20.0 BTIDEN Command The BTIDEN command is to used to identify a VAR, VARMA or VMA model. Basic references are: - Tiao, G., G. Box, M. Grupe, G. Hudak, W. Bell, I Chang,"The Wisconsin Multiple Time Series (WMTS-1) Program, A Preliminary Guide," unpublished technical report, Department of Statistics, University of Wisconsin. - Tiao, G. and G. E. P. Box, "Modeling Multiple Time Series with Applications," Journal of the American Statistical Association, 1981, Vol 76, pp 802-816. - Box, G., G. Tiao, "A Canonical Analysis of Multiple Time Series," Biometrika, 1977, Vol. 64, pp. 355-366. - Hinich, Melvin, "Testing for Gaussianity and Linearity of a Stationary Time Series," Journal of Time Series Analysis, Vol. 3, No. 5., 1982, pp. 169 - 176. - Hinich, Melvin and Douglas Patterson, "Evidence of Nonlinearity in Daily Stock Returns," Journal of Business and Economic Statistics, Vol. 3, No. 1, January 1985, pp. 69 - 77. - Hinich, Melvin, Ashley, Richard and Patterson, Douglas, "A Diagnostic Test for Nonlinear Serial Dependence in Time Series Fitting Errors," Journal of Time Series Analysis, Vol. 7, No. 3, 1986, pp 165 - 178. - Hinich, Melvin , Patterson, Douglas, "A Bispectrum Based Test on the Stationary Martingale Model," unpublished manuscript dated 13 August 1986. - Hinich, Melvin, Wolinsky, M. A. , "A Test for Aliasing Using Bispectral Estimates," Journal of the American Statistical Association, Vol. 83, No. 402, June 1988, pp. 499 - 502. - Dalle Molle, John & Melvin Hinich, "Trispectral Analysis", unpublished manuscript Applied Research Laboratories, The University of Texas at Austin, 1991. - Hinich, Melvin., "Testing for Dependence in the Input to a Linear Time Series Model," unpublished manuscript dated 28 May 1993 published in Nonparametric Statistics 6, 205-221. - Ramsey, James and Philip Rothman., "Time Irreversibility and Business Cycle Asymmetry," Journal of Money Credit and Banking," Vol. 28, No. 1 (February 1996), 1-12 - Hinich, Melvin and Philip Rothman., "Frequency-Domain Test of Time Reversibility," Macroeconomic Dynamics, Vol. 2, 1998, 72-88. - Rothman, Philip., "Fortran Programs for Running the TR Test: A Guide and Examples," in Studies in Nonlinear Dynamics and Econometrics, Vol. 1, No. 4 (January 1997), 203-208 Form of BTIDEN command. B34SEXEC BTIDEN options parameters $ TITLE=(' ') $ SERIESN VAR=Xvar1 NAME=(' ') DIF=( )( ) TM=r1 PLAM=r2$ BISPEC options parameters $ TRISPEC options parameters $ POLYSPEC options parameters $ REVERSE options parameters $ IDEN options parameters $ ESTVAR options parameters $ B34SEEND$ A BTIDEN command must specifiy either the IDEN or the ESTVAR sentences, but not both. The IDEN sentence is used to perform cross correlation analysis. If the IDEN sentence is present, the maximum number of series is 5. The ESTVAR is used to estimate a VAR model. The maximum number of series here is 30. In the BTIDEN paragraph, a SERIESN sentence must be supplied for each series loaded. The BISPEC, POLYSPEC and TRISPEC sentences allow nonlinear tests for be performed following Hinich. BTIDEN sentence parameters. IBEGIN=n1 Sets beginning observation. Defaults to 1. IEND=n2 Sets ending observation. Defaults to NOOB. NSTDER=r1 Sets number of standard errors for ACF and CCF +, - . plots. Default = 2. NSTDER must be specified as LE 5 digits and GE 0.0 . TITLE sentence. TITLE=('Any title here up to 80 characters')$ The TITLE sentence is optional. SERIESN sentence. The SERIESN sentence controls variable input, and optionally additional variable naming and transformation. Parameters for SERIESN sentence. VAR=Xvar Specify input variable. This parameter must be supplied. NAME=(' A max of 65 characters additional name description here') TM=r1 Specifies a constant to add to the data. PLAM=r21 Specifies Box - Cox Transformation. If PLAM is not set, the data is unchanged. If PLAM is set to 0.0, XNEW=DLOG(XOLD + TM). If PLAM GE .0001 XNEW=(XOLD + TM) ** PLAM. DIF=(n1,n2)(n3,n4) Specifies differencing. There is a max of two differencing factors (). The first integer in ( ) is the number of differences, the second integer is the order of the difference. For example DIF=(1,1)(1,12) is first differencing and seasonal differencing. 20.1 Hinich Nonlinearity Tests on One Series Note: The BISPEC sentence can be called from the following commands: BJIDEN, BJEST, BTIDEN, BTEST, RR, REG, ROBUST, MARS, PISPLINE. BISPEC sentence. The BISPEC sentence performs various nonlinearity and gaussianity and martingale tests suggested by Hinich. Any transformations called for on the BISPEC sentence are only for these tests and have no effect on any other options in other sentences in the command. The bispectrum tests at which frequencies there is evidence of nonlinearity, lack of gaussianity and whether the process follows a martingale process. The BISPEC sentence is the same for the BTIDEN, MARS, REG, ROBUST, BJIDEN, BJEST and BTEST paragraphs. The BISPEC sentence calls up a number of programs for analysis. - BISP is the basic program to test for gaussianity and nonlinearity using the Hinich (1982) tests. - NBISP is similar to BISP except that it uses a block read feature to allow unlimited numbers of observations. The output also has a few additional features. For small observations, BISP is more accurate since it does not use the block read approach. Unless the block size selected goes into the number observations evenly, not all observations will be used in the analysis. If aliasing is suspected use the PD region. Otherwise use IT and OT for transients. To test for aliasing change sampling rate and observe what happens to spectrum. If spectrun tapers off at high frequency, this is consistent with no aliasing problem. Aliasing is a frequency counterpart to aggregation bias. - OLDMARTIN uses a block read option to test for Martingales. The MARTIN test should not be run unless the data is white noise. An appropriate way to test for white noise is by use of the ACF. If residual is independent, then it follows a MD and is white. If residual is a MD this means that the differnece between the actual data and the conditional expectation is not predictable by past information. The error variance may or may not be predictable (See ARCH models). White noise only means that ACF is clean. It is not recommended that OLDMARTIN be used since the MARTIN program, discussed below, is far superior in power and ease of use. - MARTIN allows testing whether the Martingale assumption is violated. A process X(t) is a Martingale if E(X(t+1)) = X(t). The martin test is called by the command IMART. If only this command is given, the blocksize used (LBL) will be set as LBL =2 * IDINT(.9D+00 * DSQRT(NOB)) and the test will be run. If NBD is set > 1, then the test will be calculated with blocksizes LBL, LBL+NBD, LBL + (2*NBD), ..., LBU, where LBU =2 * IDINT(1.1D+00* DSQRT(NOB)). The V paramater allows the user to set the integer V notch size MV as IDINT(.01D+00 * V * DFLOAT(LB) + .5d+00). - CLIP allows data clipping for all programs to reduce kurtosis. Two types of clipping are possible. - Hinich (1993) suggests a normally distributed V statistic to test for second order dependence and a normally distributed H statistic to test for third order dependence. V and H can be calculated for the complete sample, or for overlapping or non overlapping window subsets. The autocorrelation function of the V and H statistics for the subset periods can be used to detect possible recurring periods of nonlinearity. - Hinich (1994?) has suggested a number of tests for nonlinearity within the sample. These are called with the POLYSPEC sentence. - Tests developed by Melvin Hinich for bivariate nonlinearity analysis are called from the MVNLTEST command documented in section 41.0. - The BISPEC sentence controls calculation of Dickey-Fuller tests, Phillips-Perron Tests and Engle Lagrangian Multiplier tests - As implemented, the Tsay test should be applied to prewhitened data such as residuals not raw series. Overview of some uses of BISPEC command. BISPEC IOLDSP $ will give default gaussianity and linearity tests. BISPEC IAUTO$ will give gaussianity and linearity tests over a range of M values. BISPEC IAUTO ITURNO $ will turn off all output but summary tables. BISPEC INEWSP IMART INAUTO IAUTO ITURNO $ will turn on all three programs and give summary tables. BISPEC IAUTO ITURNO IMART NBD=1 V=.1$ Gives gaussianity, linearity and martingale tests and reduces output. BISPEC VHTEST$ Gives V and H bicovariance tests for complete sample. BISPEC VHTEST VHWINDOW$ Gives V and H bicovariance tests for complete sample and for windows. BISPEC DF ADF(1,2,3) ADFT(1,2,3)$ Gives various Dickey-Fuller tests for complete sample. BISPEC PP APP(1,2,3) APPT(1,2,3)$ Gives various Phillips- Perron tests for complete sample. BISPEC LM(1,2,3)$ Gives various Engle Lagrangian multipler tests for complete sample. Options for BISPEC sentence. IAUTO - Searches over values (ILOW - IUPP) of M and calculates all indicated tests using BISP program. This tests the sensitivity of the test to the value of M. ISMOO - Smooths the estimated spectrum (estimated with BISP) with a cosine bell in frequency domain. If ISMOO is not set each spectral estimate will be set = to variance of series. It is important to set ISMOO if the estimated series is not white because in this situation the spectrum is not flat. If ISMOO is set see also NWD value. FREQ - Gives frequency values in BISP program. This is the default. PERIOD - Gives period values in BISP program. IOLDSP - Turns on BISP program. INEWSP - Turns on NBISP program. IMART - Turns on new MARTIN program. IOMART - Turns on old MARTIN program. NYVAR - To normalize bispectrum in NBISP by spectrum. If this option is selected the NNW parameter sets the width of the cosine bell used to smooth the spectrum. If NYVAR is not present, the bispectrum is normalized by the sample variance. NISUM - Give summary output from NBISP in condensed form on unit 37. Note. This option is rarely needed. NIBIT - Give bispec estimates from NBISP program. NIPERD - Give output from NBISP program by period instead of frequency. INAUTO - Estimate NBISP for NLB going from ILNLB to IUNLB. If this option is used, the user may want to turn off output with the ITURNO option. ITURNO - Turns off all but summary tables if IAUTO, INAUTO or IMAUTO was specified. Output is "turned off" by diecting it to unit 7 which has been made a DUMMY file in B34S JCL. BDS - Turn on BDS test for default options of BDS which are: BDSEPS=.5, BDSORDER=5 TSAY - Turn on TSAY (1986) nonlinearity test for default order which is TSAPORDER=3. ------- Old Martin Program options ---------- MIBISW - Output the bispectrum from the old MARTIN program. IMAUTO - Estimate the MATRIN program for MLB going from ILMLB to IUMLB and MV going from ILMV to IUMV. If this option is used, the user may want to turn off output with the ITURNO option. Parameters for BISPEC sentence. CLIP=r1 Sets the data clip value that will transform all series prior to running tests to reduce kurtosis. This transformation reduces bias in the Hinich tests but reduces their power. Assume clip = 2.0. This means that (x(t)-mean(x)) + (2.0 * sd) and (x(t)-mean(x)) - (2.0 * sd) are upper and lower bounds on the data. If clip is set =2.0, then the 2% is clipped from the extreams of the data. ------- BISP parameters ------------ ILOW=n1 Sets lower value of M for BISP program. Default = SQRT(NOOB/3) where NOOB is the number of observations in the series. IUPP=n2 Sets upper value for M for BISP program. Default = SQRT(N). M=n3 In BISP program M**2 = the number of terms averaged to estimate the bispectrum at the center of the square. M large means that the bandwidth is large and the resolution is small. The variance is reduced by a large M, but there will be too few terms to sort for the linearity test. If M is small, there are a lot of terms to sort, but the variance may be too large and the chi square approximation will not be good since there are fat tails. Default = SQRT(N). NWD=n4 Sets width of smoothing cosin for BISP program. Default = 3*M. NWD must be in range 0 < NWD < (N/4) . For further see ISMOO option. ISAVE=n5 Sets unit to save M G and L if IAUTO is in effect. This command is designed to be use to determine SIZE of Hinich (1982) test. It is not a command intended for the general user. --------- NBISPEC parameters ---------------- NLB =n6 Sets the blocksize for NBISP program. Default=SQRT(N). NLB must be even. (M/N) = (1/NLB). Max = 256. The NBISP program reads NLB observations at a time. If NLB does not go into N evenly, not all observations are used. NNW =n7 Sets width of smoothing cosin for NBISP program. Must be odd. If not odd, resets to NNW-1. See also NYVAR option. ILNLB=n8 Lower bound for NLB search for NBISP program. Used if INAUTO has been set. Default = .9 * SQRT(N) -1 (must be even). IUNLB=n9 Upper bound for NLB search for NBISP program. Used if INAUTO has been set. Default = 1.3* sqrt(n) + 1 (must be even). PVAL=r2 Probability value for NBISP program. Default = .05. User must input a max of 5 digits in range 0 < PVAL < .9999. --------- New Martin parameters -------------- NBD =n10 Sets blocksize delta for the new martin program. Default is nob + 1 or one pass. V = r2 Sets V notch parameters for new martin program. --------- Old Martin paramaters -------------- MLB =n11 Sets blocksize for MARTIN program. Default = SQRT(N). MLB must be even. Max = 128. If MLB does not divide into N evenly, observations will be lost. MV = n12 V notch for the MARTIN program. 0 < MV < 32. The V notch is used to remove matringale terms in the second part of the MARTIN test. Default = .1 * MLB. Suggested range .1 - .2 of MLB ILMLB=n13 Lower bound of MLB for MARTIN program. Used if IMAUTO has been set. Default = .9 * SQRT(N) -1. (ILMLB must be even). IUMLB=n14 Upper bound for MLB for MATRIN program. Used if IMAUTO has been set. Default = 1.3 * SQRT(N) + 1. (IUMLB must be even). ILMV=n15 Sets lower bound for MV in MARTIN program. Default=1. Minimum value = 1. ILMV is only used if IMAUTO has been set. IUMV=n16 Sets upper bound for MV in MATRIN program. Default= MLB/2. Max value = 31. IUMV is only used if IMAUOT has been set. ---------- V, H, unit root and ARCH tests LM This is the same as LM(1). If LM is present, cannot use form LM( ). LM(n) Calculates Engle(1982) Lagrange multiplier test. Up to 10 lags can be set. Output includes lamda and the chi squared probability. Tests runs e(t)**2 = f(e(t-1)**2,...,e(t-n)**2) for up to 10 distinct lags. ACF(n) Calculates the autocorrelation function of the variable. Max n = 999 PACF(n) Calculates the partial autocorrelation function of the variable. Max of n is the n in the ACF. ACFVARSQ(n) Calculates the Autocorrelation function of the variable squared. This is used to test the residuals for ARCH effects. Max n = 999 PACFVARSQ(n) Number of terms for partial autocorrelation function of the variable squared. Max of n is the n in ACFVARSQ. TUNITROOT Uses t statistic form of Dickey-Fuller and Phillips Perron test. This is the default. ZUNITROOT Uses z statistic form of Dickey-Fuller and Phillips Perron test. DF Calculates Dickey-Fuller test of form y(t)=f(y(t-1)) Uses Case I of table B.6 or B.5 depending whether TUNITROOT or ZUNITROOT is in effect. ADF( ) Calculates augmented Dickey-Fuller test of form y(t)=f(a, y(t-1), (y(t-1)-y(t-2),,,) depending on lags set. A max of 10 distinct lags can be used. Lag orders are in range (1,...,(T-2)). If ADF( ) is supplied, in addition lag 0 is given. This corresponds to the RATS command @DFUNIT(TTEST,LAG=0) series. Uses Case II of table B.6 or B.5 depending whether TUNITROOT or ZUNITROOT is in effect. ADFT( ) Calculates augmented Dickey-Fuller with trend test of form y(t)=f(a, t, y(t-1), (y(t-1)-y(t-2),,,) depending on lags set. A max of 10 distinct lags can be used. Lag orders are in range (1,...,(T-2)). If ADFT( ) is supplied, in addition lag 0 is given. This corresponds to the RATS command @DFUNIT(TTEST,TREND,LAG=0) series. Uses Case IV of table B.6 or B.5 depending whether TUNITROOT or ZUNITROOT is in effect. PP Calculates Phillips-Perron test of form y(t)=f(y(t-1)) Uses Case I of table B.6 or B.5 depending whether TUNITROOT or ZUNITROOT is in effect. Zero lags are assumed for the calculation of lamda squared. APP( ) Calculates augmented Phillips-Perron test of form y(t)=f(a, y(t-1)) and uses alternate lags for obtaining lamda squared. A max of 10 distinct lags can be used. Lag orders are in range (1,...,(T-2)). If APP( ) is supplied, in addition lag 0 is given. This corresponds to the RATS command @PPUNIT(TTEST,LAGS=0) series. Uses Case II of table B.6 or B.5 depending whether TUNITROOT or ZUNITROOT is in effect. APPT( ) Calculates augmented Phillips-Perron with trend test of form y(t)=f(a, t, y(t-1)) and users alternative lags for obtaining lamda squared. A max of 10 distinct lags can be used. Lag orders are in range (1,...,(T-2)). If APPT( ) is supplied, in addition lag 0 is given. This corresponds to the RATS command @PPUNIT(TTEST,TREND,LAGS=0) series. Uses Case IV of table B.6 or B.5 depending whether TUNITROOT or ZUNITROOT is in effect. Notes on Phillips-Perron tests. The B34S uses the Hamilton (1994) formulas in calculating the Phillips-Perron test. If the command B34SEXEC OPTIONS DEBUGSUBS(RATSPP)$ B34SEEND$ is placed in the command stream prior to calling the Phillips-Perron test, the corrected RATS formulas will be used. For further detail see Stokes (1997 Chapter 12 footnote 14). VHTEST Calculates V and H test for complete sample. VHWINDOW Calculates V and H test for windows of data. Unless the parameter WINDOW is supplied, the default window will be MAX0(12,NOB/30). Unless set, NAC will default to (# V and H values)/4 and NPAC will default to 0. If LM, DF, PP etc are set, these will be calculated also. VHSAVE Saves V and H data in SCA FSAVE file on unit ISCAU having name SCADSN. Series saved are WINDOWNM, OBSSTART, OBSEND, V_STAT, H_STAT, CENTER. If LM( ), DF, ADF( ), ADFT( ), PP, APP( ), APPT( ) are set, these will be saved also with the names LM001 ... DF001... PP001 etc. PLOTACF Plots ACF and PACF LISTVH List V and H statistics. ICLIPP Uses individual clipping for each window. If this is not supplied, clipping is done for the complete sample and then broken up for each window. C=r1 Sets number of lags to use. Default = .4. The number of lags L = NOB**C. WINDOW=n1 Sets number of observations in the window. Default is MAX0(12,NOB/30). WINDOW can never be set < 12 or greater that NOB. POVERL=r2 Sets percent overlap for windows. Default = .5. ISCAU=n2 Sets SCA FSAVE unit for use with VHSAVE. Default = 44. SCADSN=k Sets SCA FSAVE DSN prefix. A Max of 5 characters is allowed. Default VHSAV1..VHSAVk. NAC=n3 Sets number of autocorrelations to calculate on windows. Default is MIN0(NWIN/2,150) where NWIN = the number of observations in the window. NPAC=n4 Sets number of partial autocorrelations to calculate. NAPL=n5 Sets number of acf's to print per line. Max = 12. Default = 12. CLIPP=r3 Sets clip percentage for V and H statistic. Default = 0.0. r3 must be LT 50.00. WINDOWU=n5 Sets upper limit for window. For further detail see WINDOW above. NWINDOW=n6 Sets number of sets of windows. If WINDOWU > WINDOW and NWINDOW = 0, then NWINDOW defaults to 3. TRISPEC sentence. The TRISPEC sentence provides tests of nonlinearity and Gaussianity using the trispectrum. In words, the linearity tests whether in fact E[x(t),x(t+k),x(t+j),x(t+l)] = 0 where k > 0, l > 0, j > 0 and j NE k NE l. The subroutines used in the TRISPEC sentence were developed by Melvin Hinich and J. W. Dalle Molle. TRISPEC sentence options. SPNORM - Normalize by spectrum. This option should be used if the series in not second order white. The default is to normalize by variance. If SPNORM is set and TWIND is not set, then no smoothing is done. SPECOUT - Output the spectrun on unit SPUNIT. SPECOUT2 - Output the spectrun & spectogram on unit SPUNIT. NOSIGTRI - Turn off the default option of output showing trispectrum values that are significant at the TPV level. If this option is not used, the user can see at what periods or frequencies the 4th order linearity assumption is rejected. FREQOUT - The default is to output in periods. FREQOUT will output in frequency units. TRIOUT - Output all trispectrum values on unit TRUNIT. SUMOUT - Output summary statistics on unit SUMUNIT. TRISPEC sentence parameters. SPUNIT=n1 - Sets unit for spectrum values. Default = 51. This option is needed if SPECOUT or SPECOUT2 are supplied. TRUNIT=n2 - Sets unit for trispectrum values. Default = 52. This options is needed if TRIOUT option is used. SUMUNIT=n3 - Sets unit for summary output. Default = 6. This option is needed if SUMOUT is supplied. TLB=n4 - Sets block length for trispectrum calculation. The default is to set n4 = NOOB**(1/3). n4 should be GE 6. This implies that meaningful analysis requires the sample size be GE 216. TPV=r1 - Sets probability value to use for significant trispectrum values. Default = .005. PTAP=r2 - Sets percent taper. Default = 0.0. r2 must be set in range 0.0 LE PTAL LE 25. TWIND=n5 - Sets smoothing window width. Needed if SPNORM is set. If SPNORM is set and TWIND is not set, then no smoothing is done. TUNITS=n6 - Sets units. This is needed to meaningful period numbers. If FREQOUT option is used, TUNITS is not needed. Default = 1. The usual setting is TRISPEC $ If clipping is desired, but the bispectrum linearity tests are not desired, the commands should be BISPEC IOLDSP CLIP=5.0 $ TRISPEC $ If both bispectrum and trispectrum Gaussianity and Linearity tests are desired, then use the commands BISPEC ITURNO IAUTO$ TRISPEC$ POLYSPEC sentence options. LISTSPEC - Lists log spectrum by window LISTBISP - Lists Seven Fractiles (10%, 20%, 40%, 60%, 80%, 90%, 99%) of Normalized Bispectrun by window. Z Values for each fractile are also supplied. The top 2% Normalized Bispectral Values and Phases are also supplied. If the process is Gaussian the Bispectrum should vanish. LISTCUM2 - Lists Seven Fractiles (10%, 20%, 40%, 60%, 80%, 90%, 99%) of Normalized Cum2 values by window. Z Values for each fractile are also supplied. The top 2% Normalized Cum2 Values and Phases are also supplied. These measure autocorrelation in that window of the series. SAVESPEC - Will save estimates of the log spectrum for up to 98 windows in an SCA FSAVE file having SCA data set name POLYSCADSN on unit POLYSCAU. A second file having the primary suffex MSD is also created containing OBS, NBEGIN, NEND, MEAN, STANDEV, SKEWNESS KERTOSIS, C6, SAMPLMAX, DSAMPLMIN for each window. TSAMPLEU - Sets the sample as a time series. This is the default. The parameter SAMPLEU sets the sampling interval. FSAMPLEU - Sets the sample as a frequency. If this option is set, then the parameter SAMPLEU sets the sampling rate as a multiple of KHz. NNBISPCUM - If specified, the bispectrum and the cum2 are not normalized by products of the spectral estimates but by the variance. This is used if the data is known to be white (flat spectrum). POLYSPEC sentence parameters. POLYLW=n1 Sets window. The block length LB = POLYLW**POLYC. Default = 0. If POLYLW = 0, the complete sample is used, unless N < 250. If POLYLW > 0, then POLYLW must be set GE 250. Given POLYC = .4 (the default) this would imply a block length of 9. If the user selects POLYLW such that given the number of observations in the sample, there would be more than 99 windows, POLYLW will be adjusted. If POLYLW is set such that it does not go into the number of observations evenly, then data at the end of the series will not be used. POLYC=r1 Sets window / block conversion. 0 LE POLYC LE .5. Default = .40. POLYSRATE=r2 If TSAMPLE is set above, r2 is the sampling rate. If FSAMPLE is set above, r2 is the sampling rate as a multiple of KHz. Default = 1.0 . POLYSRATEU=k1 Sets Data unit. A max of 5 characters can be supplied. Default = obs. POLYFL=r3 Sets lower frequency for analysis. Default = 0.0. POLYFU=r4 Sets upper frequency for analysis. Default = .5 POLYFL and POLYFU, if set inside interval 0.0 - .5, allow the analysis to be restricted to a subset of the frequencies. POLYTAP=r5 Sets taper block for side lobe reduction. Default = 0.0 POLYTH=r6 Sets threshold for test statistic. Default = .9 POLYTRIM=r7 Sets % of the data to be trimmed. Default = 0.0. POLYTRIM must be in the range 0.0 - 25.0. POLYSCADSN=k2 Sets SCA DSN name. A max of 5 characters can be set. Default = POLYS. If the SAVESPEC option is set, the spectrums for each of the POLYLW windows are saved with names SPEC_01 ... SPEC_... POLYSCAU=n2 Sets SCA FSAVE file unit number. Default = 44. POLYSRATE=r1 Sets sampling rate. Default = 1.0 POLYSRATEU=k1 Sets sampling rate unit. Default = obs. NWD=n3 Sets smoothing window. Smoothing will be performed if NWD > 2. If NWD is even, it will be set to the next highest odd number. SAMPLEU=r2 If TSAMPLE is in effect, sets the # of samples per unit. If FSAMPLE is in effect, sets sampling rate as a multiple of KHz. Examples of POLYSPEC sentence usage. Example 1. Assume 5000 observations. The command polyspec polylw=1000 listspec listbisp listcum2 savespec$ will analyse 5 windows of 1000 each. The spectrun, bispectrum and CUM2 will be listed. In addition The spectrums will be saved on unit 44 in SCA dataset POLY with names SPEC_01, SPEC_02, SPEC_03, SPEC_04, SPEC_05. REVERSE sentence The REVERSE sentence performs various time reversibility tests suggested by Hinich and Rothman, using the TR1 and TR2 programs, and Hinich using the CUMSPEC program. Rothman related commands. The TR1 program is designed to calculate Ramsey and Rothman (1996) standardized TR test statistics for a raw series. An ARMA model is fitted to the series to estimate the standard deviation of the statistics. The Rothman(1994) portmanteau test is also calculated. The TR2 program is designed to calculate the TR test for residuals using equation (10) of Ramsey and Rothman (1996). If the series is not white noise, it can be filtered. The Rothman (1994) portmanteau test is also calculated. A Monti Carlo simulation is run to estimate the p-values of the maximum (in absolute value) of the standardized TR test statistics and of the portmanteau statistic. TR1(k) - Gets the order of the TR1 Test. TR2(k) - Gets the order of the TR2 Test. TR1 or TR2 is required iprintarma - Prints the ARMA estimation results. This is rarely needed. ar(i1) - Sets the orders of the ar filter. ma(j1) - Sets the orders of the ma filter. If TR1 ARMA model used to get sd. If TR2 ARMA model used to filter data. tran(key) - Provides optional transformations of the data. Key can be set as: raw - Use raw data. This is the default. log - Use log of data. diflog - First difference of log of data dif - First difference of data logdt - Log detrended data rawdt - Raw detrended data iseed(ii) - Sets the seed. This option is not usually set. It is useful only in replication testing. maxbc(i) - Maximum number of backforecasts. tolbc(r) - Convergence of backforecasting algorithm. tolss(r) - Convergence of nonlinear least squares. May have to be set > 0.0. Must be in range 0 -.9999 maxit(i) - Sets maximum iterations for simulations. Default = 100. maxit2(j) - Sets maximum iterations for arma modeling. Default = 200. rerror(d) - Sets the relative error for arma termination. Default = 0.0 Examples of Reverse Test using Rothman b34sexec options ginclude('b34sdata.mac') member(rothtr1); b34srun; b34sexec btiden; title('Rothman TR1 Test Data'); seriesn var=nomgnp; iden; reverse TR1(5) ar(1) tran(logdif) iseed(25443332) maxit(100); b34srun; b34sexec options ginclude('b34sdata.mac') member(rothtr2); b34srun; b34sexec btiden; title('Rothman TR2 Test Data'); seriesn var=gnpdefl; iden; reverse TR2(5) ar(1) tran(logdif) iseed(25443332) maxit(100) ; b34srun; Commands Related to Hinich-Rothman(1998) Frequency Domain Test hr1998 - This is required to perform test. period - Sampling rate in periods. This is the default. freq - Sampling rate in kHz. bandpass - Remove 0 fl and fu to .5 frequencies sr=r1 - Sampling rate. Default = 1. If Freq in effect sampling rate in multiple of milsec (1/khz) rb=r2 - Sets resolution bandwidth in hz. Default = 5. sb=r3 - Sets spectral smoothing bandwidth in hz. SB > RB. If SB not set => spectrun not smoothed. norm(key) - key = divide => divide bispectrun at (f1,f2)by sqrt[S(f1)S(f2)S(f1+f2)] no => do not normalize bispectrum. Here bispectrum divided by cube of sample SD. This option is used if series is white noise. filter => Filter out frequency components in range (0,fl) and above fu. fl=r4 - Lower frequency for analysis. Default = 0. Note: fl must never be set lt 0.0. fu=r5 - Upper frequency for analysis. Default = .475, the upper limit. pt=r6 - % taper of frames for sidelong reduction. Range 0.0 LE pt LT 25. Default = 0.0. Examples of Reverse Test using Hinich-Rothman 1998 b34sexec options ginclude('b34sdata.mac') member(rothtr1); b34srun; b34sexec btiden; title('Hinich-Rothman (1998) Test on TR1 Data'); seriesn var=nomgnp; iden; reverse hr1998 rb(9.5); b34srun; b34sexec options ginclude('b34sdata.mac') member(rothtr2); b34srun; b34sexec btiden; title('Hinich-Rothman (1998) Terst on TR2 Data'); seriesn var=gnpdefl; iden; reverse hr1998 rb(9.5); b34srun; IDEN sentence. The IDEN sentence is used to specify control values for VAR, VARMA and VMA cross correlation identification. IDEN sentence options. ISOP - Plot original data. ITSP - Plot transformed data. IDSP - Plot differenced data. ISACF - Plot series ACF. Note that LAGRHO must be set > 0. ISCCF - Plot series cross correlations. LAGRHO must be set > 0. IVALUE - Give both numerical and significant indicators for cross correlations. The default is only significant indicators. MQSTAT - Gives Multivariate Q Statistic. IDEN sentence parameters. LAGRHO=n1 Sets number of cross correlation matrices. Max = 120. IPER=n2 Sets markings on x axis for plots. Default is markings every 10 periods. If n2=12, markings will be 1,2,...,9,0,A,B. The range for n2 is 0 - 36 where 0 means markings every 10 periods. ESTVAR sentence. The ESTVAR sentence controls estimation of VAR models. ESTVAR sentence options. IPRINT - Print CCF matrix. Note IVALUE must be set. ICANON - Gives output associated with canonical analysis. PHICOR - Gives correlation form of (X'X)**-1 with each AR fit. This information can be used to construct the correlation matrix of the Phi estimates. ILARF - Reduces output by printing the last AR fit only. The default option will print AR(1) .... AR(MAX) in turn. RESIDUALS - Will list or optionally punch residuals. (See IRES parameter below.) If the ILARF option is in effect, only the last set of residuals is listed and/or punched. GRANGER - Will print matrix of F tests and a matrix of the sign- ificance of these F statistics to test Granger causality. If F(i,j) is significant, it implies that lags of the jth variable Granger causes the ith variable. GRANGER options not allows if LAGS( ) used. ISACF - Plot residual ACF. Note that IVALUE must be set. ISCCF - Plot residual CCF. Note that IVALUE must be set. Note: ISACF and ISCCF make a great deal of output. MQSTAT - Gives Multivariate Q Statistic. ESTVAR sentence parameters. P=n1 Maximum lag on non seasonal operator. PS=n2 Maximum lag on seasonal operator. S= n3 Seasonal factor. LAGS=(n4,n5, ) Up to 99 can be specified. NUMIRF=n4 Sets number of impulse response function terms to calculate after last VAR step. Note: For further detail see IRF under Matrix Command This option calculates the Transfer Function Impulse Response Function (TFIRF) of a VAR Model. This is not the VMA from. Assume A(L)X=e Transformed model is: X = PSI(L)e where PSI(L) = INV(A(L)) ------------------------------------------------------- This is in contrast to the Transfer function form of the model tirf that is calculated by normalizing by diagonal polynomial. Assume VAR Model for 2 Series X1 & X2: Orig. eq: 1 b11(L)X1 + b12(L)X2 = e1 Orig. eq: 2 b21(L)X1 + b22(L)X2 = e2 Trans. eq: 1 X1 + [b12(L)/b11(L)]X2 = [1/b11(L)]e1 Trans. eq: 2 X2 + [b21(L)/b22(L)]X1 = [1/b22(L)]e2 If 1 to k-1 cols are multiplied by -1 we get the alternative tirf form Alt. eq: 1 X1 = -[b12(L)/b11(L)]X2 + [1/b11(L)]e1 Alt. eq: 2 X2 = -[b21(L)/b22(L)]X1 + [1/b22(L)]e2 For one variable case [1/b11(L)] is psi(L) --------------------------------------------------------------- Note: If P=PS=0, the LAGS parameter must be given. It allows user to specify specific lags. If P NE 0 and PS NE 0, then ((P+1)*(PS+1)-1) must be LE 99. OUTPUT=key If Key = BRIEF only preliminary output, stepwise AR summary and a table summarizing the significant partial AR coefficients by lag is given. If key=NORMAL full output is given. If key=EXPANDED full output in expanded form is given. This is will occur automatically if there is more than 5 series and key = NORMAL. LAGRHO=n7 Sets number of residual cross correlation matrices. LAGRHO defaults to 12. LAGRHO must be in range 12 - 120. IVALUE=(n1,n2) Sets number of AR fits after which values in the residual correlation matrix are given. The default gives none. For example IVALUE=(1,3,5) gives residual CCF after AR(1), AR(3) and AR(5). ISCAU=n8 Saves estimated coefficients in SCA SAVEFILE in unit n8 which must be LRECL=80,RECFM=FB. The SCA SAVEFILE can be read into SAS using the PROC LINKSCA. For more information about PROC LINKSCA, get into SAS and give SAS command HELP LINKSCA; . If n8 is LT 0, file will be rewound. Otherwise dataset is added to file. SCAP=key Sets SCA SAVEFILE data set prefix. The default = MOD. Successive AR matrices are saved with DSN name MOD1 ... MODK where K is the maximum lag. In each dataset, the AR matrices are stored with AR_ where _ gives the order. The maximum number of characters in key is 6. IRES=n9 Controls residual output on unit 44 in SCA FSAVE format. If RESIDUALS option is set and n9 > 0, residuals are only outputed to a file with name RESIDUAL. If RESIDUALS is set and n9 < 0, then residuals are listed and punched. Series listed are OBSNUM, RESID1, RESID2,.. SERIES1, SERIES2,.. YHAT1, YHAT2 .... If ILARF is not in effect, the residuals and data for each AR fit will be added to unit 44. Note: Residual = actual - forecast. ************************ Sample jobs. Identify cross correlations for B-J Gas data and optionally do BISPEC tests. For + , - . plots, 2.5 standard errors are used. B34SEXEC BTIDEN NSTDER=2.5 $ TITLE=('Idenfication run with Gas Data') $ SERIESN VAR=GASIN NAME=('B-J GAS INPUT DATA') $ SERIESN VAR=GASOUT NAME=('B-J GAS OUTPUT DATA')$ IDEN LAGRHO=36 ISACF ISCCF $ BISPEC $ B34SEEND$ Estimate a VAR model with gas data for up to 6 lags. B34SEXEC BTIDEN$ TITLE=('Identification run with Gas Data') $ SERIESN VAR=GASIN NAME=('B-J GAS INPUT DATA') $ SERIESN VAR=GASOUT NAME=('B-J GAS OUTPUT DATA')$ ESTVAR P=6 OUTPUT=NORMAL$ BISPEC $ B34SEEND$