.591336 13 3 14 3.3674521 0.31200000 10.793116 14 4 1 0.37817945 0.38000000E-01 9.9520908 14 2 3 0.0000000 0.0000000 -21.783542 14 1 5 -2.1644561 0.12400000 -17.455291 14 3 7 0.0000000 0.0000000 12.492694 14 5 8 0.0000000 0.0000000 3.6250167 14 5 9 -0.58428772 0.83000000E-01 -7.0396110 14 2 11 0.0000000 0.0000000 26.022826 14 2 12 0.0000000 0.0000000 -39.591336 14 3 14 5.5260752 0.51200000 10.793116 15 4 1 1.8013284 0.18100000 9.9520908 15 2 3 -4.8359462 0.22200000 -21.783542 15 1 5 0.0000000 0.0000000 -17.455291 15 3 7 5.5967269 0.44800000 12.492694 15 5 8 0.29000134E-01 0.80000000E-02 3.6250167 15 5 9 0.0000000 0.0000000 -7.0396110 15 2 11 0.0000000 0.0000000 26.022826 15 2 12 0.0000000 0.0000000 -39.591336 15 3 14 0.0000000 0.0000000 10.793116 16 4 1 3.2244774 0.32400000 9.9520908 16 2 3 0.0000000 0.0000000 -21.783542 16 1 5 -9.2687597 0.53100000 -17.455291 16 3 7 3.0981881 0.24800000 12.492694 16 5 8 0.35887665 0.99000000E-01 3.6250167 16 5 9 0.0000000 0.0000000 -7.0396110 16 2 11 0.0000000 0.0000000 26.022826 16 2 12 0.0000000 0.0000000 -39.591336 16 3 14 0.0000000 0.0000000 10.793116 17 4 1 4.6376743 0.46600000 9.9520908 17 2 3 0.0000000 0.0000000 -21.783542 17 1 5 -0.54111403 0.31000000E-01 -17.455291 17 3 7 0.59964931 0.48000000E-01 12.492694 17 5 8 0.68875317 0.19000000 3.6250167 17 5 9 0.0000000 0.0000000 -7.0396110 17 2 11 0.0000000 0.0000000 26.022826 17 2 12 0.0000000 0.0000000 -39.591336 17 3 14 1.6405536 0.15200000 10.793116 18 4 1 6.0608233 0.60900000 9.9520908 18 2 3 -8.8659014 0.40700000 -21.783542 18 1 5 -4.9049369 0.28100000 -17.455291 18 3 7 0.0000000 0.0000000 12.492694 18 5 8 1.0186297 0.28100000 3.6250167 18 5 9 0.0000000 0.0000000 -7.0396110 18 2 11 3.7951429 0.14583900 26.022826 18 2 12 0.0000000 0.0000000 -39.591336 18 3 14 3.7991767 0.35200000 10.793116 19 4 1 7.4839723 0.75200000 9.9520908 19 2 3 -1.6119821 0.74000000E-01 -21.783542 19 1 5 0.0000000 0.0000000 -17.455291 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 147 19 3 7 0.0000000 0.0000000 12.492694 19 5 8 1.3485062 0.37200000 3.6250167 19 5 9 0.0000000 0.0000000 -7.0396110 19 2 11 0.0000000 0.0000000 26.022826 19 2 12 0.0000000 0.0000000 -39.591336 19 3 14 5.9577998 0.55200000 10.793116 20 4 1 8.9071212 0.89500000 9.9520908 20 2 3 0.0000000 0.0000000 -21.783542 20 1 5 -7.0868483 0.40600000 -17.455291 20 3 7 5.0970192 0.40800000 12.492694 20 5 8 1.6747577 0.46200000 3.6250167 20 5 9 0.0000000 0.0000000 -7.0396110 20 2 11 0.0000000 0.0000000 26.022826 20 2 12 0.0000000 0.0000000 -39.591336 20 3 14 0.0000000 0.0000000 10.793116 21 4 1 0.57722126 0.58000000E-01 9.9520908 21 2 3 -6.4479283 0.29600000 -21.783542 21 1 5 0.0000000 0.0000000 -17.455291 21 3 7 2.5984804 0.20800000 12.492694 21 5 8 2.0046342 0.55300000 3.6250167 21 5 9 0.0000000 0.0000000 -7.0396110 21 2 11 0.0000000 0.0000000 26.022826 21 2 12 0.0000000 0.0000000 -39.591336 21 3 14 0.0000000 0.0000000 10.793116 22 4 1 2.0003702 0.20100000 9.9520908 22 2 3 0.0000000 0.0000000 -21.783542 22 1 5 -2.7230255 0.15600000 -17.455291 22 3 7 0.99941552E-01 0.80000000E-02 12.492694 22 5 8 0.0000000 0.0000000 3.6250167 22 5 9 -2.4427450 0.34700000 -7.0396110 22 2 11 0.30040750 0.11544000E-01 26.022826 22 2 12 0.0000000 0.0000000 -39.591336 22 3 14 2.0722782 0.19200000 10.793116 23 4 1 3.4235192 0.34400000 9.9520908 23 2 3 0.0000000 0.0000000 -21.783542 23 1 5 0.0000000 0.0000000 -17.455291 23 3 7 0.0000000 0.0000000 12.492694 23 5 8 0.0000000 0.0000000 3.6250167 23 5 9 -1.8091800 0.25700000 -7.0396110 23 2 11 0.0000000 0.0000000 26.022826 23 2 12 -4.0313482 0.10182400 -39.591336 23 3 14 4.2309013 0.39200000 10.793116 24 4 1 4.8466682 0.48700000 9.9520908 24 2 3 -4.0299552 0.18500000 -21.783542 24 1 5 -8.1690764 0.46800000 -17.455291 24 3 7 0.0000000 0.0000000 12.492694 24 5 8 0.0000000 0.0000000 3.6250167 24 5 9 -1.1685754 0.16600000 -7.0396110 24 2 11 3.6170687 0.13899600 26.022826 24 2 12 0.0000000 0.0000000 -39.591336 24 3 14 6.3895244 0.59200000 10.793116 25 4 1 6.2698172 0.63000000 9.9520908 25 2 3 0.0000000 0.0000000 -21.783542 25 1 5 0.0000000 0.0000000 -17.455291 25 3 7 6.9959086 0.56000000 12.492694 25 5 8 0.0000000 0.0000000 3.6250167 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 148 25 5 9 -0.52797083 0.75000000E-01 -7.0396110 25 2 11 0.0000000 0.0000000 26.022826 25 2 12 -0.93752284E-01 0.23680000E-02 -39.591336 25 3 14 0.0000000 0.0000000 10.793116 26 4 1 7.6929662 0.77300000 9.9520908 26 2 3 0.0000000 0.0000000 -21.783542 26 1 5 -3.8052535 0.21800000 -17.455291 26 3 7 4.4973698 0.36000000 12.492694 26 5 8 0.58000267E-01 0.16000000E-01 3.6250167 26 5 9 0.0000000 0.0000000 -7.0396110 26 2 11 0.0000000 0.0000000 26.022826 26 2 12 0.0000000 0.0000000 -39.591336 26 3 14 0.0000000 0.0000000 10.793116 27 4 1 9.1061631 0.91500000 9.9520908 27 2 3 -10.216481 0.46900000 -21.783542 27 1 5 0.0000000 0.0000000 -17.455291 27 3 7 1.9988310 0.16000000 12.492694 27 5 8 0.38787679 0.10700000 3.6250167 27 5 9 0.0000000 0.0000000 -7.0396110 27 2 11 0.0000000 0.0000000 26.022826 27 2 12 0.0000000 0.0000000 -39.591336 27 3 14 0.43172462 0.40000000E-01 10.793116 28 4 1 0.78621517 0.79000000E-01 9.9520908 28 2 3 -2.9407781 0.13500000 -21.783542 28 1 5 -5.9871649 0.34300000 -17.455291 28 3 7 0.0000000 0.0000000 12.492694 28 5 8 0.71775331 0.19800000 3.6250167 28 5 9 0.0000000 0.0000000 -7.0396110 28 2 11 2.2046798 0.84721000E-01 26.022826 28 2 12 0.0000000 0.0000000 -39.591336 28 3 14 2.5903477 0.24000000 10.793116 29 4 1 2.1994121 0.22100000 9.9520908 29 2 3 0.0000000 0.0000000 -21.783542 29 1 5 0.0000000 0.0000000 -17.455291 29 3 7 0.0000000 0.0000000 12.492694 29 5 8 1.0476298 0.28900000 3.6250167 29 5 9 0.0000000 0.0000000 -7.0396110 29 2 11 0.0000000 0.0000000 26.022826 29 2 12 -0.76454829 0.19311000E-01 -39.591336 29 3 14 4.7489709 0.44000000 10.793116 30 4 1 3.6225610 0.36400000 9.9520908 30 2 3 -7.7985079 0.35800000 -21.783542 30 1 5 -1.6233421 0.93000000E-01 -17.455291 30 3 7 6.4962009 0.52000000 12.492694 30 5 8 1.3775063 0.38000000 3.6250167 30 5 9 0.0000000 0.0000000 -7.0396110 30 2 11 1.1374577 0.43710000E-01 26.022826 30 2 12 0.0000000 0.0000000 -39.591336 30 3 14 0.0000000 0.0000000 10.793116 31 4 1 5.0457100 0.50700000 9.9520908 31 2 3 -0.52280500 0.24000000E-01 -21.783542 31 1 5 0.0000000 0.0000000 -17.455291 31 3 7 3.9976621 0.32000000 12.492694 31 5 8 1.7073829 0.47100000 3.6250167 31 5 9 0.0000000 0.0000000 -7.0396110 31 2 11 0.0000000 0.0000000 26.022826 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 149 31 2 12 0.0000000 0.0000000 -39.591336 31 3 14 0.0000000 0.0000000 10.793116 32 4 1 6.4688590 0.65000000 9.9520908 32 2 3 0.0000000 0.0000000 -21.783542 32 1 5 -9.5305891 0.54600000 -17.455291 32 3 7 1.4991233 0.12000000 12.492694 32 5 8 2.0372594 0.56200000 3.6250167 32 5 9 0.0000000 0.0000000 -7.0396110 32 2 11 0.0000000 0.0000000 26.022826 32 2 12 0.0000000 0.0000000 -39.591336 32 3 14 0.86344925 0.80000000E-01 10.793116 33 4 1 7.8920080 0.79300000 9.9520908 33 2 3 -5.3587512 0.24600000 -21.783542 33 1 5 -0.80294340 0.46000000E-01 -17.455291 33 3 7 0.0000000 0.0000000 12.492694 33 5 8 0.0000000 0.0000000 3.6250167 33 5 9 -2.3864281 0.33900000 -7.0396110 33 2 11 0.42854390 0.16468000E-01 26.022826 33 2 12 0.0000000 0.0000000 -39.591336 33 3 14 3.0220724 0.28000000 10.793116 34 4 1 9.3151570 0.93600000 9.9520908 34 2 3 0.0000000 0.0000000 -21.783542 34 1 5 -5.1667662 0.29600000 -17.455291 34 3 7 0.0000000 0.0000000 12.492694 34 5 8 0.0000000 0.0000000 3.6250167 34 5 9 -1.7458235 0.24800000 -7.0396110 34 2 11 0.19256891 0.74000000E-02 26.022826 34 2 12 0.0000000 0.0000000 -39.591336 34 3 14 5.1806955 0.48000000 10.793116 35 4 1 0.98525699 0.99000000E-01 9.9520908 35 2 3 0.0000000 0.0000000 -21.783542 35 1 5 0.0000000 0.0000000 -17.455291 35 3 7 5.9964931 0.48000000 12.492694 35 5 8 0.0000000 0.0000000 3.6250167 35 5 9 -1.1052189 0.15700000 -7.0396110 35 2 11 0.0000000 0.0000000 26.022826 35 2 12 -2.7864382 0.70380000E-01 -39.591336 35 3 14 0.0000000 0.0000000 10.793116 36 4 1 2.4084060 0.24200000 9.9520908 36 2 3 -9.4104900 0.43200000 -21.783542 36 1 5 -7.3486777 0.42100000 -17.455291 36 3 7 3.4979543 0.28000000 12.492694 36 5 8 0.0000000 0.0000000 3.6250167 36 5 9 -0.46461433 0.66000000E-01 -7.0396110 36 2 11 5.9598517 0.22902400 26.022826 36 2 12 0.0000000 0.0000000 -39.591336 36 3 14 0.0000000 0.0000000 10.793116 37 4 1 3.8315549 0.38500000 9.9520908 37 2 3 -2.1347871 0.98000000E-01 -21.783542 37 1 5 0.0000000 0.0000000 -17.455291 37 3 7 0.99941552 0.80000000E-01 12.492694 37 5 8 0.87000401E-01 0.24000000E-01 3.6250167 37 5 9 0.0000000 0.0000000 -7.0396110 37 2 11 0.0000000 0.0000000 26.022826 37 2 12 0.0000000 0.0000000 -39.591336 37 3 14 1.2951739 0.12000000 10.793116 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 150 38 4 1 5.2547039 0.52800000 9.9520908 38 2 3 0.0000000 0.0000000 -21.783542 38 1 5 -2.9848548 0.17100000 -17.455291 38 3 7 0.0000000 0.0000000 12.492694 38 5 8 0.41687692 0.11500000 3.6250167 38 5 9 0.0000000 0.0000000 -7.0396110 38 2 11 0.0000000 0.0000000 26.022826 38 2 12 0.0000000 0.0000000 -39.591336 38 3 14 3.4537970 0.32000000 10.793116 39 4 1 6.6679008 0.67000000 9.9520908 39 2 3 -6.9925169 0.32100000 -21.783542 39 1 5 0.0000000 0.0000000 -17.455291 39 3 7 0.0000000 0.0000000 12.492694 39 5 8 0.74675344 0.20600000 3.6250167 39 5 9 0.0000000 0.0000000 -7.0396110 39 2 11 0.0000000 0.0000000 26.022826 39 2 12 0.0000000 0.0000000 -39.591336 39 3 14 5.6124201 0.52000000 10.793116 40 4 1 8.0910498 0.81300000 9.9520908 40 2 3 0.0000000 0.0000000 -21.783542 40 1 5 -8.4483610 0.48400000 -17.455291 40 3 7 5.4967854 0.44000000 12.492694 40 5 8 1.0766300 0.29700000 3.6250167 40 5 9 0.0000000 0.0000000 -7.0396110 40 2 11 1.2469097 0.47916000E-01 26.022826 40 2 12 0.0000000 0.0000000 -39.591336 40 3 14 0.0000000 0.0000000 10.793116 41 4 1 9.5141988 0.95600000 9.9520908 41 2 3 0.0000000 0.0000000 -21.783542 41 1 5 0.0000000 0.0000000 -17.455291 41 3 7 2.9982466 0.24000000 12.492694 41 5 8 1.4065065 0.38800000 3.6250167 41 5 9 0.0000000 0.0000000 -7.0396110 41 2 11 0.0000000 0.0000000 26.022826 41 2 12 -0.17166803 0.43360000E-02 -39.591336 41 3 14 0.0000000 0.0000000 10.793116 42 4 1 1.1842988 0.11900000 9.9520908 42 2 3 -4.5527602 0.20900000 -21.783542 42 1 5 -4.0845382 0.23400000 -17.455291 42 3 7 0.49970776 0.40000000E-01 12.492694 42 5 8 1.7363830 0.47900000 3.6250167 42 5 9 0.0000000 0.0000000 -7.0396110 42 2 11 1.9546786 0.75114000E-01 26.022826 42 2 12 0.0000000 0.0000000 -39.591336 42 3 14 1.7268985 0.16000000 10.793116 43 4 1 2.6074478 0.26200000 9.9520908 43 2 3 0.0000000 0.0000000 -21.783542 43 1 5 0.0000000 0.0000000 -17.455291 43 3 7 0.0000000 0.0000000 12.492694 43 5 8 2.0662595 0.57000000 3.6250167 43 5 9 0.0000000 0.0000000 -7.0396110 43 2 11 0.0000000 0.0000000 26.022826 43 2 12 -0.51603348 0.13034000E-01 -39.591336 43 3 14 3.8855216 0.36000000 10.793116 44 4 1 4.0305968 0.40500000 9.9520908 44 2 3 0.0000000 0.0000000 -21.783542 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 151 44 1 5 -6.2664496 0.35900000 -17.455291 44 3 7 0.0000000 0.0000000 12.492694 44 5 8 0.0000000 0.0000000 3.6250167 44 5 9 -2.3301113 0.33100000 -7.0396110 44 2 11 0.0000000 0.0000000 26.022826 44 2 12 0.0000000 0.0000000 -39.591336 44 3 14 6.0441447 0.56000000 10.793116 45 4 1 5.4537457 0.54800000 9.9520908 45 2 3 -8.6044989 0.39500000 -21.783542 45 1 5 0.0000000 0.0000000 -17.455291 45 3 7 4.9970776 0.40000000 12.492694 45 5 8 0.0000000 0.0000000 3.6250167 45 5 9 -1.6895067 0.24000000 -7.0396110 45 2 11 0.0000000 0.0000000 26.022826 45 2 12 0.0000000 0.0000000 -39.591336 45 3 14 0.0000000 0.0000000 10.793116 46 4 1 6.8768947 0.69100000 9.9520908 46 2 3 -1.3287960 0.61000000E-01 -21.783542 46 1 5 -1.9026268 0.10900000 -17.455291 46 3 7 2.4985388 0.20000000 12.492694 46 5 8 0.0000000 0.0000000 3.6250167 46 5 9 -1.0489020 0.14900000 -7.0396110 46 2 11 0.49071243 0.18857000E-01 26.022826 46 2 12 0.0000000 0.0000000 -39.591336 46 3 14 0.0000000 0.0000000 10.793116 47 4 1 8.3000437 0.83400000 9.9520908 47 2 3 0.0000000 0.0000000 -21.783542 47 1 5 0.0000000 0.0000000 -17.455291 47 3 7 0.0000000 0.0000000 12.492694 47 5 8 0.0000000 0.0000000 3.6250167 47 5 9 -0.40829744 0.58000000E-01 -7.0396110 47 2 11 0.0000000 0.0000000 26.022826 47 2 12 -3.0496019 0.77027000E-01 -39.591336 47 3 14 2.1586231 0.20000000 10.793116 48 4 1 9.7231927 0.97700000 9.9520908 48 2 3 -6.1647423 0.28300000 -21.783542 48 1 5 -8.9894750 0.51500000 -17.455291 48 3 7 0.0000000 0.0000000 12.492694 48 5 8 0.11962555 0.33000000E-01 3.6250167 48 5 9 0.0000000 0.0000000 -7.0396110 48 2 11 5.2936934 0.20342500 26.022826 48 2 12 0.0000000 0.0000000 -39.591336 48 3 14 4.3172462 0.40000000 10.793116 49 4 1 0.0000000 0.0000000 9.9520908 49 2 3 0.0000000 0.0000000 -21.783542 49 1 5 -0.26182937 0.15000000E-01 -17.455291 49 3 7 0.0000000 0.0000000 12.492694 49 5 8 0.44950207 0.12400000 3.6250167 49 5 9 0.0000000 0.0000000 -7.0396110 49 2 11 0.24201228E-01 0.93000000E-03 26.022826 49 2 12 0.0000000 0.0000000 -39.591336 49 3 14 6.4758694 0.60000000 10.793116 50 4 1 1.4231490 0.14300000 9.9520908 50 2 3 0.0000000 0.0000000 -21.783542 50 1 5 -4.6256522 0.26500000 -17.455291 50 3 7 6.8959671 0.55200000 12.492694 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 152 50 5 8 0.77937859 0.21500000 3.6250167 50 5 9 0.0000000 0.0000000 -7.0396110 50 2 11 0.0000000 0.0000000 26.022826 50 2 12 0.0000000 0.0000000 -39.591336 50 3 14 0.0000000 0.0000000 10.793116 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 153 Obs Y Yhat Residual 1 9.6530000 10.372752 -0.71975196 2 8.7650000 8.7239998 0.41000200E-01 3 8.2920000 8.2337444 0.58255587E-01 4 13.796000 13.766550 0.29449670E-01 5 24.134000 23.638897 0.49510300 6 17.111000 16.342792 0.76820805 7 13.420000 13.722025 -0.30202517 8 7.9510000 7.3069633 0.64403672 9 9.9390000 10.274365 -0.33536509 10 15.615000 17.370344 -1.7553438 11 16.956000 15.679362 1.2766377 12 8.9240000 8.4670661 0.45693392 13 19.789000 21.041305 -1.2523051 14 14.596000 13.346177 1.2498233 15 13.713000 12.781775 0.93122482 16 6.8620000 7.6034484 -0.74144840 17 17.263000 17.216182 0.46817748E-01 18 11.168000 11.093600 0.74399794E-01 19 21.977000 23.368962 -1.3919621 20 18.631000 18.782716 -0.15171575 21 7.9090000 8.9230735 -1.0140735 22 9.8660000 9.4978929 0.36810706 23 10.142000 12.004558 -1.8625582 24 12.161000 11.676320 0.48467970 25 22.449000 22.834669 -0.38566865 26 19.795000 18.633749 1.1612513 27 11.399000 11.898780 -0.49978042 28 5.9240000 7.5617189 -1.6377189 29 14.938000 17.422130 -2.4841304 30 13.153000 13.402542 -0.24954194 31 21.515000 20.418616 1.0963841 32 11.851000 11.528768 0.32223224 33 12.167000 12.985167 -0.81816739 34 17.204000 17.966498 -0.76249750 35 14.095000 13.280759 0.81424113 36 3.9250000 4.8330960 -0.90809597 37 14.185000 14.269024 -0.84023592E-01 38 14.717000 16.331189 -1.6141889 39 18.291000 16.225223 2.0657766 40 15.741000 17.653680 -1.9126798 41 24.748000 23.937950 0.81005029 42 11.031000 8.6553342 2.3756658 43 20.199000 18.233861 1.9651386 44 13.252000 11.668847 1.5831534 45 10.041000 10.347484 -0.30648369 46 15.079000 15.776487 -0.69748704 47 18.463000 17.191433 1.2715665 48 15.470000 14.490206 0.97979354 49 16.365000 16.878409 -0.51340921 50 15.694000 14.663508 1.0304916 Sum of squared residuals using piecewise-linear MARS model: 60.67699114872438 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 154 Sum of squared Y values 11219.48594000000 % Reduction in sum of squares (1.0 - (RESID***2/Y**2) ) 0.9945918207417688 Variance of Y 23.02616817306123 Residual Variance 1.238305941810701 Approximate R squared value 0.9462217971959650 Plot of the Residual RESIDUAL 2.3757 * . * * * * . * . * * * . * * * * . . . * . . * . * . . * . . * . * . * . * . . * . . * * *--.-.-.-------------------------.-.----------------------------------------------------------------- * . * . * . . * . . . * . * . * . *. . . * . * . * . * * . * . * * * . . * . * . * . * * * * * . -2.4841 ***************************************************************************************************** 1.0000 50.000 TIME B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 155 Analysis of MARS Forecasts by observation. Linear approximation method used. Obs # Var # Basis # Total Effect ( )+ Coef. used 51 4 1 1.3932927 0.14000000 9.9520908 51 2 3 -3.2239642 0.14800000 -21.783542 51 1 5 -1.0822281 0.62000000E-01 -17.455291 51 3 7 4.5973114 0.36800000 12.492694 51 5 8 0.0000000 0.0000000 3.6250167 51 5 9 -1.9218138 0.27300000 -7.0396110 51 2 11 0.41948796 0.16120000E-01 26.022826 51 2 12 0.0000000 0.0000000 -39.591336 51 3 14 0.0000000 0.0000000 10.793116 52 4 1 2.8164417 0.28300000 9.9520908 52 2 3 0.0000000 0.0000000 -21.783542 52 1 5 -5.4460509 0.31200000 -17.455291 52 3 7 2.0987726 0.16800000 12.492694 52 5 8 0.0000000 0.0000000 3.6250167 52 5 9 -1.2812092 0.18200000 -7.0396110 52 2 11 0.0000000 0.0000000 26.022826 52 2 12 0.0000000 0.0000000 -39.591336 52 3 14 0.34537970 0.32000000E-01 10.793116 53 4 1 4.2395907 0.42600000 9.9520908 53 2 3 -8.0599104 0.37000000 -21.783542 53 1 5 0.0000000 0.0000000 -17.455291 53 3 7 0.0000000 0.0000000 12.492694 53 5 8 0.0000000 0.0000000 3.6250167 53 5 9 -0.64060461 0.91000000E-01 -7.0396110 53 2 11 0.0000000 0.0000000 26.022826 53 2 12 0.0000000 0.0000000 -39.591336 53 3 14 2.5040028 0.23200000 10.793116 Forecasts on the Y Variable outside sample Observation Predicted Value 51 10.372752 52 8.7239998 53 8.2337444 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 156 In sample forecast decomposition. OBSNUM FORECAST ACTUALV ERROR NBASIS ABASIS RBASIS SDBASIS SDRBASIS TOTALE 1 10.4 9.65 -0.720 6 0.303E-01 0.839E-02 2.78 0.387 0.182 2 8.72 8.77 0.410E-01 5 -0.293 0.811E-01 3.29 0.459 -1.47 3 8.23 8.29 0.583E-01 4 -0.489 0.135 5.44 0.758 -1.96 4 13.8 13.8 0.294E-01 5 0.715 0.198 5.31 0.741 3.58 5 23.6 24.1 0.495 4 3.36 0.930 4.03 0.562 13.4 6 16.3 17.1 0.768 6 1.03 0.283 5.08 0.708 6.15 7 13.7 13.4 -0.302 4 0.883 0.244 0.590 0.823E-01 3.53 8 7.31 7.95 0.644 4 -0.721 0.199 5.38 0.751 -2.88 9 10.3 9.94 -0.335 4 0.209E-01 0.579E-02 6.62 0.923 0.837E-01 10 17.4 15.6 -1.76 6 1.20 0.331 3.98 0.555 7.18 11 15.7 17.0 1.28 4 1.37 0.379 4.01 0.559 5.49 12 8.47 8.92 0.457 7 -0.246 0.681E-01 5.37 0.749 -1.72 13 21.0 19.8 -1.25 3 3.62 1.00 4.97 0.693 10.9 14 13.3 14.6 1.25 4 0.789 0.218 3.33 0.464 3.16 15 12.8 13.7 0.931 4 0.648 0.179 4.33 0.604 2.59 16 7.60 6.86 -0.741 4 -0.647 0.179 5.90 0.823 -2.59 17 17.2 17.3 0.468E-01 5 1.41 0.388 1.97 0.274 7.03 18 11.1 11.2 0.744E-01 6 0.150 0.416E-01 5.82 0.811 0.903 19 23.4 22.0 -1.39 4 3.29 0.911 4.18 0.584 13.2 20 18.8 18.6 -0.152 4 2.15 0.594 6.83 0.953 8.59 21 8.92 7.91 -1.01 4 -0.317 0.876E-01 4.17 0.582 -1.27 22 9.50 9.87 0.368 6 -0.115 0.319E-01 2.08 0.291 -0.693 23 12.0 10.1 -1.86 4 0.453 0.125 4.01 0.560 1.81 24 11.7 12.2 0.485 6 0.248 0.685E-01 5.68 0.792 1.49 25 22.8 22.4 -0.386 4 3.16 0.874 4.02 0.561 12.6 26 18.6 19.8 1.16 4 2.11 0.584 5.04 0.702 8.44 27 11.9 11.4 -0.500 5 0.342 0.945E-01 6.91 0.964 1.71 28 7.56 5.92 -1.64 6 -0.438 0.121 3.35 0.467 -2.63 29 17.4 14.9 -2.48 4 1.81 0.500 2.31 0.322 7.23 30 13.4 13.2 -0.250 6 0.535 0.148 4.90 0.684 3.21 31 20.4 21.5 1.10 4 2.56 0.707 2.48 0.346 10.2 32 11.5 11.9 0.322 5 0.268 0.740E-01 5.90 0.824 1.34 33 13.0 12.2 -0.818 6 0.466 0.129 4.59 0.640 2.79 34 18.0 17.2 -0.762 5 1.56 0.430 5.73 0.799 7.78 35 13.3 14.1 0.814 4 0.773 0.214 3.81 0.531 3.09 36 4.83 3.92 -0.908 6 -0.893 0.247 6.19 0.863 -5.36 37 14.3 14.2 -0.840E-01 5 0.816 0.226 2.16 0.301 4.08 38 16.3 14.7 -1.61 4 1.54 0.424 3.61 0.504 6.14 39 16.2 18.3 2.07 4 1.51 0.417 6.23 0.869 6.03 40 17.7 15.7 -1.91 5 1.49 0.413 6.30 0.878 7.46 41 23.9 24.7 0.810 4 3.44 0.950 4.25 0.593 13.7 42 8.66 11.0 2.38 7 -0.219 0.606E-01 2.84 0.397 -1.54 43 18.2 20.2 1.97 4 2.01 0.556 1.85 0.258 8.04 44 11.7 13.3 1.58 4 0.370 0.102 5.68 0.793 1.48 45 10.3 10.0 -0.306 4 0.392E-01 0.108E-01 6.62 0.924 0.157 46 15.8 15.1 -0.697 6 0.931 0.257 3.32 0.463 5.59 47 17.2 18.5 1.27 4 1.75 0.484 4.86 0.677 7.00 48 14.5 15.5 0.980 6 0.717 0.198 7.17 1.00 4.30 49 16.9 16.4 -0.513 4 1.67 0.462 3.22 0.449 6.69 50 14.7 15.7 1.03 4 1.12 0.309 4.71 0.657 4.47 Name Mean Variance Standard Deviation B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 157 Correlation between ERROR and NBASIS = -0.2402E-01 Correlation between ERROR and ABASIS = 0.7345E-02 Correlation between ERROR and RBASIS = -0.3438E-01 Correlation between ERROR and SDBASIS = 0.1565E-01 Correlation between ERROR and BASIS1 = 0.6658E-01 Correlation between ERROR and BASIS2 = -0.3987E-01 Correlation between ERROR and BASIS3 = -0.3186E-01 Correlation between ERROR and BASIS4 = 0.8336E-01 Correlation between ERROR and BASIS5 = 0.2934E-02 Correlation between ERROR and BASIS6 = -0.4063E-02 Correlation between ERROR and BASIS7 = -0.1678 Correlation between ERROR and BASIS8 = 0.8980E-01 Correlation between ERROR and BASIS9 = 0.1700E-01 Correlation between ERROR and SD/ABASI = -0.7218E-01 Correlation between ABS(ERROR) and NBASIS = -0.1051 Correlation between ABS(ERROR) and ABASIS = 0.1969 Correlation between ABS(ERROR) and RBASIS = 0.2055 Correlation between ABS(ERROR) and SDBASIS = -0.1458 Correlation between ABS(ERROR) and BASIS1 = 0.8529E-01 Correlation between ABS(ERROR) and BASIS2 = -0.1103 Correlation between ABS(ERROR) and BASIS3 = -0.1193 Correlation between ABS(ERROR) and BASIS4 = -0.2695 Correlation between ABS(ERROR) and BASIS5 = 0.1639 Correlation between ABS(ERROR) and BASIS6 = -0.1097 Correlation between ABS(ERROR) and BASIS7 = -0.4007E-01 Correlation between ABS(ERROR) and BASIS8 = 0.2681 Correlation between ABS(ERROR) and BASIS9 = 0.4424E-01 Correlation between ABS(ERROR) and SD/ABASI = -0.1942 Regression of MARS error on contribution of each basis. OLS Estimation Dependent variable ERROR Adjusted R**2 -0.2249999999983985 Standard Error of Estimate 1.231635002229202 Sum of Squared Residuals 60.67699114864503 Model Sum of Squares 7.933209644761519E-11 Total Sum of Squares 60.67699114872436 F( 9, 40) 5.810660594667972E-12 F Significance 0.000000000000000E+00 1/Condition of XPX 6.403696947902937E-04 Number of Observations 50 Durbin-Watson 2.014497866459372 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 158 Variable Coefficient Std. Error t BASIS1 X- 1 0.12978582E-06 0.61431922E-01 0.21126771E-05 BASIS2 X- 2 0.33078186E-06 0.69996205E-01 0.47257114E-05 BASIS3 X- 3 0.37715166E-06 0.75728077E-01 0.49803411E-05 BASIS4 X- 4 0.42395820E-06 0.11840506 0.35805750E-05 BASIS5 X- 5 0.45214358E-06 0.31402674 0.14398251E-05 BASIS6 X- 6 -0.15523621E-06 0.26781587 -0.57963782E-06 BASIS7 X- 7 0.89621484E-06 0.18861279 0.47516123E-05 BASIS8 X- 8 0.56469895E-06 0.24485982 0.23062132E-05 BASIS9 X- 9 0.45284230E-06 0.12845690 0.35252471E-05 CONSTANT X-10 -0.13682532E-05 0.75591405 -0.18100646E-05 Regression of MARS absolute error on contribution of each basis. OLS Estimation Dependent variable ABSERROR Adjusted R**2 9.120646862768145E-02 Standard Error of Estimate 0.6171326313601484 Sum of Squared Residuals 15.23410738758003 Model Sum of Squares 5.300569528094554 Total Sum of Squares 20.53467691567459 F( 9, 40) 1.546404143818603 F Significance 0.8346653608579054 1/Condition of XPX 6.403696947902937E-04 Number of Observations 50 Durbin-Watson 1.599364718284275 Variable Coefficient Std. Error t BASIS1 X- 1 -0.49003422E-02 0.30781558E-01 -0.15919734 BASIS2 X- 2 0.48273508E-01 0.35072844E-01 1.3763785 BASIS3 X- 3 0.32462995E-01 0.37944901E-01 0.85552984 BASIS4 X- 4 0.33541494E-01 0.59328963E-01 0.56534772 BASIS5 X- 5 0.33476779 0.15734868 2.1275538 BASIS6 X- 6 -0.51440206E-01 0.13419391 -0.38332743 BASIS7 X- 7 0.10978973 0.94507794E-01 1.1617003 BASIS8 X- 8 -0.19369905 0.12269137 -1.5787504 BASIS9 X- 9 0.97193401E-01 0.64365614E-01 1.5100206 CONSTANT X-10 0.50470261 0.37876419 1.3324982 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 159 Multivariate Adaptive Regression Splines (MARS) Program developed by Jerome Friedman Basic reference: Multivariate Adaptive Regression Splines Annals of Statistics, 1991, Vol. 19, No. 1, pp. 1-141 Program Modified by H. H. Stokes March 2002 Real*8 storage available : 5999699 Real*8 Storage used : 6693 Exogenous Variables Var # Name Mean Variance Max Min 1 X1 0.48286000 0.81393592E-01 0.96900000 0.16000000E-01 2 X2 0.48814000 0.80952000E-01 0.96300000 0.12000000E-01 3 X3 0.48432000 0.84603324E-01 0.96800000 0.80000000E-02 4 X4 0.48298000 0.85625326E-01 0.98000000 0.30000000E-02 5 X5 0.45376000 0.78082594E-01 0.93400000 0.80000000E-02 Endogenous Variable Name Mean Variance Max Min Y 14.206480 23.026168 24.748000 3.9250000 MARS Modeling, Version 3.5 (6/16/91) - Revised (1/3/02) Input parameters (see doc.): N P NK MS MI DF IL FV IC 50 5 15 0 2 3.000 0 0.000 0 Predictor variable flags: 1 2 3 4 5 1 1 1 1 1 Ordinal Response: MIN N/4 N/2 3N/4 MAX 3.925 10.04 14.10 17.20 24.75 Number of ordinal predictor variables. 5 VAR MIN N/4 N/2 3N/4 MAX 1 0.1600E-01 0.2190 0.4690 0.7190 0.9690 2 0.1200E-01 0.2220 0.4810 0.7410 0.9630 3 0.8000E-02 0.2080 0.4800 0.7280 0.9680 4 0.3000E-02 0.2040 0.4690 0.7350 0.9800 5 0.8000E-02 0.1980 0.4550 0.6610 0.9340 Forward stepwise knot placement: BASFN(S) GCV #INDBSFNS #EFPRMS Variable Knot Parent 0 23.50 0.0 1.0 1 20.96 1.0 5.0 4. 0.3000E-02 0. 3 2 17.98 3.0 10.0 2. 0.4810 0. 5 4 13.97 5.0 15.0 1. 0.5620 0. B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 160 7 6 12.22 7.0 20.0 3. 0.5680 0. 9 8 9.847 9.0 25.0 5. 0.3640 0. 11 10 9.411 11.0 30.0 2. 0.5930 5. 13 12 11.84 13.0 35.0 2. 0.5560 4. 15 14 18.43 14.0 39.0 3. 0.3680 0. Final model after backward stepwise elimination: BSFN: 0 1 2 3 4 5 Coef: 10.19 9.952 0.000 -21.78 0.000 -17.46 BSFN: 6 7 8 9 10 11 Coef: 0.000 12.49 3.625 -7.040 0.000 26.02 BSFN: 12 13 14 15 Coef: -39.59 0.000 10.79 0.000 Piecewise Linear GCV = 5.025 # Effective Parameters= 25.43 Number of Basis for ANOVA decomposition 9 Fun. Std. Dev. -GCV #BSFNS #EFPRMS Variable(s) 1 2.883 31.07 1 2.7 4 2 3.374 24.87 1 2.7 2 3 3.259 21.84 1 2.7 1 4 1.522 9.677 2 5.4 3 5 1.346 7.938 2 5.4 5 6 1.769 6.586 2 5.4 1 2 Number of basic functions for Piecewise cubic fit 9 Generalized Cross Validation Criteria 4.553407145134045 GCV removing each variable 1 2 3 4 5 16.7088 18.9849 9.67688 31.0695 7.93815 Relative variable importance 1 2 3 4 5 66.9783 73.2123 42.2627 100.000 33.4446 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 161 Analysis of MARS Forecasts by observation. Cubic approximation method used. Obs # Var # Basis # Total Effect ( )+ Coef. used 1 4 1 1.4291155 0.14000000 10.207968 2 4 1 2.8888549 0.28300000 10.207968 3 4 1 4.3485943 0.42600000 10.207968 4 4 1 5.7981257 0.56800000 10.207968 5 4 1 7.2578651 0.71100000 10.207968 6 4 1 8.7176045 0.85400000 10.207968 7 4 1 0.17353545 0.17000000E-01 10.207968 8 4 1 1.6332748 0.16000000 10.207968 9 4 1 3.0930142 0.30300000 10.207968 10 4 1 4.5527536 0.44600000 10.207968 11 4 1 6.0124930 0.58900000 10.207968 12 4 1 7.4722324 0.73200000 10.207968 13 4 1 8.9319718 0.87500000 10.207968 14 4 1 0.38790278 0.38000000E-01 10.207968 15 4 1 1.8476422 0.18100000 10.207968 16 4 1 3.3073816 0.32400000 10.207968 17 4 1 4.7569130 0.46600000 10.207968 18 4 1 6.2166524 0.60900000 10.207968 19 4 1 7.6763918 0.75200000 10.207968 20 4 1 9.1361312 0.89500000 10.207968 21 4 1 0.59206213 0.58000000E-01 10.207968 22 4 1 2.0518015 0.20100000 10.207968 23 4 1 3.5115409 0.34400000 10.207968 24 4 1 4.9712803 0.48700000 10.207968 25 4 1 6.4310197 0.63000000 10.207968 26 4 1 7.8907591 0.77300000 10.207968 27 4 1 9.3402905 0.91500000 10.207968 28 4 1 0.80642945 0.79000000E-01 10.207968 29 4 1 2.2559609 0.22100000 10.207968 30 4 1 3.7157003 0.36400000 10.207968 31 4 1 5.1754397 0.50700000 10.207968 32 4 1 6.6351791 0.65000000 10.207968 33 4 1 8.0949184 0.79300000 10.207968 34 4 1 9.5546578 0.93600000 10.207968 35 4 1 1.0105888 0.99000000E-01 10.207968 36 4 1 2.4703282 0.24200000 10.207968 37 4 1 3.9300676 0.38500000 10.207968 38 4 1 5.3898070 0.52800000 10.207968 39 4 1 6.8393384 0.67000000 10.207968 40 4 1 8.2990778 0.81300000 10.207968 41 4 1 9.7588172 0.95600000 10.207968 42 4 1 1.2147482 0.11900000 10.207968 43 4 1 2.6744876 0.26200000 10.207968 44 4 1 4.1342270 0.40500000 10.207968 45 4 1 5.5939663 0.54800000 10.207968 46 4 1 7.0537057 0.69100000 10.207968 47 4 1 8.5134451 0.83400000 10.207968 48 4 1 9.9731845 0.97700000 10.207968 49 4 1 0.0000000 0.0000000 10.207968 50 4 1 1.4597394 0.14300000 10.207968 1 2 3 -3.8213511 0.15615129 -24.472106 2 2 3 -0.74896286E-01 0.30604757E-02 -24.472106 3 2 3 -9.0546793 0.37000000 -24.472106 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 162 4 2 3 -1.9389818 0.79232320E-01 -24.472106 5 2 3 0.0000000 0.0000000 -24.472106 6 2 3 -6.3382755 0.25900000 -24.472106 7 2 3 -0.68678740 0.28064090E-01 -24.472106 8 2 3 0.0000000 0.0000000 -24.472106 9 2 3 -10.865615 0.44400000 -24.472106 10 2 3 -3.1221990 0.12758195 -24.472106 11 2 3 -0.80042124E-02 0.32707493E-03 -24.472106 12 2 3 -8.1492114 0.33300000 -24.472106 13 2 3 -1.4540173 0.59415289E-01 -24.472106 14 2 3 0.0000000 0.0000000 -24.472106 15 2 3 -5.4369904 0.22217092 -24.472106 16 2 3 -0.41383821 0.16910609E-01 -24.472106 17 2 3 0.0000000 0.0000000 -24.472106 18 2 3 -9.9601473 0.40700000 -24.472106 19 2 3 -2.4948925 0.10194842 -24.472106 20 2 3 0.0000000 0.0000000 -24.472106 21 2 3 -7.2437435 0.29600000 -24.472106 22 2 3 -1.0293216 0.42061014E-01 -24.472106 23 2 3 0.0000000 0.0000000 -24.472106 24 2 3 -4.5927983 0.18767483 -24.472106 25 2 3 -0.21002440 0.85821954E-02 -24.472106 26 2 3 0.0000000 0.0000000 -24.472106 27 2 3 -11.477418 0.46900000 -24.472106 28 2 3 -3.5674880 0.14577772 -24.472106 29 2 3 -0.45746753E-01 0.18693427E-02 -24.472106 30 2 3 -8.7610141 0.35800000 -24.472106 31 2 3 -1.7605275 0.71940169E-01 -24.472106 32 2 3 0.0000000 0.0000000 -24.472106 33 2 3 -6.0201382 0.24600000 -24.472106 34 2 3 -0.59066072 0.24136080E-01 -24.472106 35 2 3 0.0000000 0.0000000 -24.472106 36 2 3 -10.571950 0.43200000 -24.472106 37 2 3 -2.8936302 0.11824197 -24.472106 38 2 3 -0.88871776E-03 0.36315540E-04 -24.472106 39 2 3 -7.8555461 0.32100000 -24.472106 40 2 3 -1.3003832 0.53137365E-01 -24.472106 41 2 3 0.0000000 0.0000000 -24.472106 42 2 3 -5.1320648 0.20971079 -24.472106 43 2 3 -0.34018309 0.13900850E-01 -24.472106 44 2 3 0.0000000 0.0000000 -24.472106 45 2 3 -9.6664820 0.39500000 -24.472106 46 2 3 -2.2914599 0.93635581E-01 -24.472106 47 2 3 0.0000000 0.0000000 -24.472106 48 2 3 -6.9256061 0.28300000 -24.472106 49 2 3 -0.91057756 0.37208794E-01 -24.472106 50 2 3 0.0000000 0.0000000 -24.472106 1 1 5 -1.7926926 0.94309601E-01 -19.008591 2 1 5 -5.9306804 0.31200000 -19.008591 3 1 5 -0.68433999E-02 0.36001616E-03 -19.008591 4 1 5 -8.3067542 0.43700000 -19.008591 5 1 5 -0.53216038 0.27995783E-01 -19.008591 6 1 5 -3.6453442 0.19177351 -19.008591 7 1 5 0.0000000 0.0000000 -19.008591 8 1 5 -9.5042955 0.50000000 -19.008591 9 1 5 -1.0845394 0.57055222E-01 -19.008591 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 163 10 1 5 -4.7582308 0.25032002 -19.008591 11 1 5 0.0000000 0.0000000 -19.008591 12 1 5 -7.1092130 0.37400000 -19.008591 13 1 5 -0.16653783 0.87611874E-02 -19.008591 14 1 5 -2.6465167 0.13922740 -19.008591 15 1 5 0.0000000 0.0000000 -19.008591 16 1 5 -10.093562 0.53100000 -19.008591 17 1 5 -1.4193158 0.74667072E-01 -19.008591 18 1 5 -5.3414140 0.28100000 -19.008591 19 1 5 0.0000000 0.0000000 -19.008591 20 1 5 -7.7174879 0.40600000 -19.008591 21 1 5 -0.32777356 0.17243443E-01 -19.008591 22 1 5 -3.1384652 0.16510773 -19.008591 23 1 5 0.0000000 0.0000000 -19.008591 24 1 5 -8.8960206 0.46800000 -19.008591 25 1 5 -0.78176589 0.41126977E-01 -19.008591 26 1 5 -4.1798399 0.21989215 -19.008591 27 1 5 0.0000000 0.0000000 -19.008591 28 1 5 -6.5199467 0.34300000 -19.008591 29 1 5 -0.60772108E-01 0.31970864E-02 -19.008591 30 1 5 -2.2024871 0.11586799 -19.008591 31 1 5 0.0000000 0.0000000 -19.008591 32 1 5 -10.378691 0.54600000 -19.008591 33 1 5 -1.5952968 0.83925043E-01 -19.008591 34 1 5 -5.6265429 0.29600000 -19.008591 35 1 5 0.0000000 0.0000000 -19.008591 36 1 5 -8.0026168 0.42100000 -19.008591 37 1 5 -0.42088622 0.22141895E-01 -19.008591 38 1 5 -3.3801430 0.17782186 -19.008591 39 1 5 0.0000000 0.0000000 -19.008591 40 1 5 -9.2001580 0.48400000 -19.008591 41 1 5 -0.92757051 0.48797437E-01 -19.008591 42 1 5 -4.4657977 0.23493576 -19.008591 43 1 5 0.0000000 0.0000000 -19.008591 44 1 5 -6.8240841 0.35900000 -19.008591 45 1 5 -0.10902572 0.57356025E-02 -19.008591 46 1 5 -2.4275265 0.12770681 -19.008591 47 1 5 0.0000000 0.0000000 -19.008591 48 1 5 -9.7894243 0.51500000 -19.008591 49 1 5 -1.2415702 0.65316268E-01 -19.008591 50 1 5 -5.0380008 0.26503810 -19.008591 1 3 7 4.7021014 0.36800000 12.777449 2 3 7 2.1466115 0.16800000 12.777449 3 3 7 0.22439246 0.17561600E-01 12.777449 4 3 7 0.0000000 0.0000000 12.777449 5 3 7 6.7464933 0.52800000 12.777449 6 3 7 4.1910034 0.32800000 12.777449 7 3 7 1.6355135 0.12800000 12.777449 8 3 7 0.99245384E-01 0.77672296E-02 12.777449 9 3 7 0.0000000 0.0000000 12.777449 10 3 7 6.2353953 0.48800000 12.777449 11 3 7 3.6799054 0.28800000 12.777449 12 3 7 1.1304670 0.88473600E-01 12.777449 13 3 7 0.32249904E-01 0.25239704E-02 12.777449 14 3 7 0.0000000 0.0000000 12.777449 15 3 7 5.7242974 0.44800000 12.777449 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 164 16 3 7 3.1688075 0.24800000 12.777449 17 3 7 0.72183087 0.56492563E-01 12.777449 18 3 7 0.52336433E-02 0.40960000E-03 12.777449 19 3 7 0.0000000 0.0000000 12.777449 20 3 7 5.2131994 0.40800000 12.777449 21 3 7 2.6577095 0.20800000 12.777449 22 3 7 0.42586349 0.33329304E-01 12.777449 23 3 7 0.24229830E-04 0.18962963E-05 12.777449 24 3 7 0.0000000 0.0000000 12.777449 25 3 7 7.1553717 0.56000000 12.777449 26 3 7 4.5998818 0.36000000 12.777449 27 3 7 2.0443919 0.16000000 12.777449 28 3 7 0.19383864 0.15170370E-01 12.777449 29 3 7 0.0000000 0.0000000 12.777449 30 3 7 6.6442737 0.52000000 12.777449 31 3 7 4.0887838 0.32000000 12.777449 32 3 7 1.5332939 0.12000000 12.777449 33 3 7 0.81775676E-01 0.64000000E-02 12.777449 34 3 7 0.0000000 0.0000000 12.777449 35 3 7 6.1331757 0.48000000 12.777449 36 3 7 3.5776858 0.28000000 12.777449 37 3 7 1.0388540 0.81303704E-01 12.777449 38 3 7 0.24229830E-01 0.18962963E-02 12.777449 39 3 7 0.0000000 0.0000000 12.777449 40 3 7 5.6220778 0.44000000 12.777449 41 3 7 3.0665879 0.24000000 12.777449 42 3 7 0.65420541 0.51200000E-01 12.777449 43 3 7 0.30287288E-02 0.23703704E-03 12.777449 44 3 7 0.0000000 0.0000000 12.777449 45 3 7 5.1109798 0.40000000 12.777449 46 3 7 2.5554899 0.20000000 12.777449 47 3 7 0.37859109 0.29629630E-01 12.777449 48 3 7 0.0000000 0.0000000 12.777449 49 3 7 0.0000000 0.0000000 12.777449 50 3 7 7.0531521 0.55200000 12.777449 1 5 8 0.47667160E-03 0.43032070E-04 11.077125 2 5 8 0.51163914 0.46188805E-01 11.077125 3 5 8 2.5698929 0.23200000 11.077125 4 5 8 4.7853178 0.43200000 11.077125 5 5 8 0.0000000 0.0000000 11.077125 6 5 8 0.13317094E-01 0.12022157E-02 11.077125 7 5 8 0.82546732 0.74520000E-01 11.077125 8 5 8 3.0129779 0.27200000 11.077125 9 5 8 5.2284028 0.47200000 11.077125 10 5 8 0.0000000 0.0000000 11.077125 11 5 8 0.55352036E-01 0.49969679E-02 11.077125 12 5 8 1.2406379 0.11200000 11.077125 13 5 8 3.4560629 0.31200000 11.077125 14 5 8 5.6714878 0.51200000 11.077125 15 5 8 0.0000000 0.0000000 11.077125 16 5 8 0.14208301 0.12826706E-01 11.077125 17 5 8 1.6837229 0.15200000 11.077125 18 5 8 3.8991478 0.35200000 11.077125 19 5 8 6.1145727 0.55200000 11.077125 20 5 8 0.0000000 0.0000000 11.077125 21 5 8 0.28901154 0.26090845E-01 11.077125 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 165 22 5 8 2.1268079 0.19200000 11.077125 23 5 8 4.3422328 0.39200000 11.077125 24 5 8 6.5576577 0.59200000 11.077125 25 5 8 0.0000000 0.0000000 11.077125 26 5 8 0.14532671E-02 0.13119534E-03 11.077125 27 5 8 0.56661268 0.51151603E-01 11.077125 28 5 8 2.6585099 0.24000000 11.077125 29 5 8 4.8739348 0.44000000 11.077125 30 5 8 0.0000000 0.0000000 11.077125 31 5 8 0.18892472E-01 0.17055394E-02 11.077125 32 5 8 0.90054116 0.81297376E-01 11.077125 33 5 8 3.1015949 0.28000000 11.077125 34 5 8 5.3170198 0.48000000 11.077125 35 5 8 0.0000000 0.0000000 11.077125 36 5 8 0.68626500E-01 0.61953353E-02 11.077125 37 5 8 1.3292549 0.12000000 11.077125 38 5 8 3.5446799 0.32000000 11.077125 39 5 8 5.7601048 0.52000000 11.077125 40 5 8 0.0000000 0.0000000 11.077125 41 5 8 0.16615687 0.15000000E-01 11.077125 42 5 8 1.7723399 0.16000000 11.077125 43 5 8 3.9877648 0.36000000 11.077125 44 5 8 6.2031897 0.56000000 11.077125 45 5 8 0.0000000 0.0000000 11.077125 46 5 8 0.32698509 0.29518950E-01 11.077125 47 5 8 2.2154249 0.20000000 11.077125 48 5 8 4.4308498 0.40000000 11.077125 49 5 8 6.6462747 0.60000000 11.077125 50 5 8 0.0000000 0.0000000 11.077125 1 5 9 0.0000000 0.0000000 3.3650139 2 5 9 0.0000000 0.0000000 3.3650139 3 5 9 0.44185804E-01 0.13130942E-01 3.3650139 4 5 9 0.17450329 0.51858117E-01 3.3650139 5 5 9 0.37464890 0.11133651 3.3650139 6 5 9 0.62520268 0.18579497 3.3650139 7 5 9 0.91548011 0.27205834 3.3650139 8 5 9 1.2215001 0.36300000 3.3650139 9 5 9 1.5277163 0.45400000 3.3650139 10 5 9 1.8339326 0.54500000 3.3650139 11 5 9 0.0000000 0.0000000 3.3650139 12 5 9 0.0000000 0.0000000 3.3650139 13 5 9 0.98221278E-04 0.29188966E-04 3.3650139 14 5 9 0.52423626E-01 0.15579022E-01 3.3650139 15 5 9 0.18953744 0.56325901E-01 3.3650139 16 5 9 0.39503743 0.11739548 3.3650139 17 5 9 0.65252136 0.19391342 3.3650139 18 5 9 0.94558698 0.28100537 3.3650139 19 5 9 1.2517852 0.37200000 3.3650139 20 5 9 1.5546364 0.46200000 3.3650139 21 5 9 1.8608527 0.55300000 3.3650139 22 5 9 0.0000000 0.0000000 3.3650139 23 5 9 0.0000000 0.0000000 3.3650139 24 5 9 0.87981243E-03 0.26145878E-03 3.3650139 25 5 9 0.61316738E-01 0.18221838E-01 3.3650139 26 5 9 0.20510012 0.60950749E-01 3.3650139 27 5 9 0.41582772 0.12357385 3.3650139 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 166 28 5 9 0.67709730 0.20121679 3.3650139 29 5 9 0.97248903 0.28900000 3.3650139 30 5 9 1.2787053 0.38000000 3.3650139 31 5 9 1.5849216 0.47100000 3.3650139 32 5 9 1.8911378 0.56200000 3.3650139 33 5 9 0.0000000 0.0000000 3.3650139 34 5 9 0.0000000 0.0000000 3.3650139 35 5 9 0.26800273E-02 0.79643871E-03 3.3650139 36 5 9 0.72090890E-01 0.21423653E-01 3.3650139 37 5 9 0.22118018 0.65729350E-01 3.3650139 38 5 9 0.43700863 0.12986830 3.3650139 39 5 9 0.70193710 0.20859857 3.3650139 40 5 9 0.99940914 0.29700000 3.3650139 41 5 9 1.3056254 0.38800000 3.3650139 42 5 9 1.6118417 0.47900000 3.3650139 43 5 9 1.9180579 0.57000000 3.3650139 44 5 9 0.0000000 0.0000000 3.3650139 45 5 9 0.0000000 0.0000000 3.3650139 46 5 9 0.50864842E-02 0.15115789E-02 3.3650139 47 5 9 0.82339492E-01 0.24469287E-01 3.3650139 48 5 9 0.23987480 0.71284936E-01 3.3650139 49 5 9 0.46129018 0.13708418 3.3650139 50 5 9 0.73018338 0.21699268 3.3650139 1 2 11 -2.0071134 0.27300000 -7.3520638 2 2 11 -1.3380756 0.18200000 -7.3520638 3 2 11 -0.76557733 0.10413094 -7.3520638 4 2 11 -0.38126419 0.51858117E-01 -7.3520638 5 2 11 -0.14951530 0.20336508E-01 -7.3520638 6 2 11 -0.35252954E-01 0.47949740E-02 -7.3520638 7 2 11 -0.42893458E-03 0.58342064E-04 -7.3520638 8 2 11 0.0000000 0.0000000 -7.3520638 9 2 11 0.0000000 0.0000000 -7.3520638 10 2 11 0.0000000 0.0000000 -7.3520638 11 2 11 -2.6173347 0.35600000 -7.3520638 12 2 11 -1.9482969 0.26500000 -7.3520638 13 2 11 -1.2794737 0.17402919 -7.3520638 14 2 11 -0.72475926 0.98579022E-01 -7.3520638 15 2 11 -0.35529511 0.48325901E-01 -7.3520638 16 2 11 -0.13524475 0.18395481E-01 -7.3520638 17 2 11 -0.28771704E-01 0.39134187E-02 -7.3520638 18 2 11 -0.39467857E-04 0.53682692E-05 -7.3520638 19 2 11 0.0000000 0.0000000 -7.3520638 20 2 11 0.0000000 0.0000000 -7.3520638 21 2 11 0.0000000 0.0000000 -7.3520638 22 2 11 -2.5511661 0.34700000 -7.3520638 23 2 11 -1.8894804 0.25700000 -7.3520638 24 2 11 -1.2223648 0.16626146 -7.3520638 25 2 11 -0.68537290 0.93221838E-01 -7.3520638 26 2 11 -0.33048077 0.44950749E-01 -7.3520638 27 2 11 -0.12185199 0.16573848E-01 -7.3520638 28 2 11 -0.23650045E-01 0.32167899E-02 -7.3520638 29 2 11 0.0000000 0.0000000 -7.3520638 30 2 11 0.0000000 0.0000000 -7.3520638 31 2 11 0.0000000 0.0000000 -7.3520638 32 2 11 0.0000000 0.0000000 -7.3520638 33 2 11 -2.4923496 0.33900000 -7.3520638 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 167 34 2 11 -1.8233118 0.24800000 -7.3520638 35 2 11 -1.1601295 0.15779644 -7.3520638 36 2 11 -0.64274427 0.87423653E-01 -7.3520638 37 2 11 -0.30679684 0.41729350E-01 -7.3520638 38 2 11 -0.10931266 0.14868296E-01 -7.3520638 39 2 11 -0.19104859E-01 0.25985710E-02 -7.3520638 40 2 11 0.0000000 0.0000000 -7.3520638 41 2 11 0.0000000 0.0000000 -7.3520638 42 2 11 0.0000000 0.0000000 -7.3520638 43 2 11 0.0000000 0.0000000 -7.3520638 44 2 11 -2.4335331 0.33100000 -7.3520638 45 2 11 -1.7644953 0.24000000 -7.3520638 46 2 11 -1.1065707 0.15051158 -7.3520638 47 2 11 -0.60631946 0.82469287E-01 -7.3520638 48 2 11 -0.28147329 0.38284936E-01 -7.3520638 49 2 11 -0.96195725E-01 0.13084180E-01 -7.3520638 50 2 11 -0.14650276E-01 0.19926753E-02 -7.3520638 1 2 12 0.72873113 0.24520496E-01 29.719265 2 2 12 -0.15774941 -0.53079850E-02 29.719265 3 2 12 0.51571183E-02 0.17352779E-03 29.719265 4 2 12 1.9351105 0.65113000E-01 29.719265 5 2 12 0.0000000 0.0000000 29.719265 6 2 12 2.1144654 0.71147972E-01 29.719265 7 2 12 0.0000000 0.0000000 29.719265 8 2 12 0.0000000 0.0000000 29.719265 9 2 12 0.94277543 0.31722704E-01 29.719265 10 2 12 1.6589699 0.55821364E-01 29.719265 11 2 12 0.0000000 0.0000000 29.719265 12 2 12 4.9461773 0.16643000 29.719265 13 2 12 0.29162118E-01 0.98125299E-03 29.719265 14 2 12 0.0000000 0.0000000 29.719265 15 2 12 0.0000000 0.0000000 29.719265 16 2 12 0.43868850E-01 0.14761082E-02 29.719265 17 2 12 0.0000000 0.0000000 29.719265 18 2 12 4.3342279 0.14583900 29.719265 19 2 12 0.0000000 0.0000000 29.719265 20 2 12 -0.46958671E-01 -0.15800751E-02 29.719265 21 2 12 0.20908468 0.70353249E-02 29.719265 22 2 12 0.36310914 0.12217972E-01 29.719265 23 2 12 0.0000000 0.0000000 29.719265 24 2 12 4.1308590 0.13899600 29.719265 25 2 12 -0.17396364E-01 -0.58535647E-03 29.719265 26 2 12 0.0000000 0.0000000 29.719265 27 2 12 0.0000000 0.0000000 29.719265 28 2 12 2.5178458 0.84721000E-01 29.719265 29 2 12 -0.15066376E-02 -0.50695656E-04 29.719265 30 2 12 1.6184503 0.54457953E-01 29.719265 31 2 12 0.0000000 0.0000000 29.719265 32 2 12 0.0000000 0.0000000 29.719265 33 2 12 0.89292023 0.30045165E-01 29.719265 34 2 12 0.21992256 0.74000000E-02 29.719265 35 2 12 0.0000000 0.0000000 29.719265 36 2 12 6.8064249 0.22902400 29.719265 37 2 12 0.13818858 0.46497979E-02 29.719265 38 2 12 -0.47716530E-01 -0.16055757E-02 29.719265 39 2 12 0.0000000 0.0000000 29.719265 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 168 40 2 12 1.4240283 0.47916000E-01 29.719265 41 2 12 0.0000000 0.0000000 29.719265 42 2 12 2.2412599 0.75414378E-01 29.719265 43 2 12 0.0000000 0.0000000 29.719265 44 2 12 0.0000000 0.0000000 29.719265 45 2 12 0.86422150E-01 0.29079505E-02 29.719265 46 2 12 0.65659598 0.22093278E-01 29.719265 47 2 12 0.0000000 0.0000000 29.719265 48 2 12 6.0456415 0.20342500 29.719265 49 2 12 0.12035139 0.40496086E-02 29.719265 50 2 12 0.0000000 0.0000000 29.719265 1 3 14 0.90290980E-02 -0.17671663E-03 -51.093652 2 3 14 0.0000000 0.0000000 -51.093652 3 3 14 0.0000000 0.0000000 -51.093652 4 3 14 0.0000000 0.0000000 -51.093652 5 3 14 -1.0321461 0.20201064E-01 -51.093652 6 3 14 0.0000000 0.0000000 -51.093652 7 3 14 -0.33035747E-01 0.64657244E-03 -51.093652 8 3 14 0.0000000 0.0000000 -51.093652 9 3 14 0.0000000 0.0000000 -51.093652 10 3 14 0.22921271E-03 -0.44861289E-05 -51.093652 11 3 14 -1.8904651 0.37000000E-01 -51.093652 12 3 14 0.0000000 0.0000000 -51.093652 13 3 14 0.19977489 -0.39099747E-02 -51.093652 14 3 14 -0.20150809 0.39438967E-02 -51.093652 15 3 14 0.0000000 0.0000000 -51.093652 16 3 14 0.0000000 0.0000000 -51.093652 17 3 14 -0.82551078 0.16156817E-01 -51.093652 18 3 14 0.0000000 0.0000000 -51.093652 19 3 14 0.25609705 -0.50123066E-02 -51.093652 20 3 14 0.0000000 0.0000000 -51.093652 21 3 14 0.0000000 0.0000000 -51.093652 22 3 14 0.91147295E-02 -0.17839260E-03 -51.093652 23 3 14 -5.2025601 0.10182400 -51.093652 24 3 14 0.0000000 0.0000000 -51.093652 25 3 14 -0.27648800 0.54113963E-02 -51.093652 26 3 14 -0.39347456E-01 0.77010459E-03 -51.093652 27 3 14 0.0000000 0.0000000 -51.093652 28 3 14 0.0000000 0.0000000 -51.093652 29 3 14 -1.0067617 0.19704242E-01 -51.093652 30 3 14 0.0000000 0.0000000 -51.093652 31 3 14 0.61975283 -0.12129742E-01 -51.093652 32 3 14 0.0000000 0.0000000 -51.093652 33 3 14 0.0000000 0.0000000 -51.093652 34 3 14 0.0000000 0.0000000 -51.093652 35 3 14 -3.5959713 0.70380000E-01 -51.093652 36 3 14 0.0000000 0.0000000 -51.093652 37 3 14 0.89191224E-01 -0.17456420E-02 -51.093652 38 3 14 -0.55768600E-01 0.10914976E-02 -51.093652 39 3 14 0.0000000 0.0000000 -51.093652 40 3 14 0.0000000 0.0000000 -51.093652 41 3 14 -0.89720992 0.17560105E-01 -51.093652 42 3 14 0.0000000 0.0000000 -51.093652 43 3 14 -0.66595466 0.13034000E-01 -51.093652 44 3 14 0.0000000 0.0000000 -51.093652 45 3 14 0.0000000 0.0000000 -51.093652 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 169 46 3 14 0.24367644E-01 -0.47692116E-03 -51.093652 47 3 14 -3.9355908 0.77027000E-01 -51.093652 48 3 14 0.0000000 0.0000000 -51.093652 49 3 14 0.36166781E-01 -0.70785272E-03 -51.093652 50 3 14 -0.59957290E-03 0.11734783E-04 -51.093652 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 170 Obs Y Yhat Residual 1 9.6530000 10.201354 -0.54835389 2 8.7650000 8.9987611 -0.23376107 3 8.2920000 8.3181797 -0.26179683E-01 4 13.796000 13.019114 0.77688570 5 24.134000 23.618243 0.51575731 6 17.111000 16.595778 0.51522237 7 13.420000 13.782802 -0.36280154 8 7.9510000 7.4157599 0.53524009 9 9.9390000 9.7948114 0.14418861 10 15.615000 17.353908 -1.7389081 11 16.956000 16.185004 0.77099635 12 8.9240000 8.5358505 0.38814952 13 19.789000 20.702348 -0.91334822 14 14.596000 13.492087 1.1039127 15 13.713000 12.922249 0.79075132 16 6.8620000 7.3675908 -0.50559078 17 17.263000 16.494447 0.76855296 18 11.168000 11.052305 0.11569487 19 21.977000 23.757011 -1.7800115 20 18.631000 19.092578 -0.46157760 21 7.9090000 8.9902607 -1.0812607 22 9.8660000 9.2108010 0.65519896 23 10.142000 11.714815 -1.5728147 24 12.161000 11.902550 0.25844970 25 22.449000 22.629718 -0.18071779 26 19.795000 19.100583 0.69441664 27 11.399000 11.720910 -0.32191019 28 5.9240000 7.6956936 -1.7716936 29 14.938000 17.940655 -3.0026547 30 13.153000 13.246686 -0.93685628E-01 31 21.515000 20.680320 0.83467991 32 11.851000 11.534519 0.31648146 33 12.167000 13.016482 -0.84948185 34 17.204000 18.004142 -0.80014193 35 14.095000 13.343401 0.75159895 36 3.9250000 4.7309026 -0.80590260 37 14.185000 14.078480 0.10651953 38 14.717000 16.754953 -2.0379530 39 18.291000 16.379786 1.9112135 40 15.741000 16.797109 -1.0561090 41 24.748000 23.425464 1.3225359 42 11.031000 8.8495898 2.1814102 43 20.199000 18.530259 1.6687415 44 13.252000 12.032857 1.2191434 45 10.041000 10.204422 -0.16342246 46 15.079000 15.749731 -0.67073093 47 18.463000 17.600948 0.86205239 48 15.470000 14.646104 0.82389589 49 16.365000 15.968797 0.39620323 50 15.694000 15.142881 0.55111860 Sum of squared residuals using piecewise-cubic MARS model: 54.98285591087557 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 171 Sum of squared Y values 11219.48594000000 % Reduction in sum of squares (1.0 - (RESID***2/Y**2) ) 0.9950993426788968 Variance of Y 23.02616817306123 Residual Variance 1.122099100221950 Approximate R squared value 0.9512685266698123 Plot of the Residual RESIDUAL 2.1814 * . * * * . * * . * * * * . * . * . * * . . . * . . . . . * . . * . . . . * . . * . * . * . . . *----.----------------------------------------------------------------------------------------------- * . * . . . * . * . . *. . * . * * . . . * . * . . * * * * * . * * . . . * * . * * * * * * * * * . -3.0027 ***************************************************************************************************** 1.0000 50.000 TIME B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 172 Analysis of MARS Forecasts by observation. Cubic approximation method used. Obs # Var # Basis # Total Effect ( )+ Coef. used 51 4 1 1.4291155 0.14000000 10.207968 52 4 1 2.8888549 0.28300000 10.207968 53 4 1 4.3485943 0.42600000 10.207968 51 2 3 -3.8213511 0.15615129 -24.472106 52 2 3 -0.74896286E-01 0.30604757E-02 -24.472106 53 2 3 -9.0546793 0.37000000 -24.472106 51 1 5 -1.7926926 0.94309601E-01 -19.008591 52 1 5 -5.9306804 0.31200000 -19.008591 53 1 5 -0.68433999E-02 0.36001616E-03 -19.008591 51 3 7 4.7021014 0.36800000 12.777449 52 3 7 2.1466115 0.16800000 12.777449 53 3 7 0.22439246 0.17561600E-01 12.777449 51 5 8 0.47667160E-03 0.43032070E-04 11.077125 52 5 8 0.51163914 0.46188805E-01 11.077125 53 5 8 2.5698929 0.23200000 11.077125 51 5 9 0.0000000 0.0000000 3.3650139 52 5 9 0.0000000 0.0000000 3.3650139 53 5 9 0.44185804E-01 0.13130942E-01 3.3650139 51 2 11 -2.0071134 0.27300000 -7.3520638 52 2 11 -1.3380756 0.18200000 -7.3520638 53 2 11 -0.76557733 0.10413094 -7.3520638 51 2 12 0.72873113 0.24520496E-01 29.719265 52 2 12 -0.15774941 -0.53079850E-02 29.719265 53 2 12 0.51571183E-02 0.17352779E-03 29.719265 51 3 14 0.90290980E-02 -0.17671663E-03 -51.093652 52 3 14 0.0000000 0.0000000 -51.093652 53 3 14 0.0000000 0.0000000 -51.093652 Forecasts on the Y Variable outside sample Observation Predicted Value 51 10.201354 52 8.9987611 53 8.3181797 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 173 Multivariate Adaptive Regression Splines (MARS) Program developed by Jerome Friedman Basic reference: Multivariate Adaptive Regression Splines Annals of Statistics, 1991, Vol. 19, No. 1, pp. 1-141 Program Modified by H. H. Stokes March 2002 Real*8 storage available : 5999699 Real*8 Storage used : 6693 Exogenous Variables Var # Name Mean Variance Max Min 1 X1 0.48286000 0.81393592E-01 0.96900000 0.16000000E-01 2 X2 0.48814000 0.80952000E-01 0.96300000 0.12000000E-01 3 X3 0.48432000 0.84603324E-01 0.96800000 0.80000000E-02 4 X4 0.48298000 0.85625326E-01 0.98000000 0.30000000E-02 5 X5 0.45376000 0.78082594E-01 0.93400000 0.80000000E-02 Endogenous Variable Name Mean Variance Max Min Y 14.206480 23.026168 24.748000 3.9250000 MARS Modeling, Version 3.5 (6/16/91) - Revised (1/3/02) Input parameters (see doc.): N P NK MS MI DF IL FV IC 50 5 15 0 2 3.000 0 0.000 0 Predictor variable flags: 1 2 3 4 5 1 1 1 1 1 Ordinal Response: MIN N/4 N/2 3N/4 MAX 3.925 10.04 14.10 17.20 24.75 Number of ordinal predictor variables. 5 VAR MIN N/4 N/2 3N/4 MAX 1 0.1600E-01 0.2190 0.4690 0.7190 0.9690 2 0.1200E-01 0.2220 0.4810 0.7410 0.9630 3 0.8000E-02 0.2080 0.4800 0.7280 0.9680 4 0.3000E-02 0.2040 0.4690 0.7350 0.9800 5 0.8000E-02 0.1980 0.4550 0.6610 0.9340 Forward stepwise knot placement: BASFN(S) GCV #INDBSFNS #EFPRMS Variable Knot Parent 0 23.50 0.0 1.0 1 20.96 1.0 5.0 4. 0.3000E-02 0. 3 2 17.98 3.0 10.0 2. 0.4810 0. 5 4 13.97 5.0 15.0 1. 0.5620 0. B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 174 7 6 12.22 7.0 20.0 3. 0.5680 0. 9 8 9.847 9.0 25.0 5. 0.3640 0. 11 10 9.411 11.0 30.0 2. 0.5930 5. 13 12 11.84 13.0 35.0 2. 0.5560 4. 15 14 18.43 14.0 39.0 3. 0.3680 0. Final model after backward stepwise elimination: BSFN: 0 1 2 3 4 5 Coef: 10.19 9.952 0.000 -21.78 0.000 -17.46 BSFN: 6 7 8 9 10 11 Coef: 0.000 12.49 3.625 -7.040 0.000 26.02 BSFN: 12 13 14 15 Coef: -39.59 0.000 10.79 0.000 Piecewise Linear GCV = 5.025 # Effective Parameters= 25.43 Number of Basis for ANOVA decomposition 9 Fun. Std. Dev. -GCV #BSFNS #EFPRMS Variable(s) 1 2.883 31.07 1 2.7 4 2 3.374 24.87 1 2.7 2 3 3.259 21.84 1 2.7 1 4 1.522 9.677 2 5.4 3 5 1.346 7.938 2 5.4 5 6 1.769 6.586 2 5.4 1 2 Number of basic functions for Piecewise cubic fit 9 Generalized Cross Validation Criteria 4.553407145134045 GCV removing each variable 1 2 3 4 5 16.7088 18.9849 9.67688 31.0695 7.93815 Relative variable importance 1 2 3 4 5 66.9783 73.2123 42.2627 100.000 33.4446 Sum of squared residuals using piecewise-linear MARS model 60.67699114872438 Sum of squared residuals using piecewise-cubic MARS model 54.98285591087557 Piecewise-Cubic MARS model selected B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 175 Obs Y Yhat Residual 1 9.6530000 10.201354 -0.54835389 2 8.7650000 8.9987611 -0.23376107 3 8.2920000 8.3181797 -0.26179683E-01 4 13.796000 13.019114 0.77688570 5 24.134000 23.618243 0.51575731 6 17.111000 16.595778 0.51522237 7 13.420000 13.782802 -0.36280154 8 7.9510000 7.4157599 0.53524009 9 9.9390000 9.7948114 0.14418861 10 15.615000 17.353908 -1.7389081 11 16.956000 16.185004 0.77099635 12 8.9240000 8.5358505 0.38814952 13 19.789000 20.702348 -0.91334822 14 14.596000 13.492087 1.1039127 15 13.713000 12.922249 0.79075132 16 6.8620000 7.3675908 -0.50559078 17 17.263000 16.494447 0.76855296 18 11.168000 11.052305 0.11569487 19 21.977000 23.757011 -1.7800115 20 18.631000 19.092578 -0.46157760 21 7.9090000 8.9902607 -1.0812607 22 9.8660000 9.2108010 0.65519896 23 10.142000 11.714815 -1.5728147 24 12.161000 11.902550 0.25844970 25 22.449000 22.629718 -0.18071779 26 19.795000 19.100583 0.69441664 27 11.399000 11.720910 -0.32191019 28 5.9240000 7.6956936 -1.7716936 29 14.938000 17.940655 -3.0026547 30 13.153000 13.246686 -0.93685628E-01 31 21.515000 20.680320 0.83467991 32 11.851000 11.534519 0.31648146 33 12.167000 13.016482 -0.84948185 34 17.204000 18.004142 -0.80014193 35 14.095000 13.343401 0.75159895 36 3.9250000 4.7309026 -0.80590260 37 14.185000 14.078480 0.10651953 38 14.717000 16.754953 -2.0379530 39 18.291000 16.379786 1.9112135 40 15.741000 16.797109 -1.0561090 41 24.748000 23.425464 1.3225359 42 11.031000 8.8495898 2.1814102 43 20.199000 18.530259 1.6687415 44 13.252000 12.032857 1.2191434 45 10.041000 10.204422 -0.16342246 46 15.079000 15.749731 -0.67073093 47 18.463000 17.600948 0.86205239 48 15.470000 14.646104 0.82389589 49 16.365000 15.968797 0.39620323 50 15.694000 15.142881 0.55111860 Sum of squared Y values 11219.48594000000 % Reduction in sum of squares (1.0 - (RESID***2/Y**2) ) 0.9950993426788968 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 176 Variance of Y 23.02616817306123 Residual Variance 1.122099100221950 Approximate R squared value 0.9512685266698123 Plot of Y, Yhat and Residual ********** Plot of the original series ********** Series 3 Series 2 Series 1 -3.0 2.2 4.7 24. 3.9 25. -0.411 14.2 14.3 + 1 + + 1 + + 1 + ----------------------------------------- ----------------------------------------- ------------------------------------------ I 1 I 1 I 1 I 2 I 2 I 2 I 3 I 3 I 3 I 4 I 4 I 4 I 5 I 5 I 5 I 6 I 6 I 6 I 7 I 7 I 7 I 8 I 8 I 8 I 9 I 9 I 9 10 + 0 + 0 + 0 I 1 I 1 I 1 I 2 I 2 I 2 I 3 I 3 I 3 I 4 I 4 I 4 I 5 I 5 I 5 I 6 I 6 I 6 I 7 I 7 I 7 I 8 I 8 I 8 I 9 I 9 I 9 20 + 0 + 0 + 0 I 1 I 1 I 1 I 2 I 2 I 2 I 3 I 3 I 3 I 4 I 4 I 4 I 5 I 5 I 5 I 6 I 6 I 6 I 7 I 7 I 7 I 8 I 8 I 8 I9 I 9 I 9 30 + 0 + 0 + 0 I 1 I 1 I 1 I 2 I 2 I 2 I 3 I 3 I 3 I 4 I 4 I 4 I 5 I 5 I 5 I 6 I6 I6 I 7 I 7 I 7 I 8 I 8 I 8 I 9 I 9 I 9 40 + 0 + 0 + 0 I 1 I 1 I 1 I 2 I 2 I 2 I 3 I 3 I 3 I 4 I 4 I 4 I 5 I 5 I 5 I 6 I 6 I 6 I 7 I 7 I 7 I 8 I 8 I 8 I 9 I 9 I 9 50 + 0 + 0 + 0 I I I I I I I I I I I I I I I I I I I I I I I I I I I 60 + + + Note: The number of observations plotted is 50 for each series Forecasts on the Y Variable outside sample Observation Predicted Value 51 10.201354 52 8.9987611 53 8.3181797 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 177 Multivariate Adaptive Regression Splines (MARS) Program developed by Jerome Friedman Basic reference: Multivariate Adaptive Regression Splines Annals of Statistics, 1991, Vol. 19, No. 1, pp. 1-141 Program Modified by H. H. Stokes March 2002 Real*8 storage available : 5999699 Real*8 Storage used : 6693 Exogenous Variables Var # Name Mean Variance Max Min 1 X1 0.48286000 0.81393592E-01 0.96900000 0.16000000E-01 2 X2 0.48814000 0.80952000E-01 0.96300000 0.12000000E-01 3 X3 0.48432000 0.84603324E-01 0.96800000 0.80000000E-02 4 X4 0.48298000 0.85625326E-01 0.98000000 0.30000000E-02 5 X5 0.45376000 0.78082594E-01 0.93400000 0.80000000E-02 Endogenous Variable Name Mean Variance Max Min Y 14.206480 23.026168 24.748000 3.9250000 MARS Modeling, Version 3.5 (6/16/91) - Revised (1/3/02) Input parameters (see doc.): N P NK MS MI DF IL FV IC 50 5 15 0 2 3.000 0 0.000 0 Predictor variable flags: 1 2 3 4 5 1 1 1 1 1 Ordinal Response: MIN N/4 N/2 3N/4 MAX 3.925 10.04 14.10 17.20 24.75 Number of ordinal predictor variables. 5 VAR MIN N/4 N/2 3N/4 MAX 1 0.1600E-01 0.2190 0.4690 0.7190 0.9690 2 0.1200E-01 0.2220 0.4810 0.7410 0.9630 3 0.8000E-02 0.2080 0.4800 0.7280 0.9680 4 0.3000E-02 0.2040 0.4690 0.7350 0.9800 5 0.8000E-02 0.1980 0.4550 0.6610 0.9340 Sample reuse to estimate df: Fold cross-validation. 2 #BSFNS DF ASR GCV CV 15 -1.50 1.185 1.279 21.40 8 -1.49 1.185 1.286 21.40 7 -0.52 1.186 1.966 21.46 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 178 6 1.02 1.395 4.519 20.17 5 2.08 1.927 8.310 20.76 4 2.75 3.073 12.02 20.83 3 3.38 4.804 14.85 23.34 2 4.25 7.742 18.19 26.40 1 5.33 12.78 21.15 28.00 0 5.99 20.39 22.12 29.09 Estimated optimal df( 6) = 1.02 Estimated PSE -1133021499 Forward stepwise knot placement: BASFN(S) GCV #INDBSFNS #EFPRMS Variable Knot Parent 0 23.50 0.0 1.0 1 19.23 1.0 3.0 4. 0.3000E-02 0. 2 15.86 2.0 5.0 2. 0.1200E-01 0. 4 3 11.45 4.0 8.1 1. 0.6560 2. 5 8.728 5.0 10.1 5. 0.8000E-02 0. 7 6 6.434 7.0 13.1 3. 0.5680 0. 9 8 4.631 9.0 16.1 1. 0.7660 5. 11 10 3.381 10.0 18.2 2. 0.2720 0. 13 12 3.269 12.0 21.2 3. 0.2880 5. 15 14 3.339 14.0 24.2 3. 0.8000 2. Final model after backward stepwise elimination: BSFN: 0 1 2 3 4 5 Coef: -0.9840 10.51 29.83 -33.46 -21.07 0.000 BSFN: 6 7 8 9 10 11 Coef: 0.000 6.918 58.33 0.000 -19.14 0.000 BSFN: 12 13 14 15 Coef: 14.46 17.77 32.84 0.000 Piecewise Linear GCV = 2.228 # Effective Parameters= 17.57 Number of Basis for ANOVA decomposition 10 Fun. Std. Dev. -GCV #BSFNS #EFPRMS Variable(s) 1 3.046 20.28 1 1.7 4 2 4.144 18.27 2 3.3 2 3 1.331 2.883 1 1.7 3 4 2.834 9.629 2 3.3 1 2 5 1.727 5.502 1 1.7 1 5 6 1.739 6.928 2 3.3 3 5 7 0.7724 3.024 1 1.7 2 3 Number of basic functions for Piecewise cubic fit 10 Generalized Cross Validation Criteria 2.753184814831929 GCV removing each variable 1 2 3 4 5 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 179 11.7482 17.5042 7.25911 20.2763 10.1044 Relative variable importance 1 2 3 4 5 72.6273 92.0002 52.7961 100.000 66.0600 Sum of squared residuals using piecewise-linear MARS model 46.85893832116239 Sum of squared residuals using piecewise-cubic MARS model 57.89406884487286 Piecewise-Linear MARS model selected B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 180 Obs Y Yhat Residual 1 9.6530000 10.516380 -0.86338020 2 8.7650000 9.8092024 -1.0442024 3 8.2920000 7.3329403 0.95905968 4 13.796000 12.384739 1.4112613 5 24.134000 24.777654 -0.64365372 6 17.111000 15.743346 1.3676537 7 13.420000 12.259625 1.1603751 8 7.9510000 7.7309986 0.22000141 9 9.9390000 9.3977645 0.54123547 10 15.615000 16.619575 -1.0045747 11 16.956000 15.962794 0.99320603 12 8.9240000 10.289768 -1.3657684 13 19.789000 18.735766 1.0532344 14 14.596000 13.733333 0.86266657 15 13.713000 13.795129 -0.82129400E-01 16 6.8620000 7.8832774 -1.0212774 17 17.263000 18.417971 -1.1549709 18 11.168000 10.758894 0.40910614 19 21.977000 23.318233 -1.3412326 20 18.631000 18.196429 0.43457060 21 7.9090000 7.1721883 0.73681173 22 9.8660000 8.9450928 0.92090718 23 10.142000 11.046490 -0.90448959 24 12.161000 12.124758 0.36241804E-01 25 22.449000 21.686840 0.76216034 26 19.795000 19.051117 0.74388343 27 11.399000 12.653710 -1.2547098 28 5.9240000 7.8819378 -1.9579378 29 14.938000 17.066096 -2.1280965 30 13.153000 12.452961 0.70003935 31 21.515000 22.015047 -0.50004662 32 11.851000 11.604047 0.24695292 33 12.167000 13.436974 -1.2699745 34 17.204000 16.958770 0.24522970 35 14.095000 15.291537 -1.1965366 36 3.9250000 4.1995932 -0.27459317 37 14.185000 13.541951 0.64304875 38 14.717000 15.862402 -1.1454019 39 18.291000 18.714910 -0.42390973 40 15.741000 16.722180 -0.98118035 41 24.748000 23.506479 1.2415205 42 11.031000 9.4014585 1.6295415 43 20.199000 18.915600 1.2834002 44 13.252000 13.432568 -0.18056820 45 10.041000 9.8834172 0.15758276 46 15.079000 15.497037 -0.41803739 47 18.463000 17.776557 0.68644269 48 15.470000 15.150701 0.31929945 49 16.365000 15.932587 0.43241323 50 15.694000 14.735174 0.95882594 Sum of squared Y values 11219.48594000000 % Reduction in sum of squares (1.0 - (RESID***2/Y**2) ) 0.9958234326802711 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 181 Variance of Y 23.02616817306123 Residual Variance 0.9563048636971918 Approximate R squared value 0.9584687796723386 Optimal smoothing parameter estimate (DFS) 1.022727009829788 Estimated predictive squared error (PSE) 20.17289331356621 Number of nonconstant basis functions (NBF) 6 Forecasts on the Y Variable outside sample Observation Predicted Value 51 10.516380 52 9.8092024 53 7.3329403 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 182 Multivariate Adaptive Regression Splines (MARS) Program developed by Jerome Friedman Basic reference: Multivariate Adaptive Regression Splines Annals of Statistics, 1991, Vol. 19, No. 1, pp. 1-141 Program Modified by H. H. Stokes March 2002 Real*8 storage available : 5999699 Real*8 Storage used : 6693 Exogenous Variables Var # Name Mean Variance Max Min 1 X1 0.48286000 0.81393592E-01 0.96900000 0.16000000E-01 2 X2 0.48814000 0.80952000E-01 0.96300000 0.12000000E-01 3 X3 0.48432000 0.84603324E-01 0.96800000 0.80000000E-02 4 X4 0.48298000 0.85625326E-01 0.98000000 0.30000000E-02 5 X5 0.45376000 0.78082594E-01 0.93400000 0.80000000E-02 Endogenous Variable Name Mean Variance Max Min Y 14.206480 23.026168 24.748000 3.9250000 MARS Modeling, Version 3.5 (6/16/91) - Revised (1/3/02) Input parameters (see doc.): N P NK MS MI DF IL FV IC 50 5 15 0 2 3.000 0 0.000 0 Predictor variable flags: 1 2 3 4 5 1 1 1 1 1 Ordinal Response: MIN N/4 N/2 3N/4 MAX 3.925 10.04 14.10 17.20 24.75 Number of ordinal predictor variables. 5 VAR MIN N/4 N/2 3N/4 MAX 1 0.1600E-01 0.2190 0.4690 0.7190 0.9690 2 0.1200E-01 0.2220 0.4810 0.7410 0.9630 3 0.8000E-02 0.2080 0.4800 0.7280 0.9680 4 0.3000E-02 0.2040 0.4690 0.7350 0.9800 5 0.8000E-02 0.1980 0.4550 0.6610 0.9340 Sample reuse to estimate df: Fold cross-validation. 10 #BSFNS DF ASR GCV CV 15 -1.57 0.8453 0.9030 5.666 14 -1.45 0.8469 0.9480 5.678 13 -0.83 0.8546 1.223 5.670 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 183 12 -0.18 0.9043 1.650 6.150 11 0.67 0.9660 2.420 5.925 10 1.68 1.135 4.102 5.701 9 2.14 1.407 5.321 5.835 8 2.46 1.852 6.574 6.628 7 2.86 2.337 7.784 7.176 6 3.77 3.070 10.72 7.057 4 4.53 5.675 13.82 10.73 3 6.80 7.348 18.39 11.29 0 8.95 22.51 23.54 23.69 Estimated optimal df( 15) = -1.57 Estimated PSE 1149950382 Forward stepwise knot placement: BASFN(S) GCV #INDBSFNS #EFPRMS Variable Knot Parent 0 23.50 0.0 1.0 1 17.27 1.0 0.4 4. 0.3000E-02 0. 3 2 11.91 3.0 0.9 2. 0.4810 0. 5 4 7.208 5.0 1.3 1. 0.5620 0. 7 6 4.716 7.0 1.7 3. 0.5680 0. 8 2.785 8.0 1.1 5. 0.8000E-02 0. 10 9 1.774 10.0 1.6 2. 0.5930 5. 12 11 1.191 12.0 2.0 2. 0.5560 4. 14 13 0.9578 13.0 1.4 3. 0.3680 0. 15 0.8536 14.0 0.8 2. 0.1200E-01 13. Final model after backward stepwise elimination: BSFN: 0 1 2 3 4 5 Coef: 7.372 9.631 5.032 -22.25 4.568 -17.97 BSFN: 6 7 8 9 10 11 Coef: -1.362 12.83 4.216 4.636 33.94 -64.86 BSFN: 12 13 14 15 Coef: 1.607 14.46 0.000 -5.534 Piecewise Linear GCV = 0.8536 # Effective Parameters= 0.8321 Number of Basis for ANOVA decomposition 14 Fun. Std. Dev. -GCV #BSFNS #EFPRMS Variable(s) 1 2.790 7.805 1 0.0 4 2 3.982 4.244 2 0.0 2 3 3.730 4.661 2 0.0 1 4 1.715 3.280 3 0.0 3 5 1.166 1.898 1 0.0 5 6 2.466 2.518 4 0.0 1 2 7 0.6854 0.9360 1 0.0 2 3 Number of basic functions for Piecewise cubic fit 14 Generalized Cross Validation Criteria 0.8922816635224473 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 184 GCV removing each variable 1 2 3 4 5 7.38519 8.49864 3.29148 7.80485 1.89843 Relative variable importance 1 2 3 4 5 92.4314 100.000 56.4698 95.3546 36.9687 Sum of squared residuals using piecewise-linear MARS model 41.27092732871801 Sum of squared residuals using piecewise-cubic MARS model 43.14157498780880 Piecewise-Linear MARS model selected B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 185 Obs Y Yhat Residual 1 9.6530000 9.9324813 -0.27948131 2 8.7650000 8.7701928 -0.51927503E-02 3 8.2920000 8.5376294 -0.24562940 4 13.796000 12.775607 1.0203930 5 24.134000 23.755011 0.37898892 6 17.111000 15.301631 1.8093693 7 13.420000 14.457870 -1.0378700 8 7.9510000 8.2140574 -0.26305743 9 9.9390000 10.216773 -0.27777290 10 15.615000 16.658272 -1.0432724 11 16.956000 16.604916 0.35108383 12 8.9240000 8.9885319 -0.64531880E-01 13 19.789000 20.707132 -0.91813198 14 14.596000 13.172952 1.4230479 15 13.713000 13.356496 0.35650433 16 6.8620000 6.6148235 0.24717647 17 17.263000 17.937577 -0.67457662 18 11.168000 11.529997 -0.36199747 19 21.977000 23.387217 -1.4102171 20 18.631000 18.967518 -0.33651813 21 7.9090000 8.3320955 -0.42309547 22 9.8660000 9.4659984 0.40000165 23 10.142000 11.521944 -1.3799440 24 12.161000 12.151058 0.99424969E-02 25 22.449000 22.552725 -0.10372465 26 19.795000 19.886873 -0.91872741E-01 27 11.399000 11.868290 -0.46929000 28 5.9240000 7.1491002 -1.2251002 29 14.938000 17.093092 -2.1550917 30 13.153000 12.500499 0.65250104 31 21.515000 21.238341 0.27665875 32 11.851000 12.097261 -0.24626089 33 12.167000 12.934818 -0.76781793 34 17.204000 17.295075 -0.91074708E-01 35 14.095000 13.804573 0.29042717 36 3.9250000 5.1135371 -1.1885371 37 14.185000 13.400274 0.78472589 38 14.717000 15.867830 -1.1508299 39 18.291000 17.422960 0.86803968 40 15.741000 16.595598 -0.85459794 41 24.748000 24.329179 0.41882074 42 11.031000 8.3297045 2.7012955 43 20.199000 18.600286 1.5987140 44 13.252000 12.538766 0.71323378 45 10.041000 10.233925 -0.19292463 46 15.079000 14.790447 0.28855341 47 18.463000 16.892261 1.5707392 48 15.470000 14.874600 0.59539989 49 16.365000 15.818061 0.54693939 50 15.694000 15.738145 -0.44145182E-01 Sum of squared Y values 11219.48594000000 % Reduction in sum of squares (1.0 - (RESID***2/Y**2) ) 0.9963214956951301 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 186 Variance of Y 23.02616817306123 Residual Variance 0.8422638230350614 Approximate R squared value 0.9634214509029582 Optimal smoothing parameter estimate (DFS) -1.574215594569010 Estimated predictive squared error (PSE) 5.665757246947051 Number of nonconstant basis functions (NBF) 15 Forecasts on the Y Variable outside sample Observation Predicted Value 51 9.9324813 52 8.7701928 53 8.5376294 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 187 Multivariate Adaptive Regression Splines (MARS) Program developed by Jerome Friedman Basic reference: Multivariate Adaptive Regression Splines Annals of Statistics, 1991, Vol. 19, No. 1, pp. 1-141 Program Modified by H. H. Stokes March 2002 Real*8 storage available : 5999699 Real*8 Storage used : 6693 Exogenous Variables Var # Name Mean Variance Max Min 1 X1 0.48286000 0.81393592E-01 0.96900000 0.16000000E-01 2 X2 0.48814000 0.80952000E-01 0.96300000 0.12000000E-01 3 X3 0.48432000 0.84603324E-01 0.96800000 0.80000000E-02 4 X4 0.48298000 0.85625326E-01 0.98000000 0.30000000E-02 5 X5 0.45376000 0.78082594E-01 0.93400000 0.80000000E-02 Endogenous Variable Name Mean Variance Max Min Y 14.206480 23.026168 24.748000 3.9250000 MARS Modeling, Version 3.5 (6/16/91) - Revised (1/3/02) Input parameters (see doc.): N P NK MS MI DF IL FV IC 50 5 15 0 2 3.000 0 0.000 0 Predictor variable flags: 1 2 3 4 5 1 1 1 1 1 Ordinal Response: MIN N/4 N/2 3N/4 MAX 3.925 10.04 14.10 17.20 24.75 Number of ordinal predictor variables. 5 VAR MIN N/4 N/2 3N/4 MAX 1 0.1600E-01 0.2190 0.4690 0.7190 0.9690 2 0.1200E-01 0.2220 0.4810 0.7410 0.9630 3 0.8000E-02 0.2080 0.4800 0.7280 0.9680 4 0.3000E-02 0.2040 0.4690 0.7350 0.9800 5 0.8000E-02 0.1980 0.4550 0.6610 0.9340 Sample reuse to estimate df: Number of observations between independent test set 2 #BSFNS DF ASR GCV CV 15 -1.60 0.9801 1.063 17.69 8 -1.59 0.9801 1.070 17.69 7 -0.40 0.9815 1.743 17.81 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 188 6 1.28 1.206 4.329 16.52 5 2.56 1.703 8.790 15.37 3 3.58 4.522 13.86 23.26 1 5.10 10.01 15.94 28.98 0 6.36 15.92 17.28 33.56 Estimated optimal df( 5) = 2.56 Estimated PSE 1667024575 Forward stepwise knot placement: BASFN(S) GCV #INDBSFNS #EFPRMS Variable Knot Parent 0 23.50 0.0 1.0 1 20.56 1.0 4.6 4. 0.3000E-02 0. 2 18.27 2.0 8.1 2. 0.1200E-01 0. 4 3 14.46 4.0 12.7 1. 0.6560 2. 5 12.19 5.0 16.2 5. 0.8000E-02 0. 7 6 10.26 7.0 20.8 3. 0.5680 0. 9 8 8.742 9.0 25.4 1. 0.7660 5. 11 10 7.707 10.0 28.9 2. 0.2720 0. 13 12 9.936 12.0 33.5 3. 0.2880 5. 15 14 15.51 14.0 38.0 3. 0.8000 2. Final model after backward stepwise elimination: BSFN: 0 1 2 3 4 5 Coef: -0.9840 10.51 29.83 -33.46 -21.07 0.000 BSFN: 6 7 8 9 10 11 Coef: 0.000 6.918 58.33 0.000 -19.14 0.000 BSFN: 12 13 14 15 Coef: 14.46 17.77 32.84 0.000 Piecewise Linear GCV = 4.608 # Effective Parameters= 27.45 Number of Basis for ANOVA decomposition 10 Fun. Std. Dev. -GCV #BSFNS #EFPRMS Variable(s) 1 3.046 37.10 1 2.6 4 2 4.144 30.11 2 5.3 2 3 1.331 5.276 1 2.6 3 4 2.834 15.87 2 5.3 1 2 5 1.727 10.07 1 2.6 1 5 6 1.739 11.42 2 5.3 3 5 7 0.7724 5.534 1 2.6 2 3 Number of basic functions for Piecewise cubic fit 10 Generalized Cross Validation Criteria 5.692602279375831 GCV removing each variable 1 2 3 4 5 17.6802 22.6695 10.0878 37.1048 15.2064 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 189 Relative variable importance 1 2 3 4 5 63.4248 74.5519 41.0657 100.000 57.1093 Sum of squared residuals using piecewise-linear MARS model 46.85893832116239 Sum of squared residuals using piecewise-cubic MARS model 57.89406884487286 Piecewise-Linear MARS model selected B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 190 Obs Y Yhat Residual 1 9.6530000 10.516380 -0.86338020 2 8.7650000 9.8092024 -1.0442024 3 8.2920000 7.3329403 0.95905968 4 13.796000 12.384739 1.4112613 5 24.134000 24.777654 -0.64365372 6 17.111000 15.743346 1.3676537 7 13.420000 12.259625 1.1603751 8 7.9510000 7.7309986 0.22000141 9 9.9390000 9.3977645 0.54123547 10 15.615000 16.619575 -1.0045747 11 16.956000 15.962794 0.99320603 12 8.9240000 10.289768 -1.3657684 13 19.789000 18.735766 1.0532344 14 14.596000 13.733333 0.86266657 15 13.713000 13.795129 -0.82129400E-01 16 6.8620000 7.8832774 -1.0212774 17 17.263000 18.417971 -1.1549709 18 11.168000 10.758894 0.40910614 19 21.977000 23.318233 -1.3412326 20 18.631000 18.196429 0.43457060 21 7.9090000 7.1721883 0.73681173 22 9.8660000 8.9450928 0.92090718 23 10.142000 11.046490 -0.90448959 24 12.161000 12.124758 0.36241804E-01 25 22.449000 21.686840 0.76216034 26 19.795000 19.051117 0.74388343 27 11.399000 12.653710 -1.2547098 28 5.9240000 7.8819378 -1.9579378 29 14.938000 17.066096 -2.1280965 30 13.153000 12.452961 0.70003935 31 21.515000 22.015047 -0.50004662 32 11.851000 11.604047 0.24695292 33 12.167000 13.436974 -1.2699745 34 17.204000 16.958770 0.24522970 35 14.095000 15.291537 -1.1965366 36 3.9250000 4.1995932 -0.27459317 37 14.185000 13.541951 0.64304875 38 14.717000 15.862402 -1.1454019 39 18.291000 18.714910 -0.42390973 40 15.741000 16.722180 -0.98118035 41 24.748000 23.506479 1.2415205 42 11.031000 9.4014585 1.6295415 43 20.199000 18.915600 1.2834002 44 13.252000 13.432568 -0.18056820 45 10.041000 9.8834172 0.15758276 46 15.079000 15.497037 -0.41803739 47 18.463000 17.776557 0.68644269 48 15.470000 15.150701 0.31929945 49 16.365000 15.932587 0.43241323 50 15.694000 14.735174 0.95882594 Sum of squared Y values 11219.48594000000 % Reduction in sum of squares (1.0 - (RESID***2/Y**2) ) 0.9958234326802711 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 191 Variance of Y 23.02616817306123 Residual Variance 0.9563048636971918 Approximate R squared value 0.9584687796723386 Optimal smoothing parameter estimate (DFS) 2.558888312272577 Estimated predictive squared error (PSE) 15.37004385478519 Number of nonconstant basis functions (NBF) 5 Forecasts on the Y Variable outside sample Observation Predicted Value 51 10.516380 52 9.8092024 53 7.3329403 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 192 Pi Spline Program (PISPLINE Option) Program developed by Leo Breiman 1991 Basic reference: The Pi Method for Estimating Multivariate Functions From Noisy Data Technometrics May 1991, Vol. 33, No. 2, pp. 125-160 Program Modified by Houston H. Stokes March 1992 REAL*8 words available, 5999699 Space used 19339 Assumptions of the Estimated Model Center 0.000000000000000E+00 KMB (lower bound on # of knots) 2 KMT (upper bound on # of knots) 7 MNFIT (max number of products to be fit) 3 NG (grid size) 50 JRDF (deletion termination control) -1 TH (convergence tolerence) 2.000000000000000E-02 EDTH (deletion control parameter) 0.1000000000000000 CPTH (model selection parameter) 0.000000000000000E+00 RADD (product selection parameter) 1.000000000000000 NOINTR (forecast interpolation (on=0)) 0 NOCORNER (on=1) 0 Exogenous variables Var # Name Mean Variance 1 X1 0.48286000 0.81393592E-01 2 X2 0.48814000 0.80952000E-01 3 X3 0.48432000 0.84603324E-01 4 X4 0.48298000 0.85625326E-01 5 X5 0.45376000 0.78082594E-01 Endogenous variable Name Mean Variance Y 14.206480 23.026168 CENTER used = 0.000000000000000E+00 Selecting the Number of initial knots: Initial Knots No. Prod. PEGCV 2 3 149.75392 3 3 134.21396 4 2 251.40634 5 1 325.84360 Deletion Progress: D.F. Remaining PEGCV 48 134.21396 46 25.403447 45 17.425035 44 13.297971 43 14.071856 Number of Initial Knots 3 Number of Products 3 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 193 Final D. F. 44 Final PEGCV 13.27019726933301 Final RSS 0.1910908406783953 Final R-Squared 0.9998306356035551 IMP Matrix 1 2 3 1 4508.79 -24.8156 -42.4325 2 -24.8156 1281.53 -5.28900 3 -42.4325 -5.28900 253.987 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 194 Obs Y Yhat Residual 1 9.6530000 9.6115060 0.41493965E-01 2 8.7650000 8.7491347 0.15865254E-01 3 8.2920000 8.1985931 0.93406862E-01 4 13.796000 13.890841 -0.94841416E-01 5 24.134000 24.048831 0.85169384E-01 6 17.111000 17.069698 0.41302034E-01 7 13.420000 13.436216 -0.16215567E-01 8 7.9510000 7.8531789 0.97821050E-01 9 9.9390000 9.9784265 -0.39426543E-01 10 15.615000 15.568621 0.46378595E-01 11 16.956000 17.060913 -0.10491298 12 8.9240000 9.0204101 -0.96410138E-01 13 19.789000 19.793416 -0.44164675E-02 14 14.596000 14.621880 -0.25879949E-01 15 13.713000 13.663898 0.49102082E-01 16 6.8620000 6.8069787 0.55021298E-01 17 17.263000 17.215078 0.47921612E-01 18 11.168000 10.992831 0.17516852 19 21.977000 22.012200 -0.35199618E-01 20 18.631000 18.656359 -0.25358765E-01 21 7.9090000 7.9427941 -0.33794129E-01 22 9.8660000 9.8251949 0.40805104E-01 23 10.142000 10.177367 -0.35366848E-01 24 12.161000 12.151432 0.95683343E-02 25 22.449000 22.498656 -0.49656203E-01 26 19.795000 19.857601 -0.62601349E-01 27 11.399000 11.458152 -0.59151697E-01 28 5.9240000 5.9876287 -0.63628744E-01 29 14.938000 14.933943 0.40574367E-02 30 13.153000 13.245420 -0.92420151E-01 31 21.515000 21.497354 0.17645967E-01 32 11.851000 11.844462 0.65382004E-02 33 12.167000 12.144110 0.22889521E-01 34 17.204000 17.215148 -0.11147931E-01 35 14.095000 14.021810 0.73190494E-01 36 3.9250000 4.0675357 -0.14253567 37 14.185000 14.234820 -0.49820342E-01 38 14.717000 14.810654 -0.93653623E-01 39 18.291000 18.287353 0.36474744E-02 40 15.741000 15.746835 -0.58345902E-02 41 24.748000 24.722036 0.25963964E-01 42 11.031000 11.066368 -0.35368449E-01 43 20.199000 20.193250 0.57500856E-02 44 13.252000 13.196277 0.55723289E-01 45 10.041000 9.9727542 0.68245841E-01 46 15.079000 14.999779 0.79220808E-01 47 18.463000 18.458789 0.42112620E-02 48 15.470000 15.471447 -0.14468135E-02 49 16.365000 16.321578 0.43422116E-01 50 15.694000 15.768650 -0.74650146E-01 Sum of Squared Y Values 11219.48594000000 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP MARS TEST DATA PAGE 195 % Reduction in Sum of Squares 0.9999829250394607 Variance of Y 23.02616817306123 Residual Variance 3.908840683657912E-03 Approximate R Squared Value 0.9998302089026812 Forecasts on the Y variable outside sample. Observation Predicted Value 51 9.5543732 52 8.0273124 53 7.8211963 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 DATA STEP PIMPLE DATA PAGE 196 Variable # Cases Mean Std Deviation Variance Maximum Minimum Y 1 88 1.957375000 1.132710170 1.283032329 4.028000000 0.3700000000 E_RATIO 2 88 0.9264772727 0.2035687902 0.4144025235E-01 1.232000000 0.5350000000 C_RATIO 3 88 12.03409091 3.932472720 15.46434169 18.00000000 7.500000000 CONSTANT 4 88 1.000000000 0.000000000 0.000000000 1.000000000 1.000000000 Number of observations in data file 88 Current missing variable code 1.000000000000000E+31 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP PIMPLE DATA PAGE 197 Pi Spline Program (PISPLINE Option) Program developed by Leo Breiman 1991 Basic reference: The Pi Method for Estimating Multivariate Functions From Noisy Data Technometrics May 1991, Vol. 33, No. 2, pp. 125-160 Program Modified by Houston H. Stokes March 1992 REAL*8 words available, 5999735 Space used 16689 Assumptions of the Estimated Model Center 2.526000000000000 KMB (lower bound on # of knots) 2 KMT (upper bound on # of knots) 7 MNFIT (max number of products to be fit) 3 NG (grid size) 50 JRDF (deletion termination control) -1 TH (convergence tolerence) 2.000000000000000E-02 EDTH (deletion control parameter) 0.1000000000000000 CPTH (model selection parameter) 0.000000000000000E+00 RADD (product selection parameter) 1.000000000000000 NOINTR (forecast interpolation (on=0)) 0 NOCORNER (on=1) 0 Exogenous variables Var # Name Mean Variance 1 E_RATIO 0.92647727 0.41440252E-01 2 C_RATIO 12.034091 15.464342 Endogenous variable Name Mean Variance Y 1.9573750 1.2830323 CENTER used = 2.526000000000000 Selecting the Number of initial knots: Initial Knots No. Prod. PEGCV 2 2 14.473445 3 2 16.609316 4 2 3.4622288 5 2 3.2028616 6 2 3.4555725 7 3 3.4674152 Deletion Progress: D.F. Remaining PEGCV 18 3.2028616 16 3.0124061 15 2.9389844 14 2.8764885 13 2.7955487 12 2.8054663 11 2.8479106 Number of Initial Knots 5 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP PIMPLE DATA PAGE 198 Number of Products 2 Final D. F. 13 Final PEGCV 2.795088047208920 Final RSS 2.030264755365467 Final R-Squared 0.9818115444400189 IMP Matrix 1 2 1 53.2064 -1.40682 2 -1.40682 3.56675 Number of basis functions for ith Var at jth product 1 2 1 6 5 2 1 5 (((COEF(I,J,K),I=1,KMT+2),J=1,MV),K=1,NFIT) Coef for ith remaining basis function for jth Var. for kth product. COEF(I,J, 1) 1 2 1 -865.889 -0.111987 2 2969.00 0.00000 3 -944.676 0.00000 4 -5781.84 0.00000 5 6777.99 0.00000 6 -40.3393 0.00000 7 41.8968 0.00000 8 0.00000 0.00000 9 0.00000 0.00000 COEF(I,J, 2) 1 2 1 195.994 0.190162E-01 2 -336.803 -0.215886E-01 3 176.724 0.291694E-02 4 -21.9870 -0.112463 5 10.7212 0.982901 6 0.00000 0.00000 7 0.00000 0.00000 8 0.00000 0.00000 9 0.00000 0.00000 The remaining knots at locations T(MP,IT) where the kth remaining knot is located at MMAP(K,M,IT) I. E. if MP=MMAP(K,M,IT) => knot in T(MP,1)..T(MP,IT) FOR IT=1,NFIT B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP PIMPLE DATA PAGE 199 T(KMT,MV) .. 1 2 1 0.535000 7.50000 2 0.693409 7.97727 3 0.820136 12.2727 4 0.978545 0.00000 5 1.10527 0.00000 6 1.04191 0.00000 7 1.13695 0.00000 Location of remaining knots in T (((MMAP(I,J,K),I=1,KMT-2),J=1,MV),K=1,NFIT) MMAP(I,J, 1) 1 2 1 1 5 2 2 5 3 4 5 4 5 5 5 6 5 6 7 6 7 7 7 MMAP(I,J, 2) 1 2 1 1 1 2 2 2 3 4 3 4 6 4 5 7 5 6 7 6 7 7 7 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP PIMPLE DATA PAGE 200 Obs Y Yhat Residual 1 3.7410000 3.8473593 -0.10635927 2 2.2950000 2.4395852 -0.14458521 3 1.4980000 1.3317330 0.16626699 4 2.8810000 2.9253204 -0.44320383E-01 5 0.76000000 0.75575065 0.42493498E-02 6 3.1200000 3.1111379 0.88621171E-02 7 0.63800000 0.68052093 -0.42520933E-01 8 1.1700000 1.1437430 0.26256999E-01 9 2.3580000 2.4493793 -0.91379348E-01 10 0.60600000 0.69509992 -0.89099923E-01 11 3.6690000 3.8311873 -0.16218732 12 1.0000000 0.92126229 0.78737713E-01 13 0.98100000 1.0341020 -0.53101974E-01 14 1.1920000 1.1031996 0.88800435E-01 15 0.92600000 0.85843327 0.67566730E-01 16 1.5900000 1.4114912 0.17850883 17 1.8060000 1.8940346 -0.88034561E-01 18 1.9620000 1.8959553 0.66044664E-01 19 4.0280000 3.9437296 0.84270421E-01 20 3.1480000 2.9148284 0.23317159 21 1.8360000 1.8792968 -0.43296789E-01 22 2.8450000 2.8357358 0.92642474E-02 23 1.0130000 0.95703133 0.55968665E-01 24 0.41400000 0.62829263 -0.21429263 25 0.81200000 0.80684855 0.51514529E-02 26 0.37400000 0.57905337 -0.20505337 27 3.6230000 3.5973889 0.25611106E-01 28 1.8690000 1.8436811 0.25318873E-01 29 2.8360000 2.8800409 -0.44040881E-01 30 3.5670000 3.6840080 -0.11700800 31 0.86600000 0.92926876 -0.63268758E-01 32 1.3690000 1.7204079 -0.35140792 33 0.54200000 0.65062683 -0.10862683 34 2.7390000 2.6175576 0.12144244 35 1.2000000 1.1555987 0.44401310E-01 36 1.7190000 1.7090808 0.99191917E-02 37 3.4230000 3.5436127 -0.12061269 38 1.6340000 1.7669966 -0.13299664 39 1.0210000 0.94417746 0.76822537E-01 40 2.1570000 2.2424343 -0.85434295E-01 41 3.3610000 3.5975522 -0.23655219 42 1.3900000 1.3067553 0.83244750E-01 43 1.9470000 2.0437548 -0.96754847E-01 44 0.96200000 0.65335928 0.30864072 45 0.57100000 0.77832430 -0.20732430 46 2.2190000 1.8315160 0.38748396 47 1.4190000 1.5807129 -0.16171290 48 3.5190000 3.5715921 -0.52592120E-01 49 1.7320000 1.8129802 -0.80980218E-01 50 3.2060000 3.2535241 -0.47524147E-01 51 2.4710000 2.5029429 -0.31942897E-01 52 1.7770000 1.5179896 0.25901042 53 2.5710000 2.5419102 0.29089849E-01 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP PIMPLE DATA PAGE 201 54 3.9520000 3.8879996 0.64000412E-01 55 3.9310000 3.7104369 0.22056305 56 1.5870000 1.6107479 -0.23747876E-01 57 1.3970000 1.2780638 0.11893621 58 3.5360000 3.4292530 0.10674701 59 2.2020000 2.4603246 -0.25832464 60 0.75600000 0.82561147 -0.69611466E-01 61 1.6200000 1.5696296 0.50370385E-01 62 3.6560000 3.3469313 0.30906867 63 2.9640000 2.9372557 0.26744312E-01 64 3.7600000 3.7706994 -0.10699378E-01 65 0.67200000 0.62583528 0.46164723E-01 66 3.6770000 3.6807224 -0.37223866E-02 67 3.5170000 3.1594565 0.35754350 68 3.2900000 3.1592946 0.13070542 69 1.1390000 1.3385113 -0.19951133 70 0.72700000 0.73400560 -0.70055997E-02 71 2.5810000 2.6236632 -0.42663208E-01 72 0.92300000 0.82769773 0.95302271E-01 73 1.5270000 1.7329531 -0.20595311 74 3.3880000 3.4075555 -0.19555473E-01 75 2.0850000 2.5983352 -0.51333524 76 0.96600000 0.78081811 0.18518189 77 3.4880000 3.3834782 0.10452180 78 0.75400000 0.71579711 0.38202889E-01 79 0.79700000 0.78583418 0.11165815E-01 80 2.0640000 2.2702170 -0.20621701 81 3.7320000 3.5813697 0.15063033 82 0.58600000 0.70437859 -0.11837859 83 0.56100000 0.34562080 0.21537920 84 0.56300000 0.58810671 -0.25106709E-01 85 0.67800000 0.56588880 0.11211120 86 0.37000000 0.53753485 -0.16753485 87 0.53000000 0.47594597 0.54054030E-01 88 1.9000000 1.6822655 0.21773450 Sum of Squared Y Values 448.7796989999998 % Reduction in Sum of Squares 0.9954760000649780 Variance of Y 1.283032329022989 Residual Variance 2.333638267691082E-02 Approximate R Squared Value 0.9818114138787224 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP PIMPLE DATA PAGE 202 Plot of Y, YHAT and Residual ********** Plot of the original series ********** Series 3 Series 2 Series 1 -0.51 0.39 0.35 3.9 0.37 4.0 -0.629E-01 2.14 2.20 + 1 + + 1 + + 1 + ----------------------------------------- ----------------------------------------- ------------------------------------------ I 1 I 1 I 1 I 2 I 2 I 2 I 3 I 3 I 3 I 4 I 4 I 4 I 5 I 5 I 5 I 6 I 6 I 6 I 7 I 7 I 7 I 8 I 8 I 8 I 9 I 9 I 9 10 + 0 + 0 + 0 I 1 I 1 I 1 I 2 I 2 I 2 I 3 I 3 I 3 I 4 I 4 I 4 I 5 I 5 I 5 I 6 I 6 I 6 I 7 I 7 I 7 I 8 I 8 I 8 I 9 I 9 I 9 20 + 0 + 0 + 0 I 1 I 1 I 1 I 2 I 2 I 2 I 3 I 3 I 3 I 4 I 4 I 4 I 5 I 5 I 5 I 6 I 6 I 6 I 7 I 7 I 7 I 8 I 8 I 8 I 9 I 9 I 9 30 + 0 + 0 + 0 I 1 I 1 I 1 I 2 I 2 I 2 I 3 I 3 I 3 I 4 I 4 I 4 I 5 I 5 I 5 I 6 I 6 I 6 I 7 I 7 I 7 I 8 I 8 I 8 I 9 I 9 I 9 40 + 0 + 0 + 0 I 1 I 1 I 1 I 2 I 2 I 2 I 3 I 3 I 3 I 4 I 4 I 4 I 5 I 5 I 5 I 6 I 6 I 6 I 7 I 7 I 7 I 8 I 8 I 8 I 9 I 9 I 9 50 + 0 + 0 + 0 I 1 I 1 I 1 I 2 I 2 I 2 I 3 I 3 I 3 I 4 I 4 I 4 I 5 I 5 I 5 I 6 I 6 I 6 I 7 I 7 I 7 I 8 I 8 I 8 I 9 I 9 I 9 60 + 0 + 0 + 0 I 1 I 1 I 1 I 2 I 2 I 2 I 3 I 3 I 3 I 4 I 4 I 4 I 5 I 5 I 5 I 6 I 6 I 6 I 7 I 7 I 7 I 8 I 8 I 8 I 9 I 9 I 9 70 + 0 + 0 + 0 I 1 I 1 I 1 I 2 I 2 I 2 I 3 I 3 I 3 I 4 I 4 I 4 I5 I 5 I 5 I 6 I 6 I 6 I 7 I 7 I 7 I 8 I 8 I 8 I 9 I 9 I 9 80 + 0 + 0 + 0 I 1 I 1 I 1 I 2 I 2 I 2 I 3 I3 I 3 I 4 I 4 I 4 I 5 I 5 I 5 I 6 I 6 I6 I 7 I 7 I 7 I 8 I 8 I 8 I I I 90 + + + Note: The number of observations plotted is 88 for each series Summary Table for Residuals from PISPLINE Model Mean= -0.39937770E-03 Variance= 0.23071197E-01 Standard Deviation= 0.15189206 Skewness= -0.10542287 Kurtosis= 0.92123003 # of observations 88 Hinich bispectrum summary table. M G L BICOH Lamda 5 -2.4301802 -1.0811090 1.1097120 0.10000000E-15 6 -0.89544572 0.63073228 1.2676001 0.10000000E-15 7 -1.6489028 -0.93956749 1.1116339 0.10000000E-15 8 -1.6525802 -0.60905251 1.0620731 0.10000000E-15 9 -1.8349981 -1.0494527 0.98610594 0.10000000E-15 10 -1.2997358 -0.25486247 1.0670071 0.10000000E-15 Mean for G = -1.6269738 Mean for L = -0.55055198 For the above table NWD = 21 WT = 0.36166692 M = # of terms averaged to estimate bispectrum. G = (Z) statistic to test for Gaussianity. L = (Z) statistic to test for linearity. BICOH = average skewness (measure of nonlinear predictability). LAMDA = estimate of non-centrality. WT = whiteness statistic. Smoothing has not been done. Residuals from PISPLINE Model Dickey-Fuller Unit Root Test (I) Lag 0 t test -10.818598 Prob of I(1) 0.1000 Aug. Dickey-Fuller Test (II) Lag 0 t test -10.753140 Prob of I(1) 0.1000 Aug. Dickey-Fuller Test (II) Lag 0 t test -10.753140 Prob of I(1) 0.1000 Forecasts on the Y variable outside sample. Observation Predicted Value 89 3.8588624 90 2.6512688 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP PIMPLE DATA PAGE 203 Pi Spline Program (PISPLINE Option) Program developed by Leo Breiman 1991 Basic reference: The Pi Method for Estimating Multivariate Functions From Noisy Data Technometrics May 1991, Vol. 33, No. 2, pp. 125-160 Program Modified by Houston H. Stokes March 1992 REAL*8 words available, 5999735 Space used 130089 Assumptions of the Estimated Model Center 2.526000000000000 KMB (lower bound on # of knots) 2 KMT (upper bound on # of knots) 7 MNFIT (max number of products to be fit) 3 NG (grid size) 200 JRDF (deletion termination control) -1 TH (convergence tolerence) 2.000000000000000E-02 EDTH (deletion control parameter) 0.1000000000000000 CPTH (model selection parameter) 0.000000000000000E+00 RADD (product selection parameter) 1.000000000000000 NOINTR (forecast interpolation (on=0)) 0 NOCORNER (on=1) 0 Exogenous variables Var # Name Mean Variance 1 E_RATIO 0.92647727 0.41440252E-01 2 C_RATIO 12.034091 15.464342 Endogenous variable Name Mean Variance Y 1.9573750 1.2830323 CENTER used = 2.526000000000000 Selecting the Number of initial knots: Initial Knots No. Prod. PEGCV 2 2 14.473445 3 2 16.609316 4 2 3.4622288 5 2 3.2028616 6 2 3.4555725 7 3 3.4674152 Deletion Progress: D.F. Remaining PEGCV 18 3.2028616 16 3.0124061 15 2.9389844 14 2.8764885 13 2.7955487 12 2.8054663 11 2.8479106 Number of Initial Knots 5 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP PIMPLE DATA PAGE 204 Number of Products 2 Final D. F. 13 Final PEGCV 2.795088047208920 Final RSS 2.030264755365467 Final R-Squared 0.9818115444400189 IMP Matrix 1 2 1 53.2064 -1.40682 2 -1.40682 3.56675 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP PIMPLE DATA PAGE 205 Obs Y Yhat Residual 1 3.7410000 3.8473593 -0.10635927 2 2.2950000 2.4395852 -0.14458521 3 1.4980000 1.3317330 0.16626699 4 2.8810000 2.9253204 -0.44320383E-01 5 0.76000000 0.75575065 0.42493498E-02 6 3.1200000 3.1111379 0.88621171E-02 7 0.63800000 0.68052093 -0.42520933E-01 8 1.1700000 1.1437430 0.26256999E-01 9 2.3580000 2.4493793 -0.91379348E-01 10 0.60600000 0.69509992 -0.89099923E-01 11 3.6690000 3.8311873 -0.16218732 12 1.0000000 0.92126229 0.78737713E-01 13 0.98100000 1.0341020 -0.53101974E-01 14 1.1920000 1.1031996 0.88800435E-01 15 0.92600000 0.85843327 0.67566730E-01 16 1.5900000 1.4114912 0.17850883 17 1.8060000 1.8940346 -0.88034561E-01 18 1.9620000 1.8959553 0.66044664E-01 19 4.0280000 3.9437296 0.84270421E-01 20 3.1480000 2.9148284 0.23317159 21 1.8360000 1.8792968 -0.43296789E-01 22 2.8450000 2.8357358 0.92642474E-02 23 1.0130000 0.95703133 0.55968665E-01 24 0.41400000 0.62829263 -0.21429263 25 0.81200000 0.80684855 0.51514529E-02 26 0.37400000 0.57905337 -0.20505337 27 3.6230000 3.5973889 0.25611106E-01 28 1.8690000 1.8436811 0.25318873E-01 29 2.8360000 2.8800409 -0.44040881E-01 30 3.5670000 3.6840080 -0.11700800 31 0.86600000 0.92926876 -0.63268758E-01 32 1.3690000 1.7204079 -0.35140792 33 0.54200000 0.65062683 -0.10862683 34 2.7390000 2.6175576 0.12144244 35 1.2000000 1.1555987 0.44401310E-01 36 1.7190000 1.7090808 0.99191917E-02 37 3.4230000 3.5436127 -0.12061269 38 1.6340000 1.7669966 -0.13299664 39 1.0210000 0.94417746 0.76822537E-01 40 2.1570000 2.2424343 -0.85434295E-01 41 3.3610000 3.5975522 -0.23655219 42 1.3900000 1.3067553 0.83244750E-01 43 1.9470000 2.0437548 -0.96754847E-01 44 0.96200000 0.65335928 0.30864072 45 0.57100000 0.77832430 -0.20732430 46 2.2190000 1.8315160 0.38748396 47 1.4190000 1.5807129 -0.16171290 48 3.5190000 3.5715921 -0.52592120E-01 49 1.7320000 1.8129802 -0.80980218E-01 50 3.2060000 3.2535241 -0.47524147E-01 51 2.4710000 2.5029429 -0.31942897E-01 52 1.7770000 1.5179896 0.25901042 53 2.5710000 2.5419102 0.29089849E-01 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP PIMPLE DATA PAGE 206 54 3.9520000 3.8879996 0.64000412E-01 55 3.9310000 3.7104369 0.22056305 56 1.5870000 1.6107479 -0.23747876E-01 57 1.3970000 1.2780638 0.11893621 58 3.5360000 3.4292530 0.10674701 59 2.2020000 2.4603246 -0.25832464 60 0.75600000 0.82561147 -0.69611466E-01 61 1.6200000 1.5696296 0.50370385E-01 62 3.6560000 3.3469313 0.30906867 63 2.9640000 2.9372557 0.26744312E-01 64 3.7600000 3.7706994 -0.10699378E-01 65 0.67200000 0.62583528 0.46164723E-01 66 3.6770000 3.6807224 -0.37223866E-02 67 3.5170000 3.1594565 0.35754350 68 3.2900000 3.1592946 0.13070542 69 1.1390000 1.3385113 -0.19951133 70 0.72700000 0.73400560 -0.70055997E-02 71 2.5810000 2.6236632 -0.42663208E-01 72 0.92300000 0.82769773 0.95302271E-01 73 1.5270000 1.7329531 -0.20595311 74 3.3880000 3.4075555 -0.19555473E-01 75 2.0850000 2.5983352 -0.51333524 76 0.96600000 0.78081811 0.18518189 77 3.4880000 3.3834782 0.10452180 78 0.75400000 0.71579711 0.38202889E-01 79 0.79700000 0.78583418 0.11165815E-01 80 2.0640000 2.2702170 -0.20621701 81 3.7320000 3.5813697 0.15063033 82 0.58600000 0.70437859 -0.11837859 83 0.56100000 0.34562080 0.21537920 84 0.56300000 0.58810671 -0.25106709E-01 85 0.67800000 0.56588880 0.11211120 86 0.37000000 0.53753485 -0.16753485 87 0.53000000 0.47594597 0.54054030E-01 88 1.9000000 1.6822655 0.21773450 Sum of Squared Y Values 448.7796989999998 % Reduction in Sum of Squares 0.9954760000649780 Variance of Y 1.283032329022989 Residual Variance 2.333638267691082E-02 Approximate R Squared Value 0.9818114138787224 Summary Table for Residuals from PISPLINE Model Mean= -0.39937770E-03 Variance= 0.23071197E-01 Standard Deviation= 0.15189206 Skewness= -0.10542287 Kurtosis= 0.92123003 # of observations 88 Hinich bispectrum summary table. M G L BICOH Lamda 5 -2.4301802 -1.0811090 1.1097120 0.10000000E-15 6 -0.89544572 0.63073228 1.2676001 0.10000000E-15 7 -1.6489028 -0.93956749 1.1116339 0.10000000E-15 8 -1.6525802 -0.60905251 1.0620731 0.10000000E-15 9 -1.8349981 -1.0494527 0.98610594 0.10000000E-15 10 -1.2997358 -0.25486247 1.0670071 0.10000000E-15 Mean for G = -1.6269738 Mean for L = -0.55055198 For the above table NWD = 21 WT = 0.36166692 M = # of terms averaged to estimate bispectrum. G = (Z) statistic to test for Gaussianity. L = (Z) statistic to test for linearity. BICOH = average skewness (measure of nonlinear predictability). LAMDA = estimate of non-centrality. WT = whiteness statistic. Smoothing has not been done. Residuals from PISPLINE Model Dickey-Fuller Unit Root Test (I) Lag 0 t test -10.818598 Prob of I(1) 0.1000 Aug. Dickey-Fuller Test (II) Lag 0 t test -10.753140 Prob of I(1) 0.1000 Aug. Dickey-Fuller Test (II) Lag 0 t test -10.753140 Prob of I(1) 0.1000 Forecasts on the Y variable outside sample. Observation Predicted Value 89 3.8539508 90 2.4927647 1 th input series value 0.50000000 < min of 0.53500000 The value has been reset to the minimum. Interpret forecast accordingly. 2 th input series value 50.000000 > max of 18.000000 The value has been reset to the maximum. Interpret forecast accordingly. 91 0.47587404 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP PIMPLE DATA PAGE 207 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP PIMPLE DATA PAGE 208 Pi Spline Program (PISPLINE Option) Program developed by Leo Breiman 1991 Basic reference: The Pi Method for Estimating Multivariate Functions From Noisy Data Technometrics May 1991, Vol. 33, No. 2, pp. 125-160 Program Modified by Houston H. Stokes March 1992 REAL*8 words available, 5999735 Space used 16689 Assumptions of the Estimated Model Center 2.526000000000000 KMB (lower bound on # of knots) 2 KMT (upper bound on # of knots) 7 MNFIT (max number of products to be fit) 3 NG (grid size) 50 JRDF (deletion termination control) -1 TH (convergence tolerence) 2.000000000000000E-02 EDTH (deletion control parameter) 0.1000000000000000 CPTH (model selection parameter) 0.000000000000000E+00 RADD (product selection parameter) 1.000000000000000 NOINTR (forecast interpolation (on=0)) 0 NOCORNER (on=1) 0 Exogenous variables Var # Name Mean Variance 1 E_RATIO 0.92647727 0.41440252E-01 2 C_RATIO 12.034091 15.464342 Endogenous variable Name Mean Variance Y 1.9573750 1.2830323 CENTER used = 2.526000000000000 Selecting the Number of initial knots: Initial Knots No. Prod. PEGCV 2 2 14.473445 3 2 16.609316 4 2 3.4622288 5 2 3.2028616 6 2 3.4555725 7 3 3.4674152 Deletion Progress: D.F. Remaining PEGCV 18 3.2028616 16 3.0124061 15 2.9389844 14 2.8764885 13 2.7955487 12 2.8054663 11 2.8479106 Number of Initial Knots 5 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP PIMPLE DATA PAGE 209 Number of Products 2 Final D. F. 13 Final PEGCV 2.795088047208920 Final RSS 2.030264755365467 Final R-Squared 0.9818115444400189 IMP Matrix 1 2 1 53.2064 -1.40682 2 -1.40682 3.56675 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP PIMPLE DATA PAGE 210 Obs Y Yhat Residual 1 3.7410000 3.8473593 -0.10635927 2 2.2950000 2.4395852 -0.14458521 3 1.4980000 1.3317330 0.16626699 4 2.8810000 2.9253204 -0.44320383E-01 5 0.76000000 0.75575065 0.42493498E-02 6 3.1200000 3.1111379 0.88621171E-02 7 0.63800000 0.68052093 -0.42520933E-01 8 1.1700000 1.1437430 0.26256999E-01 9 2.3580000 2.4493793 -0.91379348E-01 10 0.60600000 0.69509992 -0.89099923E-01 11 3.6690000 3.8311873 -0.16218732 12 1.0000000 0.92126229 0.78737713E-01 13 0.98100000 1.0341020 -0.53101974E-01 14 1.1920000 1.1031996 0.88800435E-01 15 0.92600000 0.85843327 0.67566730E-01 16 1.5900000 1.4114912 0.17850883 17 1.8060000 1.8940346 -0.88034561E-01 18 1.9620000 1.8959553 0.66044664E-01 19 4.0280000 3.9437296 0.84270421E-01 20 3.1480000 2.9148284 0.23317159 21 1.8360000 1.8792968 -0.43296789E-01 22 2.8450000 2.8357358 0.92642474E-02 23 1.0130000 0.95703133 0.55968665E-01 24 0.41400000 0.62829263 -0.21429263 25 0.81200000 0.80684855 0.51514529E-02 26 0.37400000 0.57905337 -0.20505337 27 3.6230000 3.5973889 0.25611106E-01 28 1.8690000 1.8436811 0.25318873E-01 29 2.8360000 2.8800409 -0.44040881E-01 30 3.5670000 3.6840080 -0.11700800 31 0.86600000 0.92926876 -0.63268758E-01 32 1.3690000 1.7204079 -0.35140792 33 0.54200000 0.65062683 -0.10862683 34 2.7390000 2.6175576 0.12144244 35 1.2000000 1.1555987 0.44401310E-01 36 1.7190000 1.7090808 0.99191917E-02 37 3.4230000 3.5436127 -0.12061269 38 1.6340000 1.7669966 -0.13299664 39 1.0210000 0.94417746 0.76822537E-01 40 2.1570000 2.2424343 -0.85434295E-01 41 3.3610000 3.5975522 -0.23655219 42 1.3900000 1.3067553 0.83244750E-01 43 1.9470000 2.0437548 -0.96754847E-01 44 0.96200000 0.65335928 0.30864072 45 0.57100000 0.77832430 -0.20732430 46 2.2190000 1.8315160 0.38748396 47 1.4190000 1.5807129 -0.16171290 48 3.5190000 3.5715921 -0.52592120E-01 49 1.7320000 1.8129802 -0.80980218E-01 50 3.2060000 3.2535241 -0.47524147E-01 51 2.4710000 2.5029429 -0.31942897E-01 52 1.7770000 1.5179896 0.25901042 53 2.5710000 2.5419102 0.29089849E-01 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP PIMPLE DATA PAGE 211 54 3.9520000 3.8879996 0.64000412E-01 55 3.9310000 3.7104369 0.22056305 56 1.5870000 1.6107479 -0.23747876E-01 57 1.3970000 1.2780638 0.11893621 58 3.5360000 3.4292530 0.10674701 59 2.2020000 2.4603246 -0.25832464 60 0.75600000 0.82561147 -0.69611466E-01 61 1.6200000 1.5696296 0.50370385E-01 62 3.6560000 3.3469313 0.30906867 63 2.9640000 2.9372557 0.26744312E-01 64 3.7600000 3.7706994 -0.10699378E-01 65 0.67200000 0.62583528 0.46164723E-01 66 3.6770000 3.6807224 -0.37223866E-02 67 3.5170000 3.1594565 0.35754350 68 3.2900000 3.1592946 0.13070542 69 1.1390000 1.3385113 -0.19951133 70 0.72700000 0.73400560 -0.70055997E-02 71 2.5810000 2.6236632 -0.42663208E-01 72 0.92300000 0.82769773 0.95302271E-01 73 1.5270000 1.7329531 -0.20595311 74 3.3880000 3.4075555 -0.19555473E-01 75 2.0850000 2.5983352 -0.51333524 76 0.96600000 0.78081811 0.18518189 77 3.4880000 3.3834782 0.10452180 78 0.75400000 0.71579711 0.38202889E-01 79 0.79700000 0.78583418 0.11165815E-01 80 2.0640000 2.2702170 -0.20621701 81 3.7320000 3.5813697 0.15063033 82 0.58600000 0.70437859 -0.11837859 83 0.56100000 0.34562080 0.21537920 84 0.56300000 0.58810671 -0.25106709E-01 85 0.67800000 0.56588880 0.11211120 86 0.37000000 0.53753485 -0.16753485 87 0.53000000 0.47594597 0.54054030E-01 88 1.9000000 1.6822655 0.21773450 Sum of Squared Y Values 448.7796989999998 % Reduction in Sum of Squares 0.9954760000649780 Variance of Y 1.283032329022989 Residual Variance 2.333638267691082E-02 Approximate R Squared Value 0.9818114138787224 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP PIMPLE DATA PAGE 212 Plot of the Residual RESIDUAL 0.38748 * . * * . * * * . . * * . * * . * . . . * * . . * . . * . * . . . * . . . * . . . . . * . . . * . . . . . . * . .. . . * .. . . . . *-----------------------------------------------------------------------.-.----.--------------------- * . . . . * . . . . . . . . * . . * . . . . *. . . . * . . . * . . * . . * . * . * . . . . . * . * * . * * * * * . * * * * * * * * . -0.51334 ***************************************************************************************************** 1.0000 88.000 TIME Summary Table for Residuals from PISPLINE Model Mean= -0.39937770E-03 Variance= 0.23071197E-01 Standard Deviation= 0.15189206 Skewness= -0.10542287 Kurtosis= 0.92123003 # of observations 88 Hinich bispectrum summary table. M G L BICOH Lamda 5 -2.4301802 -1.0811090 1.1097120 0.10000000E-15 6 -0.89544572 0.63073228 1.2676001 0.10000000E-15 7 -1.6489028 -0.93956749 1.1116339 0.10000000E-15 8 -1.6525802 -0.60905251 1.0620731 0.10000000E-15 9 -1.8349981 -1.0494527 0.98610594 0.10000000E-15 10 -1.2997358 -0.25486247 1.0670071 0.10000000E-15 Mean for G = -1.6269738 Mean for L = -0.55055198 For the above table NWD = 21 WT = 0.36166692 M = # of terms averaged to estimate bispectrum. G = (Z) statistic to test for Gaussianity. L = (Z) statistic to test for linearity. BICOH = average skewness (measure of nonlinear predictability). LAMDA = estimate of non-centrality. WT = whiteness statistic. Smoothing has not been done. Residuals from PISPLINE Model Dickey-Fuller Unit Root Test (I) Lag 0 t test -10.818598 Prob of I(1) 0.1000 Aug. Dickey-Fuller Test (II) Lag 0 t test -10.753140 Prob of I(1) 0.1000 Aug. Dickey-Fuller Test (II) Lag 0 t test -10.753140 Prob of I(1) 0.1000 Forecasts on the Y variable outside sample. Observation Predicted Value 89 3.8588624 90 2.6512688 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP PIMPLE DATA PAGE 213 Multivariate Adaptive Regression Splines (MARS) Program developed by Jerome Friedman Basic reference: Multivariate Adaptive Regression Splines Annals of Statistics, 1991, Vol. 19, No. 1, pp. 1-141 Program Modified by H. H. Stokes March 2002 Real*8 storage available : 5999735 Real*8 Storage used : 9807 Exogenous Variables Var # Name Mean Variance Max Min 1 E_RATIO 0.92647727 0.41440252E-01 1.2320000 0.53500000 2 C_RATIO 12.034091 15.464342 18.000000 7.5000000 Endogenous Variable Name Mean Variance Max Min Y 1.9573750 1.2830323 4.0280000 0.37000000 MARS Modeling, Version 3.5 (6/16/91) - Revised (1/3/02) Input parameters (see doc.): N P NK MS MI DF IL FV IC 88 2 20 0 3 3.000 0 0.000 0 Predictor variable flags: 1 2 1 1 Ordinal Response: MIN N/4 N/2 3N/4 MAX 0.3700 0.9260 1.732 2.964 4.028 Number of ordinal predictor variables. 2 VAR MIN N/4 N/2 3N/4 MAX 1 0.5350 0.7610 0.9300 1.108 1.232 2 7.500 7.500 12.00 15.00 18.00 Forward stepwise knot placement: BASFN(S) GCV #INDBSFNS #EFPRMS Variable Knot Parent 0 1.298 0.0 1.0 2 1 0.1699 2.0 6.0 1. 0.9300 0. 3 0.1233 3.0 10.0 2. 7.500 2. 5 4 0.8896E-01 4.0 14.0 1. 1.138 0. 7 6 0.6596E-01 6.0 19.0 2. 9.000 5. 9 8 0.6664E-01 7.0 23.0 1. 0.8920 0. 11 10 0.6797E-01 8.0 27.0 1. 1.001 0. 13 12 0.6846E-01 9.0 31.0 1. 0.6930 0. 15 14 0.6779E-01 10.0 35.0 1. 1.045 0. 17 16 0.7310E-01 12.0 40.0 2. 15.00 9. B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP PIMPLE DATA PAGE 214 19 18 0.8325E-01 13.0 44.0 2. 12.00 2. 20 0.1000 14.0 48.0 2. 7.500 15. Final model after backward stepwise elimination: BSFN: 0 1 2 3 4 5 Coef: 4.316 0.000 -14.36 0.000 8.985 0.000 BSFN: 6 7 8 9 10 11 Coef: 0.3502 -0.8632 -13.40 0.000 0.000 0.000 BSFN: 12 13 14 15 16 17 Coef: 0.000 0.000 0.000 0.000 0.000 0.4324 BSFN: 18 19 20 Coef: 0.000 0.000 0.000 Piecewise Linear GCV = 0.5999E-01 # Effective Parameters= 21.14 Number of Basis for ANOVA decomposition 6 Fun. Std. Dev. -GCV #BSFNS #EFPRMS Variable(s) 1 1.243 1.490 3 10.1 1 2 0.4708 0.1759 3 10.1 1 2 Number of basic functions for Piecewise cubic fit 6 Generalized Cross Validation Criteria 5.837656914444581E-02 GCV removing each variable 1 2 1.29778 0.175903 Relative variable importance 1 2 100.000 30.6013 Sum of squared residuals using piecewise-linear MARS model 3.047195905620862 Sum of squared residuals using piecewise-cubic MARS model 2.965183135503988 Piecewise-Cubic MARS model selected B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP PIMPLE DATA PAGE 215 Obs Y Yhat Residual 1 3.7410000 3.9628306 -0.22183065 2 2.2950000 2.4759224 -0.18092244 3 1.4980000 1.4788688 0.19131237E-01 4 2.8810000 2.7416238 0.13937617 5 0.76000000 0.78556468 -0.25564679E-01 6 3.1200000 2.8196669 0.30033310 7 0.63800000 0.59290256 0.45097437E-01 8 1.1700000 1.2790333 -0.10903331 9 2.3580000 2.3611858 -0.31858224E-02 10 0.60600000 0.66629765 -0.60297655E-01 11 3.6690000 3.8946360 -0.22563597 12 1.0000000 1.0217842 -0.21784154E-01 13 0.98100000 1.1639505 -0.18295052 14 1.1920000 1.2251557 -0.33155676E-01 15 0.92600000 0.96859323 -0.42593228E-01 16 1.5900000 1.5248125 0.65187490E-01 17 1.8060000 1.9442126 -0.13821260 18 1.9620000 1.9841211 -0.22121071E-01 19 4.0280000 4.0612284 -0.33228425E-01 20 3.1480000 2.8983218 0.24967818 21 1.8360000 1.8795817 -0.43581658E-01 22 2.8450000 2.5252113 0.31978873 23 1.0130000 1.0820559 -0.69055883E-01 24 0.41400000 0.60207695 -0.18807695 25 0.81200000 0.85766482 -0.45664817E-01 26 0.37400000 0.33335862 0.40641377E-01 27 3.6230000 3.5222402 0.10075979 28 1.8690000 1.9132665 -0.44266532E-01 29 2.8360000 2.5657379 0.27026208 30 3.5670000 3.7024065 -0.13540647 31 0.86600000 1.0290992 -0.16309921 32 1.3690000 1.8168906 -0.44789056 33 0.54200000 0.58831537 -0.46315370E-01 34 2.7390000 2.5525181 0.18648193 35 1.2000000 1.3065483 -0.10654834 36 1.7190000 1.7557251 -0.36725059E-01 37 3.4230000 3.5607500 -0.13774997 38 1.6340000 1.8388523 -0.20485230 39 1.0210000 1.0659188 -0.44918821E-01 40 2.1570000 2.0846153 0.72384672E-01 41 3.3610000 3.5578935 -0.19689347 42 1.3900000 1.4561336 -0.66133617E-01 43 1.9470000 2.1138342 -0.16683419 44 0.96200000 0.64794888 0.31405112 45 0.57100000 0.75450298 -0.18350298 46 2.2190000 1.8537660 0.36523395 47 1.4190000 1.6342525 -0.21525248 48 3.5190000 3.5901319 -0.71131860E-01 49 1.7320000 1.8834439 -0.15144389 50 3.2060000 3.3092182 -0.10321825 51 2.4710000 2.5627915 -0.91791463E-01 52 1.7770000 1.6151302 0.16186979 53 2.5710000 2.5140342 0.56965773E-01 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 6 STAT. PROC. STEP PIMPLE DATA PAGE 216 54 3.9520000 3.8380853 0.11391470 55 3.9310000 3.8316366 0.99363352E-01 56 1.5870000 1.7100763 -0.12307626 57 1.3970000 1.3713557 0.25644342E-01 58 3.5360000 3.4456673 0.90332704E-01 59 2.2020000 2.5202801 -0.31828008 60 0.75600000 0.89540492 -0.13940492 61 1.6200000 1.6485694 -0.28569441E-01 62 3.6560000 3.3913426 0.26465742 63 2.9640000 2.6202327 0.34376735 64 3.7600000 3.7506551 0.93449487E-02 65 0.67200000 0.59748976 0.74510243E-01 66 3.6770000 3.6493258 0.27674228E-01 67 3.5170000 3.2127291 0.30427092 68 3.2900000 2.9639247 0.32607527 69 1.1390000 1.4198721 -0.28087209 70 0.72700000 0.73969275 -0.12692746E-01 71 2.5810000 2.4035770 0.17742300 72 0.92300000 0.73687931 0.18612069 73 1.5270000 1.8287588 -0.30175881 74 3.3880000 3.4799402 -0.91940209E-01 75 2.0850000 2.5374209 -0.45242090 76 0.96600000 0.82342585 0.14257415 77 3.4880000 3.4194693 0.68530724E-01 78 0.75400000 0.61125134 0.14274866 79 0.79700000 0.82828385 -0.31283847E-01 80 2.0640000 2.3315494 -0.26754943 81 3.7320000 3.4654283 0.26657166 82 0.58600000 0.73051836 -0.14451836 83 0.56100000 0.17299210 0.38800790 84 0.56300000 0.42745715 0.13554285 85 0.67800000 0.33910292 0.33889708 86 0.37000000 0.26214909 0.10785091 87 0.53000000 0.49649975 0.33500249E-01 88 1.9000000 1.8213287 0.78671294E-01 Sum of squared Y values 448.7796989999998 % Reduction in sum of squares (1.0 - (RESID***2/Y**2) ) 0.9933927868348074 Variance of Y 1.283032329022989 Residual Variance 3.408256477590790E-02 Approximate R squared value 0.9734359267456173 For the 3 th forecast. 1 th input series value 50.000000 > max of 1.2320000 The value has been reset to the maximum. Interpret forecast accordingly. For the 3 th forecast. 2 th input series value 0.50000000 < min of 7.5000000 The value has been reset to the minimum. Interpret forecast accordingly. Forecasts on the Y Variable outside sample Observation Predicted Value 89 3.9628306 90 2.4759224 91 0.58831537 B34S(r) Matrix Command. Version February 2004. Date of Run d/m/y 15/ 7/04. Time of Run h:m:s 14:46: 6. => * MATH WITH MATRIX AND VECTORS $ => * FOR BIGGER PROBLEMS, CHANGE N$ => N=3$ => RIGHT=INTEGERS(1,((N*N)-1))+10$ => CALL PRINT('Right ',RIGHT)$ Right RIGHT = Array of 8 elements 11 12 13 14 15 16 17 18 => X=MATRIX(N,N:RIGHT,-7)$ => X2=X*2.$ => V=VECTOR(N:INTEGERS(1,N))$ => CALL PRINT('X, 2*x v' ,X,X2,V) $ X, 2*x v X = Matrix of 3 by 3 elements 1 2 3 1 11.0000 12.0000 13.0000 2 14.0000 15.0000 16.0000 3 17.0000 18.0000 -7.00000 X2 = Matrix of 3 by 3 elements 1 2 3 1 22.0000 24.0000 26.0000 2 28.0000 30.0000 32.0000 3 34.0000 36.0000 -14.0000 V = Vector of 3 elements 1.00000 2.00000 3.00000 => CALL PRINT('Inverse of x (INV)' ,(1./X)) $ Inverse of x (INV) Matrix of 3 by 3 elements 1 2 3 1 -5.03846 4.07692 -0.384615E-01 2 4.74359 -3.82051 0.769231E-01 3 -0.384615E-01 0.769231E-01 -0.384615E-01 => CALL PRINT('X*inv' ,X*(1./X))$ X*inv Matrix of 3 by 3 elements 1 2 3 1 1.00000 -0.444089E-15 -0.111022E-14 2 -0.124345E-13 1.00000 -0.155431E-14 3 0.111022E-15 0.193179E-13 1.00000 => CALL PRINT('Vector times matrix (v*x)' ,V*X) $ Vector times matrix (v*x) Vector of 3 elements 90.0000 96.0000 24.0000 => CALL PRINT('Matrix times vector (x*v)' ,X*V) $ Matrix times vector (x*v) Vector of 3 elements 74.0000 92.0000 32.0000 => CALL PRINT('Matrix times matrix (x*x2)' ,X*X2) $ Matrix times matrix (x*x2) Matrix of 3 by 3 elements 1 2 3 1 1020.00 1092.00 488.000 2 1272.00 1362.00 620.000 3 640.000 696.000 1116.00 => CALL PRINT('Matrix times scaler (x*2.)' ,X*2.) $ Matrix times scaler (x*2.) Matrix of 3 by 3 elements 1 2 3 1 22.0000 24.0000 26.0000 2 28.0000 30.0000 32.0000 3 34.0000 36.0000 -14.0000 => CALL PRINT('Scaler times Matrix (3.*x)' ,3.*X) $ Scaler times Matrix (3.*x) Matrix of 3 by 3 elements 1 2 3 1 33.0000 36.0000 39.0000 2 42.0000 45.0000 48.0000 3 51.0000 54.0000 -21.0000 => CALL PRINT('Vector plus matrix (v+x)' ,V+X) $ Vector plus matrix (v+x) Matrix of 3 by 3 elements 1 2 3 1 12.0000 12.0000 13.0000 2 14.0000 17.0000 16.0000 3 17.0000 18.0000 -4.00000 => CALL PRINT('Matrix plus vector (x+v)' ,X+V) $ Matrix plus vector (x+v) Matrix of 3 by 3 elements 1 2 3 1 12.0000 12.0000 13.0000 2 14.0000 17.0000 16.0000 3 17.0000 18.0000 -4.00000 => CALL PRINT('Matrix plus matrix (x+x2)' ,X+X2) $ Matrix plus matrix (x+x2) Matrix of 3 by 3 elements 1 2 3 1 33.0000 36.0000 39.0000 2 42.0000 45.0000 48.0000 3 51.0000 54.0000 -21.0000 => CALL PRINT('Matrix plus scaler (x+2.)' ,X+2.) $ Matrix plus scaler (x+2.) Matrix of 3 by 3 elements 1 2 3 1 13.0000 12.0000 13.0000 2 14.0000 17.0000 16.0000 3 17.0000 18.0000 -5.00000 => CALL PRINT('Scaler plus matrix (3.+x)' ,3.+X) $ Scaler plus matrix (3.+x) Matrix of 3 by 3 elements 1 2 3 1 14.0000 12.0000 13.0000 2 14.0000 18.0000 16.0000 3 17.0000 18.0000 -4.00000 => CALL PRINT('Vector minus matrix (v-x)' ,V-X) $ Vector minus matrix (v-x) Matrix of 3 by 3 elements 1 2 3 1 -10.0000 12.0000 13.0000 2 14.0000 -13.0000 16.0000 3 17.0000 18.0000 10.0000 => CALL PRINT('Matrix minus vector (x-v)' ,X-V) $ Matrix minus vector (x-v) Matrix of 3 by 3 elements 1 2 3 1 10.0000 12.0000 13.0000 2 14.0000 13.0000 16.0000 3 17.0000 18.0000 -10.0000 => CALL PRINT('Matrix minus matrix (x-x2)' ,X-X2) $ Matrix minus matrix (x-x2) Matrix of 3 by 3 elements 1 2 3 1 -11.0000 -12.0000 -13.0000 2 -14.0000 -15.0000 -16.0000 3 -17.0000 -18.0000 7.00000 => CALL PRINT('Matrix minus scaler (x-2.)' ,X-2.) $ Matrix minus scaler (x-2.) Matrix of 3 by 3 elements 1 2 3 1 9.00000 12.0000 13.0000 2 14.0000 13.0000 16.0000 3 17.0000 18.0000 -9.00000 => CALL PRINT('Scaler minus matrix (3.-x)' ,3.-X) $ Scaler minus matrix (3.-x) Matrix of 3 by 3 elements 1 2 3 1 -8.00000 12.0000 13.0000 2 14.0000 -12.0000 16.0000 3 17.0000 18.0000 10.0000 => CALL PRINT('Array Math Here ')$ Array Math Here => X=AFAM(X)$ => V=AFAM(V)$ => X2=X*2.$ => CALL PRINT('X, 2*x v' ,X,X2,V) $ X, 2*x v X = Array of 3 by 3 elements 1 2 3 1 11.0000 12.0000 13.0000 2 14.0000 15.0000 16.0000 3 17.0000 18.0000 -7.00000 X2 = Array of 3 by 3 elements 1 2 3 1 22.0000 24.0000 26.0000 2 28.0000 30.0000 32.0000 3 34.0000 36.0000 -14.0000 V = Array of 3 elements 1.00000 2.00000 3.00000 => CALL PRINT('Inverse of x (INV)' ,(1./X)) $ Inverse of x (INV) Array of 3 by 3 elements 1 2 3 1 0.909091E-01 0.833333E-01 0.769231E-01 2 0.714286E-01 0.666667E-01 0.625000E-01 3 0.588235E-01 0.555556E-01 -0.142857 => CALL PRINT('X*inv' ,X*(1./X))$ X*inv Array of 3 by 3 elements 1 2 3 1 1.00000 1.00000 1.00000 2 1.00000 1.00000 1.00000 3 1.00000 1.00000 1.00000 => CALL PRINT('Array(1) times Array(2) (v*x)' ,V*X) $ Array(1) times Array(2) (v*x) Array of 3 by 3 elements 1 2 3 1 11.0000 12.0000 13.0000 2 28.0000 30.0000 32.0000 3 51.0000 54.0000 -21.0000 => CALL PRINT('Array(2) times Array(1) (x*v)' ,X*V) $ Array(2) times Array(1) (x*v) Array of 3 by 3 elements 1 2 3 1 11.0000 24.0000 39.0000 2 14.0000 30.0000 48.0000 3 17.0000 36.0000 -21.0000 => CALL PRINT('Array(2) times Array(2) (x*x2)' ,X*X2) $ Array(2) times Array(2) (x*x2) Array of 3 by 3 elements 1 2 3 1 242.000 288.000 338.000 2 392.000 450.000 512.000 3 578.000 648.000 98.0000 => CALL PRINT('Array(2) times Scaler (x*2.)' ,X*2.) $ Array(2) times Scaler (x*2.) Array of 3 by 3 elements 1 2 3 1 22.0000 24.0000 26.0000 2 28.0000 30.0000 32.0000 3 34.0000 36.0000 -14.0000 => CALL PRINT('Scaler times Array(2) (3.*x)' ,3.*X) $ Scaler times Array(2) (3.*x) Array of 3 by 3 elements 1 2 3 1 33.0000 36.0000 39.0000 2 42.0000 45.0000 48.0000 3 51.0000 54.0000 -21.0000 => CALL PRINT('Array(1) plus Array(2) (v+x)' ,V+X) $ Array(1) plus Array(2) (v+x) Array of 3 by 3 elements 1 2 3 1 12.0000 13.0000 14.0000 2 16.0000 17.0000 18.0000 3 20.0000 21.0000 -4.00000 => CALL PRINT('Array(2) plus Array(1) (x+v)' ,X+V) $ Array(2) plus Array(1) (x+v) Array of 3 by 3 elements 1 2 3 1 12.0000 14.0000 16.0000 2 15.0000 17.0000 19.0000 3 18.0000 20.0000 -4.00000 => CALL PRINT('Array(2) plus Array(2) (x+x2)' ,X+X2) $ Array(2) plus Array(2) (x+x2) Array of 3 by 3 elements 1 2 3 1 33.0000 36.0000 39.0000 2 42.0000 45.0000 48.0000 3 51.0000 54.0000 -21.0000 => CALL PRINT('Array(2) plus Scaler (x+2.)' ,X+2.) $ Array(2) plus Scaler (x+2.) Array of 3 by 3 elements 1 2 3 1 13.0000 14.0000 15.0000 2 16.0000 17.0000 18.0000 3 19.0000 20.0000 -5.00000 => CALL PRINT('Scaler plus Array(2) (3.+x)' ,3.+X) $ Scaler plus Array(2) (3.+x) Array of 3 by 3 elements 1 2 3 1 14.0000 15.0000 16.0000 2 17.0000 18.0000 19.0000 3 20.0000 21.0000 -4.00000 => CALL PRINT('Array(1) minus Array(2) (v-x)' ,V-X) $ Array(1) minus Array(2) (v-x) Array of 3 by 3 elements 1 2 3 1 -10.0000 -11.0000 -12.0000 2 -12.0000 -13.0000 -14.0000 3 -14.0000 -15.0000 10.0000 => CALL PRINT('Array(2) minus Array(1) (x-v)' ,X-V) $ Array(2) minus Array(1) (x-v) Array of 3 by 3 elements 1 2 3 1 10.0000 10.0000 10.0000 2 13.0000 13.0000 13.0000 3 16.0000 16.0000 -10.0000 => CALL PRINT('Array(2) minus Array(2) (x-x2)' ,X-X2) $ Array(2) minus Array(2) (x-x2) Array of 3 by 3 elements 1 2 3 1 -11.0000 -12.0000 -13.0000 2 -14.0000 -15.0000 -16.0000 3 -17.0000 -18.0000 7.00000 => CALL PRINT('Array(2) minus scaler (x-2.)' ,X-2.) $ Array(2) minus scaler (x-2.) Array of 3 by 3 elements 1 2 3 1 9.00000 10.0000 11.0000 2 12.0000 13.0000 14.0000 3 15.0000 16.0000 -9.00000 => CALL PRINT('Scaler minus Array(2) (3.-x)' ,3.-X) $ Scaler minus Array(2) (3.-x) Array of 3 by 3 elements 1 2 3 1 -8.00000 -9.00000 -10.0000 2 -11.0000 -12.0000 -13.0000 3 -14.0000 -15.0000 10.0000 => CALL PRINT(' Complex Results ' => '++++++++++++++++++++++++++++++++++++++++')$ Complex Results ++++++++++++++++++++++++++++++++++++++++ => X=MFAM(COMPLEX(X,X2))$ => V=VFAM(COMPLEX(V,V+8.0))$ => X2=MFAM(COMPLEX(X2))$ => CALL PRINT('X, x2 v' ,X,X2,V) $ X, x2 v X = Complex Matrix of 3 by 3 elements 1 2 3 1 ( 11.00 , 22.00 ) ( 12.00 , 24.00 ) ( 13.00 , 26.00 ) 2 ( 14.00 , 28.00 ) ( 15.00 , 30.00 ) ( 16.00 , 32.00 ) 3 ( 17.00 , 34.00 ) ( 18.00 , 36.00 ) ( -7.000 , -14.00 ) X2 = Complex Matrix of 3 by 3 elements 1 2 3 1 ( 22.00 , 0.000 ) ( 24.00 , 0.000 ) ( 26.00 , 0.000 ) 2 ( 28.00 , 0.000 ) ( 30.00 , 0.000 ) ( 32.00 , 0.000 ) 3 ( 34.00 , 0.000 ) ( 36.00 , 0.000 ) ( -14.00 , 0.000 ) V = Complex Vector of 3 elements ( 1.000 , 9.000 ) ( 2.000 , 10.00 ) ( 3.000 , 11.00 ) => CALL PRINT('Inverse of x (INV)' , (COMPLEX(1.)/X)) $ Inverse of x (INV) Complex Matrix of 3 by 3 elements 1 2 3 1 ( -1.008 , 2.015 ) ( 0.8154 , -1.631 ) ( -0.7692E-02, 0.1538E-01) 2 ( 0.9487 , -1.897 ) ( -0.7641 , 1.528 ) ( 0.1538E-01, -0.3077E-01) 3 ( -0.7692E-02, 0.1538E-01) ( 0.1538E-01, -0.3077E-01) ( -0.7692E-02, 0.1538E-01) => CALL PRINT('X*inv' , X*(COMPLEX(1.)/X))$ X*inv Complex Matrix of 3 by 3 elements 1 2 3 1 ( 1.000 , 0.000 ) ( 0.1421E-13, 0.000 ) ( -0.7883E-14, 0.000 ) 2 ( -0.2220E-14, 0.000 ) ( 1.000 , 0.000 ) ( -0.9992E-14, 0.000 ) 3 ( -0.4330E-14, 0.000 ) ( 0.8660E-14, 0.000 ) ( 1.000 , 0.000 ) => CALL PRINT('Vector times matrix (v*x)' ,V*X) $ Vector times matrix (v*x) Complex Vector of 3 elements ( -762.0 , 606.0 ) ( -816.0 , 648.0 ) ( -376.0 , 248.0 ) => CALL PRINT('Matrix times vector (x*v)' ,X*V) $ Matrix times vector (x*v) Complex Vector of 3 elements ( -650.0 , 510.0 ) ( -812.0 , 636.0 ) ( -480.0 , 320.0 ) => CALL PRINT('Matrix times matrix (x*x2)' ,X*X2) $ Matrix times matrix (x*x2) Complex Matrix of 3 by 3 elements 1 2 3 1 ( 1020. , 2040. ) ( 1092. , 2184. ) ( 488.0 , 976.0 ) 2 ( 1272. , 2544. ) ( 1362. , 2724. ) ( 620.0 , 1240. ) 3 ( 640.0 , 1280. ) ( 696.0 , 1392. ) ( 1116. , 2232. ) => CALL PRINT('Matrix times scaler (x*2.)',X*COMPLEX(2.)) $ Matrix times scaler (x*2.) Complex Matrix of 3 by 3 elements 1 2 3 1 ( 22.00 , 44.00 ) ( 24.00 , 48.00 ) ( 26.00 , 52.00 ) 2 ( 28.00 , 56.00 ) ( 30.00 , 60.00 ) ( 32.00 , 64.00 ) 3 ( 34.00 , 68.00 ) ( 36.00 , 72.00 ) ( -14.00 , -28.00 ) => CALL PRINT('Scaler times Matrix (3.*x)',COMPLEX(3.)*X) $ Scaler times Matrix (3.*x) Complex Matrix of 3 by 3 elements 1 2 3 1 ( 33.00 , 66.00 ) ( 36.00 , 72.00 ) ( 39.00 , 78.00 ) 2 ( 42.00 , 84.00 ) ( 45.00 , 90.00 ) ( 48.00 , 96.00 ) 3 ( 51.00 , 102.0 ) ( 54.00 , 108.0 ) ( -21.00 , -42.00 ) => CALL PRINT('Vector plus matrix (v+x)',V+X) $ Vector plus matrix (v+x) Complex Matrix of 3 by 3 elements 1 2 3 1 ( 12.00 , 31.00 ) ( 12.00 , 24.00 ) ( 13.00 , 26.00 ) 2 ( 14.00 , 28.00 ) ( 17.00 , 40.00 ) ( 16.00 , 32.00 ) 3 ( 17.00 , 34.00 ) ( 18.00 , 36.00 ) ( -4.000 , -3.000 ) => CALL PRINT('Matrix plus vector (x+v)',X+V) $ Matrix plus vector (x+v) Complex Matrix of 3 by 3 elements 1 2 3 1 ( 12.00 , 31.00 ) ( 12.00 , 24.00 ) ( 13.00 , 26.00 ) 2 ( 14.00 , 28.00 ) ( 17.00 , 40.00 ) ( 16.00 , 32.00 ) 3 ( 17.00 , 34.00 ) ( 18.00 , 36.00 ) ( -4.000 , -3.000 ) => CALL PRINT('Matrix plus matrix (x+x2)',X+X2) $ Matrix plus matrix (x+x2) Complex Matrix of 3 by 3 elements 1 2 3 1 ( 33.00 , 22.00 ) ( 36.00 , 24.00 ) ( 39.00 , 26.00 ) 2 ( 42.00 , 28.00 ) ( 45.00 , 30.00 ) ( 48.00 , 32.00 ) 3 ( 51.00 , 34.00 ) ( 54.00 , 36.00 ) ( -21.00 , -14.00 ) => CALL PRINT('Matrix plus scaler (x+2.)',X+COMPLEX(2.)) $ Matrix plus scaler (x+2.) Complex Matrix of 3 by 3 elements 1 2 3 1 ( 13.00 , 22.00 ) ( 12.00 , 24.00 ) ( 13.00 , 26.00 ) 2 ( 14.00 , 28.00 ) ( 17.00 , 30.00 ) ( 16.00 , 32.00 ) 3 ( 17.00 , 34.00 ) ( 18.00 , 36.00 ) ( -5.000 , -14.00 ) => CALL PRINT('Scaler plus matrix (3.+x)',COMPLEX(3.)+X) $ Scaler plus matrix (3.+x) Complex Matrix of 3 by 3 elements 1 2 3 1 ( 14.00 , 22.00 ) ( 12.00 , 24.00 ) ( 13.00 , 26.00 ) 2 ( 14.00 , 28.00 ) ( 18.00 , 30.00 ) ( 16.00 , 32.00 ) 3 ( 17.00 , 34.00 ) ( 18.00 , 36.00 ) ( -4.000 , -14.00 ) => CALL PRINT('Vector minus matrix (v-x)',,V-X) $ Vector minus matrix (v-x) Complex Matrix of 3 by 3 elements 1 2 3 1 ( -10.00 , -13.00 ) ( 12.00 , 24.00 ) ( 13.00 , 26.00 ) 2 ( 14.00 , 28.00 ) ( -13.00 , -20.00 ) ( 16.00 , 32.00 ) 3 ( 17.00 , 34.00 ) ( 18.00 , 36.00 ) ( 10.00 , 25.00 ) => CALL PRINT('Matrix minus vector (x-v)' ,X-V) $ Matrix minus vector (x-v) Complex Matrix of 3 by 3 elements 1 2 3 1 ( 10.00 , 13.00 ) ( 12.00 , 24.00 ) ( 13.00 , 26.00 ) 2 ( 14.00 , 28.00 ) ( 13.00 , 20.00 ) ( 16.00 , 32.00 ) 3 ( 17.00 , 34.00 ) ( 18.00 , 36.00 ) ( -10.00 , -25.00 ) => CALL PRINT('Matrix minus matrix (x-x2)',X-X2) $ Matrix minus matrix (x-x2) Complex Matrix of 3 by 3 elements 1 2 3 1 ( -11.00 , 22.00 ) ( -12.00 , 24.00 ) ( -13.00 , 26.00 ) 2 ( -14.00 , 28.00 ) ( -15.00 , 30.00 ) ( -16.00 , 32.00 ) 3 ( -17.00 , 34.00 ) ( -18.00 , 36.00 ) ( 7.000 , -14.00 ) => CALL PRINT('Matrix minus scaler (x-2.)',X-COMPLEX(2.)) $ Matrix minus scaler (x-2.) Complex Matrix of 3 by 3 elements 1 2 3 1 ( 9.000 , 22.00 ) ( 12.00 , 24.00 ) ( 13.00 , 26.00 ) 2 ( 14.00 , 28.00 ) ( 13.00 , 30.00 ) ( 16.00 , 32.00 ) 3 ( 17.00 , 34.00 ) ( 18.00 , 36.00 ) ( -9.000 , -14.00 ) => CALL PRINT('Scaler minus matrix (3.-x)',COMPLEX(3.)-X) $ Scaler minus matrix (3.-x) Complex Matrix of 3 by 3 elements 1 2 3 1 ( -8.000 , -22.00 ) ( 12.00 , 24.00 ) ( 13.00 , 26.00 ) 2 ( 14.00 , 28.00 ) ( -12.00 , -30.00 ) ( 16.00 , 32.00 ) 3 ( 17.00 , 34.00 ) ( 18.00 , 36.00 ) ( 10.00 , 14.00 ) => CALL PRINT('Array Math Here ')$ Array Math Here => X=AFAM(X)$ => V=AFAM(V)$ => X2=AFAM(X2)$ => CALL PRINT('X, 2*x v' ,X,X2,V) $ X, 2*x v X = Complex Array of 3 by 3 elements 1 2 3 1 ( 11.00 , 22.00 ) ( 12.00 , 24.00 ) ( 13.00 , 26.00 ) 2 ( 14.00 , 28.00 ) ( 15.00 , 30.00 ) ( 16.00 , 32.00 ) 3 ( 17.00 , 34.00 ) ( 18.00 , 36.00 ) ( -7.000 , -14.00 ) X2 = Complex Array of 3 by 3 elements 1 2 3 1 ( 22.00 , 0.000 ) ( 24.00 , 0.000 ) ( 26.00 , 0.000 ) 2 ( 28.00 , 0.000 ) ( 30.00 , 0.000 ) ( 32.00 , 0.000 ) 3 ( 34.00 , 0.000 ) ( 36.00 , 0.000 ) ( -14.00 , 0.000 ) V = Complex Array of 3 elements ( 1.000 , 9.000 ) ( 2.000 , 10.00 ) ( 3.000 , 11.00 ) => CALL PRINT('Inverse of x (INV)', (COMPLEX(1.)/X)) $ Inverse of x (INV) Complex Array of 3 by 3 elements 1 2 3 1 ( 0.1818E-01, -0.3636E-01) ( 0.1667E-01, -0.3333E-01) ( 0.1538E-01, -0.3077E-01) 2 ( 0.1429E-01, -0.2857E-01) ( 0.1333E-01, -0.2667E-01) ( 0.1250E-01, -0.2500E-01) 3 ( 0.1176E-01, -0.2353E-01) ( 0.1111E-01, -0.2222E-01) ( -0.2857E-01, 0.5714E-01) => CALL PRINT('X*inv' , X*(COMPLEX(1.)/X))$ X*inv Complex Array of 3 by 3 elements 1 2 3 1 ( 1.000 , 0.000 ) ( 1.000 , 0.000 ) ( 1.000 , 0.000 ) 2 ( 1.000 , 0.000 ) ( 1.000 , 0.000 ) ( 1.000 , 0.000 ) 3 ( 1.000 , 0.000 ) ( 1.000 , 0.000 ) ( 1.000 , 0.000 ) => CALL PRINT('Array(1) times Array(2) (v*x)' ,V*X) $ Array(1) times Array(2) (v*x) Complex Array of 3 by 3 elements 1 2 3 1 ( -187.0 , 121.0 ) ( -204.0 , 132.0 ) ( -221.0 , 143.0 ) 2 ( -252.0 , 196.0 ) ( -270.0 , 210.0 ) ( -288.0 , 224.0 ) 3 ( -323.0 , 289.0 ) ( -342.0 , 306.0 ) ( 133.0 , -119.0 ) => CALL PRINT('Array(2) times Array(1) (x*v)' ,X*V) $ Array(2) times Array(1) (x*v) Complex Array of 3 by 3 elements 1 2 3 1 ( -187.0 , 121.0 ) ( -216.0 , 168.0 ) ( -247.0 , 221.0 ) 2 ( -238.0 , 154.0 ) ( -270.0 , 210.0 ) ( -304.0 , 272.0 ) 3 ( -289.0 , 187.0 ) ( -324.0 , 252.0 ) ( 133.0 , -119.0 ) => CALL PRINT('Array(2) times Array(2) (x*x2)' ,X*X2) $ Array(2) times Array(2) (x*x2) Complex Array of 3 by 3 elements 1 2 3 1 ( 242.0 , 484.0 ) ( 288.0 , 576.0 ) ( 338.0 , 676.0 ) 2 ( 392.0 , 784.0 ) ( 450.0 , 900.0 ) ( 512.0 , 1024. ) 3 ( 578.0 , 1156. ) ( 648.0 , 1296. ) ( 98.00 , 196.0 ) => CALL PRINT('Array(2) times Scaler (x*complex(2.))',X*COMPLEX(2.))$ Array(2) times Scaler (x*complex(2.)) Complex Array of 3 by 3 elements 1 2 3 1 ( 22.00 , 44.00 ) ( 24.00 , 48.00 ) ( 26.00 , 52.00 ) 2 ( 28.00 , 56.00 ) ( 30.00 , 60.00 ) ( 32.00 , 64.00 ) 3 ( 34.00 , 68.00 ) ( 36.00 , 72.00 ) ( -14.00 , -28.00 ) => CALL PRINT('Scaler times Array(2) (complex(3.)*x)',COMPLEX(3.)*X)$ Scaler times Array(2) (complex(3.)*x) Complex Array of 3 by 3 elements 1 2 3 1 ( 33.00 , 66.00 ) ( 36.00 , 72.00 ) ( 39.00 , 78.00 ) 2 ( 42.00 , 84.00 ) ( 45.00 , 90.00 ) ( 48.00 , 96.00 ) 3 ( 51.00 , 102.0 ) ( 54.00 , 108.0 ) ( -21.00 , -42.00 ) => CALL PRINT('Array(1) plus Array(2) (v+x)' ,V+X) $ Array(1) plus Array(2) (v+x) Complex Array of 3 by 3 elements 1 2 3 1 ( 12.00 , 31.00 ) ( 13.00 , 33.00 ) ( 14.00 , 35.00 ) 2 ( 16.00 , 38.00 ) ( 17.00 , 40.00 ) ( 18.00 , 42.00 ) 3 ( 20.00 , 45.00 ) ( 21.00 , 47.00 ) ( -4.000 , -3.000 ) => CALL PRINT('Array(2) plus Array(1) (x+v)' ,X+V) $ Array(2) plus Array(1) (x+v) Complex Array of 3 by 3 elements 1 2 3 1 ( 12.00 , 31.00 ) ( 14.00 , 34.00 ) ( 16.00 , 37.00 ) 2 ( 15.00 , 37.00 ) ( 17.00 , 40.00 ) ( 19.00 , 43.00 ) 3 ( 18.00 , 43.00 ) ( 20.00 , 46.00 ) ( -4.000 , -3.000 ) => CALL PRINT('Array(2) plus Array(2) (x+x2)' ,X+X2) $ Array(2) plus Array(2) (x+x2) Complex Array of 3 by 3 elements 1 2 3 1 ( 33.00 , 22.00 ) ( 36.00 , 24.00 ) ( 39.00 , 26.00 ) 2 ( 42.00 , 28.00 ) ( 45.00 , 30.00 ) ( 48.00 , 32.00 ) 3 ( 51.00 , 34.00 ) ( 54.00 , 36.00 ) ( -21.00 , -14.00 ) => CALL PRINT('Array(2) plus Scaler (x+complex(2.))',X+COMPLEX(2.))$ Array(2) plus Scaler (x+complex(2.)) Complex Array of 3 by 3 elements 1 2 3 1 ( 13.00 , 22.00 ) ( 14.00 , 24.00 ) ( 15.00 , 26.00 ) 2 ( 16.00 , 28.00 ) ( 17.00 , 30.00 ) ( 18.00 , 32.00 ) 3 ( 19.00 , 34.00 ) ( 20.00 , 36.00 ) ( -5.000 , -14.00 ) => CALL PRINT('Scaler plus Array(2) (complex(3.)+x)',COMPLEX(3.)+X)$ Scaler plus Array(2) (complex(3.)+x) Complex Array of 3 by 3 elements 1 2 3 1 ( 14.00 , 22.00 ) ( 15.00 , 24.00 ) ( 16.00 , 26.00 ) 2 ( 17.00 , 28.00 ) ( 18.00 , 30.00 ) ( 19.00 , 32.00 ) 3 ( 20.00 , 34.00 ) ( 21.00 , 36.00 ) ( -4.000 , -14.00 ) => CALL PRINT('Array(1) minus Array(2) (v-x)' ,V-X) $ Array(1) minus Array(2) (v-x) Complex Array of 3 by 3 elements 1 2 3 1 ( -10.00 , -13.00 ) ( -11.00 , -15.00 ) ( -12.00 , -17.00 ) 2 ( -12.00 , -18.00 ) ( -13.00 , -20.00 ) ( -14.00 , -22.00 ) 3 ( -14.00 , -23.00 ) ( -15.00 , -25.00 ) ( 10.00 , 25.00 ) => CALL PRINT('Array(2) minus Array(1) (x-v)' ,X-V) $ Array(2) minus Array(1) (x-v) Complex Array of 3 by 3 elements 1 2 3 1 ( 10.00 , 13.00 ) ( 10.00 , 14.00 ) ( 10.00 , 15.00 ) 2 ( 13.00 , 19.00 ) ( 13.00 , 20.00 ) ( 13.00 , 21.00 ) 3 ( 16.00 , 25.00 ) ( 16.00 , 26.00 ) ( -10.00 , -25.00 ) => CALL PRINT('Array(2) minus Array(2) (x-x2)' ,X-X2) $ Array(2) minus Array(2) (x-x2) Complex Array of 3 by 3 elements 1 2 3 1 ( -11.00 , 22.00 ) ( -12.00 , 24.00 ) ( -13.00 , 26.00 ) 2 ( -14.00 , 28.00 ) ( -15.00 , 30.00 ) ( -16.00 , 32.00 ) 3 ( -17.00 , 34.00 ) ( -18.00 , 36.00 ) ( 7.000 , -14.00 ) => CALL PRINT('Array(2) minus scaler (x-complex(2.))',X-COMPLEX(2.))$ Array(2) minus scaler (x-complex(2.)) Complex Array of 3 by 3 elements 1 2 3 1 ( 9.000 , 22.00 ) ( 10.00 , 24.00 ) ( 11.00 , 26.00 ) 2 ( 12.00 , 28.00 ) ( 13.00 , 30.00 ) ( 14.00 , 32.00 ) 3 ( 15.00 , 34.00 ) ( 16.00 , 36.00 ) ( -9.000 , -14.00 ) => CALL PRINT('Scaler minus Array(2) (complex(3.)-x)',COMPLEX(3.)-X)$ Scaler minus Array(2) (complex(3.)-x) Complex Array of 3 by 3 elements 1 2 3 1 ( -8.000 , -22.00 ) ( -9.000 , -24.00 ) ( -10.00 , -26.00 ) 2 ( -11.00 , -28.00 ) ( -12.00 , -30.00 ) ( -13.00 , -32.00 ) 3 ( -14.00 , -34.00 ) ( -15.00 , -36.00 ) ( 10.00 , 14.00 ) B34S Matrix Command Ending. Last Command reached. Space available in allocator 5874187, peak space used 709 Number variables used 17, peak number used 20 Number temp variables used 169, # user temp clean 0 B34S(r) Matrix Command. Version February 2004. Date of Run d/m/y 15/ 7/04. Time of Run h:m:s 14:46: 7. => * TEST CASE FOR REAL MATRIX FROM IMSL MATH (10) PP 295-297$ => * EIGENVECTORS HAVE NOT BEEN NORMALIZED BUT ARE TESTED BELOW$ => A=MATRIX(3,3:8.,-1.,-5.,-4., 4.,-2.,18.,-5.,-7.)$ => CALL PRINT('A Matrix',A)$ A Matrix A = Matrix of 3 by 3 elements 1 2 3 1 8.00000 -1.00000 -5.00000 2 -4.00000 4.00000 -2.00000 3 18.0000 -5.00000 -7.00000 => E=EIGENVAL(A)$ => CALL PRINT('Eigenvalues of a', E, => 'Sum of the eigenvalues of General Martix A',SUM(E), => 'Trace of General Matrix A',TRACE(A), => 'Product of the eigenvalues of Martix A',PROD(E), => 'Determinant of Matrix A',DET(A))$ Eigenvalues of a E = Complex Vector of 3 elements ( 2.000 , 4.000 ) ( 2.000 , -4.000 ) ( 1.000 , 0.000 ) Sum of the eigenvalues of General Martix A (4.999999999999999,0.000000000000000E+00) Trace of General Matrix A 5.0000000 Product of the eigenvalues of Martix A (20.00000000000003,0.000000000000000E+00) Determinant of Matrix A 20.000000 => EE=EIGENVAL(A,EVEC:)$ => CALL PRINT('Non scaled Eigenvectors',EVEC)$ Non scaled Eigenvectors EVEC = Complex Matrix of 3 by 3 elements 1 2 3 1 ( 0.3162 , 0.3162 ) ( 0.3162 , -0.3162 ) ( 0.4082 , 0.000 ) 2 ( -0.9992E-15, 0.6325 ) ( -0.9992E-15, -0.6325 ) ( 0.8165 , 0.000 ) 3 ( 0.6325 , 0.000 ) ( 0.6325 , 0.000 ) ( 0.4082 , 0.000 ) => EE=EIGENVAL(A,EVEC)$ => CALL PRINT('Scaled Eigenvectors',EVEC)$ Scaled Eigenvectors EVEC = Complex Matrix of 3 by 3 elements 1 2 3 1 ( 0.1129 , 0.5397 ) ( 0.1129 , -0.5397 ) ( 2.367 , 0.000 ) 2 ( -0.4268 , 0.6526 ) ( -0.4268 , -0.6526 ) ( 4.735 , 0.000 ) 3 ( 0.6526 , 0.4268 ) ( 0.6526 , -0.4268 ) ( 2.367 , 0.000 ) => CALL PRINT('Test transpose(evec)*evec ', => TRANSPOSE(EVEC)*EVEC , => ' ' => 'Test evec*transpose(evec) ', => EVEC*TRANSPOSE(EVEC)) $ Test transpose(evec)*evec Complex Matrix of 3 by 3 elements 1 2 3 1 ( -0.2785 , 0.1219 ) ( 1.520 , 0.000 ) ( -0.2083 , 5.378 ) 2 ( 1.520 , 0.000 ) ( -0.2785 , -0.1219 ) ( -0.2083 , -5.378 ) 3 ( -0.2083 , 5.378 ) ( -0.2083 , -5.378 ) ( 33.63 , 0.000 ) Test evec*transpose(evec) Complex Matrix of 3 by 3 elements 1 2 3 1 ( 5.048 , 0.000 ) ( 10.41 , 0.000 ) ( 5.292 , 0.000 ) 2 ( 10.41 , 0.000 ) ( 21.93 , 0.000 ) ( 10.10 , 0.000 ) 3 ( 5.292 , 0.000 ) ( 10.10 , 0.000 ) ( 6.093 , 0.000 ) => * COMPLEX CASE SEE IMSL MATH (10) PP 302-304 $ => R=MATRIX(4,4:5., 5.,-6.,-7., => 3., 6.,-5.,-6., => 2., 3.,-1.,-5., => 1., 2.,-3.,0.0)$ => I=MATRIX(4,4:9., 5.,-6.,-7., => 3.,10.,-5.,-6., => 2., 3., 3.,-5., => 1., 2.,-3., 4.)$ => CA=COMPLEX(R,I)$ => CALL PRINT('CA Complex Matrix',CA)$ CA Complex Matrix CA = Complex Matrix of 4 by 4 elements 1 2 3 4 1 ( 5.000 , 9.000 ) ( 5.000 , 5.000 ) ( -6.000 , -6.000 ) ( -7.000 , -7.000 ) 2 ( 3.000 , 3.000 ) ( 6.000 , 10.00 ) ( -5.000 , -5.000 ) ( -6.000 , -6.000 ) 3 ( 2.000 , 2.000 ) ( 3.000 , 3.000 ) ( -1.000 , 3.000 ) ( -5.000 , -5.000 ) 4 ( 1.000 , 1.000 ) ( 2.000 , 2.000 ) ( -3.000 , -3.000 ) ( 0.000 , 4.000 ) => CE=EIGENVAL(CA,CEVEC:)$ => CALL PRINT('Non scaled Eigenvectors of CA',CEVEC)$ Non scaled Eigenvectors of CA CEVEC = Complex Matrix of 4 by 4 elements 1 2 3 4 1 ( 0.3780 , 0.1027E-14) ( 0.5774 , 0.000 ) ( 0.5774 , -0.1277E-14) ( 0.7559 , 0.000 ) 2 ( 0.7559 , 0.000 ) ( 0.5774 , 0.7216E-15) ( 0.5774 , 0.000 ) ( 0.3780 , -0.1416E-14) 3 ( 0.3780 , -0.8327E-16) ( 0.5774 , -0.3886E-15) ( 0.3232E-14, 0.5416E-14) ( 0.3780 , -0.9159E-15) 4 ( 0.3780 , 0.5551E-16) ( 0.9159E-15, 0.3518E-15) ( 0.5774 , -0.4885E-14) ( 0.3780 , -0.3053E-15) => EE=EIGENVAL(CA,CEVEC)$ => CALL PRINT('Scaled Eigenvectors of CA',CEVEC)$ Scaled Eigenvectors of CA CEVEC = Complex Matrix of 4 by 4 elements 1 2 3 4 1 ( 0.3898 , 5.149 ) ( 0.7692 , -0.9113E-01) ( 1.290 , 0.4025E-01) ( 0.9056 , 3.344 ) 2 ( 0.3898 , 5.149 ) ( 1.538 , -0.1823 ) ( 1.290 , 0.4025E-01) ( 0.4528 , 1.672 ) 3 ( 0.3898 , 5.149 ) ( 0.7692 , -0.9113E-01) ( -0.3886E-14, -0.9714E-16) ( 0.4528 , 1.672 ) 4 ( -0.4238E-14, 0.1237E-13) ( 0.7692 , -0.9113E-01) ( 1.290 , 0.4025E-01) ( 0.4528 , 1.672 ) => CALL PRINT('Eigenvalues of ca', CE, => 'Sum of the eigenvalues of General Martix CA',SUM(CE), => 'Trace of General Matrix CA',TRACE(CA), => 'Product of the eigenvalues of Martix CA',PROD(CE), => 'Determinant of Matrix CA',DET(CA))$ Eigenvalues of ca CE = Complex Vector of 4 elements ( 2.000 , 6.000 ) ( 4.000 , 8.000 ) ( 3.000 , 7.000 ) ( 1.000 , 5.000 ) Sum of the eigenvalues of General Martix CA (9.999999999999998,26.00000000000000) Trace of General Matrix CA (10.00000000000000,26.00000000000000) Product of the eigenvalues of Martix CA (400.0000000000005,-2160.000000000000) Determinant of Matrix CA (400.0000000000008,-2160.000000000003) B34S Matrix Command Ending. Last Command reached. Space available in allocator 5874635, peak space used 1706 Number variables used 39, peak number used 41 Number temp variables used 106, # user temp clean 0 B34S(r) Matrix Command. Version February 2004. Date of Run d/m/y 15/ 7/04. Time of Run h:m:s 14:46: 7. => * EXAMPLE FROM LIMDEP 7.0 MANUAL PAGE 376 $ => * EIGENALYSIS OF KLEIN MODEL 1 $ => R=MATRIX(3,3:.172,-.051,-.008,1.511,.848,.743,-.287,-.161,.818)$ => CALL PRINT(R,EIGENVAL(R))$ R = Matrix of 3 by 3 elements 1 2 3 1 0.172000 -0.510000E-01 -0.800000E-02 2 1.51100 0.848000 0.743000 3 -0.287000 -0.161000 0.818000 Complex Vector of 3 elements ( 0.2995 , 0.000 ) ( 0.7692 , 0.3494 ) ( 0.7692 , -0.3494 ) B34S Matrix Command Ending. Last Command reached. Space available in allocator 5874951, peak space used 517 Number variables used 13, peak number used 18 Number temp variables used 18, # user temp clean 0 B34S(r) Matrix Command. Version February 2004. Date of Run d/m/y 15/ 7/04. Time of Run h:m:s 14:46: 7. => * TEST PROBLEM OF FFT FROM MATLAB PAGE 6-32 $ => X=ARRAY(8:4., 3., 7., -9., 1., 0., 0., 0.)$ => CALL PRINT(X,FFT(X))$ X = Array of 8 elements 4.00000 3.00000 7.00000 -9.00000 1.00000 0.00000 0.00000 0.00000 Array of 8 elements 6.00000 11.4853 -2.75736 -2.00000 -12.0000 -5.48528 11.2426 18.0000 B34S Matrix Command Ending. Last Command reached. Space available in allocator 5874959, peak space used 368 Number variables used 11, peak number used 12 Number temp variables used 12, # user temp clean 0 B34S 8.10R (D:M:Y) 15/ 7/04 (H:M:S) 14:46: 7 STAT. PROC. STEP PIMPLE DATA PAGE 217 B34S normal exit on Date (D:M:Y) 15/ 7/04 at Time (H:M:S) 14:46: 7