B34SI 8.11F (D:M:Y) 14/10/11 (H:M:S) 9:30:15 DATA STEP PAGE 1 Variable Label # Cases Mean Std. Dev. Variance Maximum Minimum TIME 1 296 148.500 85.5921 7326.00 296.000 1.00000 GASIN 2 Input gas rate in cu. ft / min 296 -0.568345E-01 1.07277 1.15083 2.83400 -2.71600 GASOUT 3 Percent CO2 in outlet gas 296 53.5091 3.20212 10.2536 60.5000 45.6000 CONSTANT 4 296 1.00000 0.00000 0.00000 1.00000 1.00000 Number of observations in data file 296 Current missing variable code 1.000000000000000E+031 B34SI 8.11F (D:M:Y) 14/10/11 (H:M:S) 9:30:15 DATA STEP Data from prior step PAGE 2 Variable Label # Cases Mean Std. Dev. Variance Maximum Minimum TIME 1 296 148.500 85.5921 7326.00 296.000 1.00000 GASIN 2 Input gas rate in cu. ft / min 296 -0.568345E-01 1.07277 1.15083 2.83400 -2.71600 GASOUT 3 Percent CO2 in outlet gas 296 53.5091 3.20212 10.2536 60.5000 45.6000 COUNT 4 296 148.500 85.5921 7326.00 296.000 1.00000 CONSTANT 5 296 1.00000 0.00000 0.00000 1.00000 1.00000 Number of observations in data file 296 Current missing variable code 1.000000000000000E+031 B34SI 8.11F (D:M:Y) 14/10/11 (H:M:S) 9:30:25 PGMCALL STEP Data from prior step PAGE 3 output from stata ___ ____ ____ ____ ____ (R) /__ / ____/ / ____/ ___/ / /___/ / /___/ 12.0 Copyright 1985-2011 StataCorp LP Statistics/Data Analysis StataCorp 4905 Lakeway Drive College Station, Texas 77845 USA 800-STATA-PC http://www.stata.com 979-696-4600 stata@stata.com 979-696-4601 (fax) Single-user Stata perpetual license: Serial number: 3012042652 Licensed to: Houston H. Stokes U of Illinois Notes: 1. Stata running in batch mode . do stata.do . * File built by B34S on 14/10/11 at 9:30:15 . run statdata.do . describe Contains data obs: 296 vars: 5 size: 11,840 --------------------------------------------------------------------------------------- storage display value variable name type format label variable label --------------------------------------------------------------------------------------- time double %10.0g gasin double %10.0g Input gas rate in cu. ft / min gasout double %10.0g Percent CO2 in outlet gas count double %10.0g constant double %10.0g --------------------------------------------------------------------------------------- Sorted by: Note: dataset has changed since last saved . *clear . *set more off, perm . *insheet using "M:\ECON 537\Box Jenkins Series J (Gas Data) with Obs.txt" . rename time obs . tsset obs time variable: obs, 1 to 296 delta: 1 unit B34SI 8.11F (D:M:Y) 14/10/11 (H:M:S) 9:30:25 PGMCALL STEP Data from prior step PAGE 4 . *inspect . *describe . *summarize . *tab gasin . *tab gasout . plot gasin gasout obs 60.5 + | B | BBBB BB BBB B BBBB BB | BBB BBBBB B BB BB BBBB B BBBBBBB BBB B BB B B | BBB BB BB BB BB BBBBB B BBBBBBBBBB BBB BBBBBBB | BBBBB BBBBB B BBB BB BB | BB | | | | | | | | | | | | | AAAAAAAAAAA AA AAAAA AA A A AAAA -2.716 + AAAAA AA AA AAAAAA AAAAAAA A AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA +----------------------------------------------------------------+ 1 obs 296 . *tsline gasin gasout . *line gasin obs . *line gasout obs . corrgram gasin, lags(24) -1 0 1 -1 0 1 LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor] ------------------------------------------------------------------------------- 1 0.9525 0.9526 271.26 0.0000 |------- |------- 2 0.8341 -0.7898 480 0.0000 |------ ------| 3 0.6819 0.3424 619.96 0.0000 |----- |-- 4 0.5312 0.1230 705.21 0.0000 |---- | 5 0.4075 0.0571 755.55 0.0000 |--- | 6 0.3182 -0.1159 786.35 0.0000 |-- | 7 0.2602 0.0539 807.01 0.0000 |-- | 8 0.2275 0.1030 822.86 0.0000 |- | 9 0.2131 0.0145 836.82 0.0000 |- | 10 0.2083 -0.0712 850.2 0.0000 |- | 11 0.2028 -0.0971 862.94 0.0000 |- | 12 0.1893 0.0455 874.07 0.0000 |- | 13 0.1673 0.0877 882.79 0.0000 |- | 14 0.1375 -0.1436 888.71 0.0000 |- -| 15 0.1048 0.0475 892.16 0.0000 | | 16 0.0754 0.0463 893.95 0.0000 | | B34SI 8.11F (D:M:Y) 14/10/11 (H:M:S) 9:30:25 PGMCALL STEP Data from prior step PAGE 5 17 0.0520 -0.0184 894.8 0.0000 | | 18 0.0371 0.0228 895.24 0.0000 | | 19 0.0340 0.0944 895.61 0.0000 | | 20 0.0424 -0.0351 896.18 0.0000 | | 21 0.0564 -0.0915 897.2 0.0000 | | 22 0.0694 0.0388 898.75 0.0000 | | 23 0.0765 0.0340 900.64 0.0000 | | 24 0.0761 0.0073 902.52 0.0000 | | . *corrgram gasin, lags(24) yw . *ac gasin, lags(24) . *pac gasin, lags(24) . *pac gasin, lags(24) yw . dfuller gasin Dickey-Fuller test for unit root Number of obs = 295 ---------- Interpolated Dickey-Fuller --------- Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value ------------------------------------------------------------------------------ Z(t) -2.665 -3.456 -2.878 -2.570 ------------------------------------------------------------------------------ MacKinnon approximate p-value for Z(t) = 0.0802 . pperron gasin Phillips-Perron test for unit root Number of obs = 295 Newey-West lags = 5 ---------- Interpolated Dickey-Fuller --------- Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value ------------------------------------------------------------------------------ Z(rho) -33.910 -20.336 -14.000 -11.200 Z(t) -4.131 -3.456 -2.878 -2.570 ------------------------------------------------------------------------------ MacKinnon approximate p-value for Z(t) = 0.0009 . *kpss gasin . *dfgls gasin . *dfuller gasin, lags(2) . *dfuller gasin, lags(15) . *dfuller gasin, lags(16) . corrgram gasout, lags(24) -1 0 1 -1 0 1 LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor] ------------------------------------------------------------------------------- 1 0.9708 0.9747 281.78 0.0000 |------- |------- 2 0.8960 -0.8575 522.67 0.0000 |------- ------| 3 0.7925 0.4651 711.77 0.0000 |------ |--- 4 0.6800 0.2152 851.43 0.0000 |----- |- 5 0.5745 -0.0903 951.47 0.0000 |---- | 6 0.4854 -0.0580 1023.2 0.0000 |--- | 7 0.4161 -0.0080 1076 0.0000 |--- | B34SI 8.11F (D:M:Y) 14/10/11 (H:M:S) 9:30:25 PGMCALL STEP Data from prior step PAGE 6 8 0.3656 0.1319 1116.9 0.0000 |-- |- 9 0.3304 -0.0332 1150.5 0.0000 |-- | 10 0.3065 -0.0666 1179.5 0.0000 |-- | 11 0.2880 -0.0937 1205.1 0.0000 |-- | 12 0.2693 0.0666 1227.7 0.0000 |-- | 13 0.2473 0.0236 1246.7 0.0000 |- | 14 0.2215 0.0200 1262.1 0.0000 |- | 15 0.1930 -0.0661 1273.7 0.0000 |- | 16 0.1649 0.0958 1282.3 0.0000 |- | 17 0.1398 0.0141 1288.5 0.0000 |- | 18 0.1210 0.0696 1293.1 0.0000 | | 19 0.1103 -0.0354 1297 0.0000 | | 20 0.1078 -0.0092 1300.7 0.0000 | | 21 0.1112 -0.0623 1304.7 0.0000 | | 22 0.1171 0.0314 1309.1 0.0000 | | 23 0.1228 0.0367 1314 0.0000 | | 24 0.1259 0.0008 1319.1 0.0000 |- | . *corrgram gasout, lags(24) yw . *ac gasout, lags(24) . *pac gasout, lags(24) . *pac gasout, lags(24) yw . dfuller gasout Dickey-Fuller test for unit root Number of obs = 295 ---------- Interpolated Dickey-Fuller --------- Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value ------------------------------------------------------------------------------ Z(t) -1.864 -3.456 -2.878 -2.570 ------------------------------------------------------------------------------ MacKinnon approximate p-value for Z(t) = 0.3492 . pperron gasout Phillips-Perron test for unit root Number of obs = 295 Newey-West lags = 5 ---------- Interpolated Dickey-Fuller --------- Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value ------------------------------------------------------------------------------ Z(rho) -23.969 -20.336 -14.000 -11.200 Z(t) -3.423 -3.456 -2.878 -2.570 ------------------------------------------------------------------------------ MacKinnon approximate p-value for Z(t) = 0.0102 . *kpss gasout . *dfgls gasout . *dfuller gasout, lags(2) . *dfuller gasout, lags(15) . *dfuller gasout, lags(16) . arima gasin, ar(1/3) (setting optimization to BHHH) B34SI 8.11F (D:M:Y) 14/10/11 (H:M:S) 9:30:25 PGMCALL STEP Data from prior step PAGE 7 Iteration 0: log likelihood = 72.55475 Iteration 1: log likelihood = 72.567127 Iteration 2: log likelihood = 72.568412 Iteration 3: log likelihood = 72.568683 Iteration 4: log likelihood = 72.568793 (switching optimization to BFGS) Iteration 5: log likelihood = 72.568843 Iteration 6: log likelihood = 72.568884 Iteration 7: log likelihood = 72.568899 Iteration 8: log likelihood = 72.568902 Iteration 9: log likelihood = 72.568903 Iteration 10: log likelihood = 72.568903 ARIMA regression Sample: 1 - 296 Number of obs = 296 Wald chi2(3) = 18662.04 Log likelihood = 72.5689 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ | OPG gasin | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- gasin | _cons | -.0607873 .2112943 -0.29 0.774 -.4749165 .353342 -------------+---------------------------------------------------------------- ARMA | ar | L1. | 1.969063 .0297688 66.15 0.000 1.910718 2.027409 L2. | -1.365142 .0690584 -19.77 0.000 -1.500494 -1.22979 L3. | .3394078 .0488192 6.95 0.000 .243724 .4350916 -------------+---------------------------------------------------------------- /sigma | .1878718 .0040316 46.60 0.000 .17997 .1957736 ------------------------------------------------------------------------------ Note: The test of the variance against zero is one sided, and the two-sided confidence interval is truncated at zero. . predict alpha, residuals . corrgram alpha, lags(24) -1 0 1 -1 0 1 LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor] ------------------------------------------------------------------------------- 1 -0.0352 -0.0352 .36967 0.5432 | | 2 0.0709 0.0699 1.8759 0.3914 | | 3 0.0578 0.0632 2.8834 0.4100 | | 4 -0.1426 -0.1451 9.0243 0.0605 -| -| 5 -0.0094 -0.0284 9.051 0.1070 | | 6 0.0585 0.0792 10.094 0.1208 | | 7 0.0145 0.0400 10.158 0.1798 | | 8 0.0024 -0.0286 10.16 0.2540 | | 9 -0.0542 -0.0766 11.062 0.2715 | | 10 0.0365 0.0545 11.473 0.3219 | | 11 0.1434 0.1807 17.841 0.0854 |- |- 12 -0.0761 -0.0804 19.64 0.0742 | | B34SI 8.11F (D:M:Y) 14/10/11 (H:M:S) 9:30:25 PGMCALL STEP Data from prior step PAGE 8 13 0.0988 0.0320 22.681 0.0457 | | 14 0.0423 0.0645 23.24 0.0565 | | 15 -0.0819 -0.0212 25.344 0.0455 | | 16 0.0172 -0.0304 25.437 0.0625 | | 17 0.0653 0.0613 26.784 0.0613 | | 18 -0.0523 -0.0234 27.651 0.0676 | | 19 -0.0787 -0.1140 29.625 0.0568 | | 20 0.0229 0.0149 29.792 0.0733 | | 21 0.0153 0.0549 29.868 0.0947 | | 22 0.0305 0.0306 30.167 0.1145 | | 23 0.0449 0.0111 30.82 0.1273 | | 24 0.0042 -0.0454 30.826 0.1589 | | . *corrgram alpha, lags(24) yw . *ac alpha, lags(24) . *pac alpha, lags(24) . *pac alpha, lags(24) yw . rename gasin gasin1 . rename gasout gasin . predict beta, resid . rename gasin gasout . rename gasin1 gasin . summarize alpha Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- alpha | 296 .0000753 .1882882 -.9202943 .9906531 . scalar s_alpha = r(sd) . *summarize beta . summarize beta in 2/l Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- beta | 295 3.042023 .377452 2.075001 4.701234 . scalar s_beta = r(sd) . *xcorr alpha beta in 2/l . xcorr alpha beta in 2/l , generate(cross) table -1 0 1 LAG CORR [Cross-correlation] ------------------------------------ -20 -0.0519 | -19 0.0269 | -18 -0.0434 | -17 -0.0462 | -16 -0.0272 | -15 0.0358 | B34SI 8.11F (D:M:Y) 14/10/11 (H:M:S) 9:30:25 PGMCALL STEP Data from prior step PAGE 9 -14 -0.0023 | -13 0.0210 | -12 0.0029 | -11 0.0119 | -10 0.0197 | -9 -0.0087 | -8 -0.0965 | -7 -0.0325 | -6 -0.1195 | -5 -0.0103 | -4 -0.0208 | -3 -0.0378 | -2 0.0033 | -1 -0.0307 | 0 0.0010 | 1 0.0573 | 2 -0.0285 | 3 -0.2771 --| 4 -0.3248 --| 5 -0.4435 ---| 6 -0.2633 --| 7 -0.1669 -| 8 -0.0283 | 9 0.0287 | 10 -0.0519 | 11 -0.0305 | 12 -0.0156 | 13 -0.0642 | 14 0.0026 | 15 -0.0150 | 16 -0.0583 | 17 -0.0472 | 18 -0.0299 | 19 -0.1122 | 20 0.0090 | . generate lag =_n-21 . generate std = -2/sqrt(296) . generate zero = 0 . generate ir = (s_beta/s_alpha)*cross (255 missing values generated) . list lag cross ir std if ir != . & lag >=0 & cross < std +-----------------------------------------+ | lag cross ir std | |-----------------------------------------| 24. | 3 -.277086 -.5554605 -.1162476 | 25. | 4 -.3247883 -.651087 -.1162476 | 26. | 5 -.44353 -.8891224 -.1162476 | 27. | 6 -.263278 -.5277803 -.1162476 | 28. | 7 -.1669317 -.3346396 -.1162476 | +-----------------------------------------+ B34SI 8.11F (D:M:Y) 14/10/11 (H:M:S) 9:30:25 PGMCALL STEP Data from prior step PAGE 10 . arima gasout l(3/7).gasin (setting optimization to BHHH) Iteration 0: log likelihood = -363.30666 Iteration 1: log likelihood = -363.30666 ARIMA regression Sample: 8 - 296 Number of obs = 289 Wald chi2(5) = 1725.43 Log likelihood = -363.3067 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ | OPG gasout | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- gasout | gasin | L3. | -.69922 .3150716 -2.22 0.026 -1.316749 -.0816911 L4. | -.549606 .7044174 -0.78 0.435 -1.930239 .8310268 L5. | -1.016879 .8318417 -1.22 0.222 -2.647259 .6135005 L6. | .1387499 .6717633 0.21 0.836 -1.177882 1.455382 L7. | -1.014285 .2799282 -3.62 0.000 -1.562934 -.4656354 | _cons | 53.32959 .0837679 636.64 0.000 53.16541 53.49377 -------------+---------------------------------------------------------------- /sigma | .8505925 .0248751 34.19 0.000 .8018383 .8993468 ------------------------------------------------------------------------------ Note: The test of the variance against zero is one sided, and the two-sided confidence interval is truncated at zero. . predict n, resid (7 missing values generated) . corrgram n, lags(24) -1 0 1 -1 0 1 LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor] ------------------------------------------------------------------------------- 1 0.8850 0.9640 228.7 0.0000 |------- |------- 2 0.6999 -0.5440 372.23 0.0000 |----- ----| 3 0.4924 -0.0406 443.53 0.0000 |--- | 4 0.3124 0.1915 472.32 0.0000 |-- |- 5 0.1818 0.0376 482.11 0.0000 |- | 6 0.0951 -0.0130 484.8 0.0000 | | 7 0.0385 -0.0852 485.24 0.0000 | | 8 0.0016 0.0437 485.25 0.0000 | | 9 -0.0164 0.1025 485.33 0.0000 | | 10 -0.0085 -0.0079 485.35 0.0000 | | 11 0.0021 -0.1440 485.35 0.0000 | -| 12 -0.0072 -0.1036 485.37 0.0000 | | 13 -0.0358 -0.0296 485.76 0.0000 | | 14 -0.0754 -0.0640 487.49 0.0000 | | 15 -0.1198 -0.1037 491.9 0.0000 | | 16 -0.1509 -0.0108 498.91 0.0000 -| | B34SI 8.11F (D:M:Y) 14/10/11 (H:M:S) 9:30:25 PGMCALL STEP Data from prior step PAGE 11 17 -0.1721 -0.0683 508.07 0.0000 -| | 18 -0.1748 0.0324 517.54 0.0000 -| | 19 -0.1526 0.0541 524.8 0.0000 -| | 20 -0.1021 0.1211 528.06 0.0000 | | 21 -0.0352 -0.0152 528.45 0.0000 | | 22 0.0264 -0.0402 528.67 0.0000 | | 23 0.0761 0.0485 530.5 0.0000 | | 24 0.1092 0.1523 534.28 0.0000 | |- . *corrgram n, lags(24) yw . arima gasout l(3/7).gasin, ar(1/2) (setting optimization to BHHH) Iteration 0: log likelihood = -41.695688 Iteration 1: log likelihood = -23.171676 Iteration 2: log likelihood = -5.7969037 Iteration 3: log likelihood = -2.1599846 Iteration 4: log likelihood = -1.46693 (switching optimization to BFGS) Iteration 5: log likelihood = -1.2422095 Iteration 6: log likelihood = -.85329125 Iteration 7: log likelihood = -.83458599 Iteration 8: log likelihood = -.8235703 Iteration 9: log likelihood = -.82149641 Iteration 10: log likelihood = -.82088421 Iteration 11: log likelihood = -.82068942 Iteration 12: log likelihood = -.82067534 Iteration 13: log likelihood = -.8206748 Iteration 14: log likelihood = -.82067474 ARIMA regression Sample: 8 - 296 Number of obs = 289 Wald chi2(7) = 6547.92 Log likelihood = -.8206747 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ | OPG gasout | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- gasout | gasin | L3. | -.555776 .0653626 -8.50 0.000 -.6838843 -.4276677 L4. | -.6444716 .0744986 -8.65 0.000 -.7904862 -.4984571 L5. | -.859805 .0784266 -10.96 0.000 -1.013518 -.7060916 L6. | -.4835749 .0862468 -5.61 0.000 -.6526155 -.3145344 L7. | -.3633093 .0776425 -4.68 0.000 -.5154859 -.2111327 | _cons | 53.37647 .1876201 284.49 0.000 53.00874 53.7442 -------------+---------------------------------------------------------------- ARMA | ar | L1. | 1.537904 .0386701 39.77 0.000 1.462112 1.613696 L2. | -.6291055 .0426486 -14.75 0.000 -.7126952 -.5455158 -------------+---------------------------------------------------------------- /sigma | .2413085 .007408 32.57 0.000 .226789 .2558279 B34SI 8.11F (D:M:Y) 14/10/11 (H:M:S) 9:30:25 PGMCALL STEP Data from prior step PAGE 12 ------------------------------------------------------------------------------ Note: The test of the variance against zero is one sided, and the two-sided confidence interval is truncated at zero. . predict residual, residuals (7 missing values generated) . corrgram residual, lags(24) -1 0 1 -1 0 1 LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor] ------------------------------------------------------------------------------- 1 0.0323 0.0325 .30472 0.5809 | | 2 0.0710 0.0707 1.7816 0.4103 | | 3 -0.0749 -0.0801 3.4294 0.3300 | | 4 -0.0673 -0.0694 4.7668 0.3121 | | 5 -0.0639 -0.0519 5.9774 0.3084 | | 6 0.0978 0.1093 8.819 0.1840 | | 7 0.0272 0.0237 9.04 0.2498 | | 8 0.0340 0.0065 9.3852 0.3108 | | 9 -0.0548 -0.0561 10.288 0.3277 | | 10 0.0893 0.1260 12.692 0.2414 | |- 11 0.0600 0.1142 13.783 0.2452 | | 12 0.1148 0.1267 17.783 0.1224 | |- 13 -0.0280 -0.0158 18.022 0.1567 | | 14 0.0634 0.1098 19.252 0.1555 | | 15 -0.0798 0.0022 21.204 0.1304 | | 16 -0.0024 0.0232 21.206 0.1707 | | 17 -0.0745 -0.0738 22.924 0.1517 | | 18 -0.0112 -0.0585 22.963 0.1920 | | 19 -0.1106 -0.1399 26.772 0.1101 | -| 20 -0.0003 -0.0691 26.772 0.1418 | | 21 0.0078 -0.0367 26.792 0.1779 | | 22 0.0995 0.0230 29.907 0.1207 | | 23 0.0095 -0.0348 29.936 0.1513 | | 24 -0.0044 -0.0807 29.942 0.1867 | | . *corrgram residual, lags(24) yw . *xcorr alpha residual . predict gasouthat (option xb assumed; predicted values) (7 missing values generated) . tsline gasout gasouthat . * HHS Old file starts . regress gasout gasin Source | SS df MS Number of obs = 296 -------------+------------------------------ F( 1, 294) = 90.16 Model | 709.899127 1 709.899127 Prob > F = 0.0000 Residual | 2314.90625 294 7.87383077 R-squared = 0.2347 -------------+------------------------------ Adj R-squared = 0.2321 Total | 3024.80537 295 10.2535775 Root MSE = 2.806 ------------------------------------------------------------------------------ B34SI 8.11F (D:M:Y) 14/10/11 (H:M:S) 9:30:25 PGMCALL STEP Data from prior step PAGE 13 gasout | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- gasin | -1.446047 .152292 -9.50 0.000 -1.745768 -1.146327 _cons | 53.42694 .163327 327.12 0.000 53.1055 53.74837 ------------------------------------------------------------------------------ . predict error, resid . dfuller error Dickey-Fuller test for unit root Number of obs = 295 ---------- Interpolated Dickey-Fuller --------- Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value ------------------------------------------------------------------------------ Z(t) -3.037 -3.456 -2.878 -2.570 ------------------------------------------------------------------------------ MacKinnon approximate p-value for Z(t) = 0.0316 . dfuller gasout Dickey-Fuller test for unit root Number of obs = 295 ---------- Interpolated Dickey-Fuller --------- Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value ------------------------------------------------------------------------------ Z(t) -1.864 -3.456 -2.878 -2.570 ------------------------------------------------------------------------------ MacKinnon approximate p-value for Z(t) = 0.3492 . dfuller gasin Dickey-Fuller test for unit root Number of obs = 295 ---------- Interpolated Dickey-Fuller --------- Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value ------------------------------------------------------------------------------ Z(t) -2.665 -3.456 -2.878 -2.570 ------------------------------------------------------------------------------ MacKinnon approximate p-value for Z(t) = 0.0802 . prais gasout gasin Iteration 0: rho = 0.0000 Iteration 1: rho = 0.9368 Iteration 2: rho = 0.9822 Iteration 3: rho = 0.9829 Iteration 4: rho = 0.9829 Iteration 5: rho = 0.9829 Prais-Winsten AR(1) regression -- iterated estimates Source | SS df MS Number of obs = 296 B34SI 8.11F (D:M:Y) 14/10/11 (H:M:S) 9:30:25 PGMCALL STEP Data from prior step PAGE 14 -------------+------------------------------ F( 1, 294) = 197.20 Model | 97.648063 1 97.648063 Prob > F = 0.0000 Residual | 145.581758 294 .495176047 R-squared = 0.4015 -------------+------------------------------ Adj R-squared = 0.3994 Total | 243.229821 295 .824507867 Root MSE = .70369 ------------------------------------------------------------------------------ gasout | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- gasin | .737902 .1248389 5.91 0.000 .4922109 .983593 _cons | 54.10677 2.030883 26.64 0.000 50.10986 58.10368 -------------+---------------------------------------------------------------- rho | .9829089 ------------------------------------------------------------------------------ Durbin-Watson statistic (original) 0.130225 Durbin-Watson statistic (transformed) 0.348879 . prais gasout gasin, corc Iteration 0: rho = 0.0000 Iteration 1: rho = 0.9368 Iteration 2: rho = 0.9822 Iteration 3: rho = 0.9829 Iteration 4: rho = 0.9830 Iteration 5: rho = 0.9830 Cochrane-Orcutt AR(1) regression -- iterated estimates Source | SS df MS Number of obs = 295 -------------+------------------------------ F( 1, 293) = 34.83 Model | 17.3034472 1 17.3034472 Prob > F = 0.0000 Residual | 145.579322 293 .496857755 R-squared = 0.1062 -------------+------------------------------ Adj R-squared = 0.1032 Total | 162.882769 294 .554023025 Root MSE = .70488 ------------------------------------------------------------------------------ gasout | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- gasin | .7379504 .125048 5.90 0.000 .4918442 .9840567 _cons | 54.19831 2.410471 22.48 0.000 49.45428 58.94235 -------------+---------------------------------------------------------------- rho | .9829742 ------------------------------------------------------------------------------ Durbin-Watson statistic (original) 0.130225 Durbin-Watson statistic (transformed) 0.348503 . nl (gasout = {alpha} + {beta} * gasin ) (obs = 296) Iteration 0: residual SS = 2314.906 Iteration 1: residual SS = 2314.906 Source | SS df MS -------------+------------------------------ Number of obs = 296 Model | 709.899127 1 709.899127 R-squared = 0.2347 Residual | 2314.90625 294 7.87383077 Adj R-squared = 0.2321 B34SI 8.11F (D:M:Y) 14/10/11 (H:M:S) 9:30:25 PGMCALL STEP Data from prior step PAGE 15 -------------+------------------------------ Root MSE = 2.806035 Total | 3024.80537 295 10.2535775 Res. dev. = 1448.814 ------------------------------------------------------------------------------ gasout | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- /alpha | 53.42694 .163327 327.12 0.000 53.1055 53.74837 /beta | -1.446047 .152292 -9.50 0.000 -1.745768 -1.146327 ------------------------------------------------------------------------------ Parameter alpha taken as constant term in model & ANOVA table . regress gasout l(1/12)gasout l(1/12)gasin Source | SS df MS Number of obs = 284 -------------+------------------------------ F( 24, 259) = 2112.21 Model | 2999.62521 24 124.984384 Prob > F = 0.0000 Residual | 15.3256017 259 .059172207 R-squared = 0.9949 -------------+------------------------------ Adj R-squared = 0.9944 Total | 3014.95081 283 10.6535364 Root MSE = .24325 ------------------------------------------------------------------------------ gasout | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- gasout | L1. | 1.544434 .0622908 24.79 0.000 1.421773 1.667095 L2. | -.5756952 .1140565 -5.05 0.000 -.8002914 -.351099 L3. | -.1592496 .119036 -1.34 0.182 -.3936512 .075152 L4. | .0585101 .119948 0.49 0.626 -.1776873 .2947076 L5. | .0256611 .1201854 0.21 0.831 -.2110038 .262326 L6. | .1608521 .1197887 1.34 0.181 -.0750317 .3967359 L7. | -.1640967 .1195484 -1.37 0.171 -.3995073 .0713139 L8. | .0295304 .1207615 0.24 0.807 -.2082689 .2673298 L9. | -.0659401 .1219845 -0.54 0.589 -.3061479 .1742676 L10. | .1659071 .1209659 1.37 0.171 -.0722948 .404109 L11. | -.1004767 .1065565 -0.94 0.347 -.310304 .1093507 L12. | .0192767 .0454421 0.42 0.672 -.0702063 .1087596 | gasin | L1. | .0616913 .0787969 0.78 0.434 -.0934729 .2168554 L2. | -.1362779 .1711898 -0.80 0.427 -.4733791 .2008232 L3. | -.4574647 .1948763 -2.35 0.020 -.8412084 -.0737211 L4. | .1993523 .1969437 1.01 0.312 -.1884625 .587167 L5. | -.1635301 .1967979 -0.83 0.407 -.5510578 .2239977 L6. | .3321055 .1975501 1.68 0.094 -.0569035 .7211144 L7. | -.1336421 .1985508 -0.67 0.501 -.5246215 .2573374 L8. | .0950641 .1978562 0.48 0.631 -.2945475 .4846756 L9. | .0144592 .1970891 0.07 0.942 -.373642 .4025603 L10. | -.138103 .1967449 -0.70 0.483 -.5255263 .2493204 L11. | .076864 .1868232 0.41 0.681 -.2910218 .4447498 L12. | .0419241 .1202223 0.35 0.728 -.1948135 .2786618 | _cons | 3.274352 1.536346 2.13 0.034 .2490314 6.299672 ------------------------------------------------------------------------------ . end of do-file B34SI 8.11F (D:M:Y) 14/10/11 (H:M:S) 9:30:25 PGMCALL STEP Data from prior step PAGE 16 Autocorrelation Function Data - VAR=GASIN Input gas rate in cu. ft / min 296 Observations Original Series Mean of the Series -5.683445945945946E-002 St. Dev. of Series 1.07095186710252 Number of observations 296 S. E. of mean 6.235322838747232E-002 T value of mean (against zero) -0.911491849408047 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.) 0.913035443823571 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. Partial Autocorrelations Data - VAR=GASIN Input gas rate in cu. ft / min 296 Observations Original Series Mean of the Series -5.683445945945946E-002 St. Dev. of Series 1.07095186710252 Number of observations 296 S. E. of mean 6.235322838747232E-002 T value of mean (against zero) -0.911491849408047 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 Autocorrelation Function Data - VAR=GASOUT Percent CO2 in outlet gas 296 Observations Original Series Mean of the Series 53.5091216216216 St. Dev. of Series 3.19670722248523 Number of observations 296 S. E. of mean 0.186119490197800 T value of mean (against zero) 287.498754508484 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.) 287.985628277260 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. Partial Autocorrelations Data - VAR=GASOUT Percent CO2 in outlet gas 296 Observations Original Series Mean of the Series 53.5091216216216 St. Dev. of Series 3.19670722248523 Number of observations 296 S. E. of mean 0.186119490197800 T value of mean (against zero) 287.498754508484 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 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 118.479298418800 Iteration stops - Relative parameter change < 4.000000189989805E-003 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-002 Number of residuals 293 Residual Standard error 0.190016173065653 Backforecasting not used in Estimation Autocorrelation Function Data - THE ESTIMATED RESIDUALS - MODEL 1 293 Observations Original Series Mean of the Series -2.758565560279432E-013 St. Dev. of Series 0.188714677111274 Number of observations 293 S. E. of mean 1.104369115092541E-002 T value of mean (against zero) -2.497865543847880E-011 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-011 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-013 St. Dev. of Series 0.188714677111274 Number of observations 293 S. E. of mean 1.104369115092541E-002 T value of mean (against zero) -2.497865543847880E-011 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 Summary Table for Residuals from estimated model Mean= -0.27585585E-12 Variance= 0.35613229E-01 Standard Deviation= 0.18871468 Skewness= 0.78343172E-02 Kurtosis= 6.3201472 # of observations 293 Hinich bispectrum summary table. M G L BICOH Lamda 9 12.924348 7.6724597 2.3451054 0.40675741 10 11.242793 8.2436821 2.3008230 0.21076810 11 9.3701131 7.1396421 2.2333046 0.40679021 12 13.382187 3.7096489 2.6755511 1.8909417 13 11.891754 6.0411717 2.6242230 1.1406348 14 6.9803116 1.0960646 2.1902098 0.86138195 15 4.0282174 3.8945406 1.8776985 0.32462502 16 7.2726627 7.3241324 2.3040494 0.10000000E-15 17 8.7747687 5.3004569 2.5411264 2.3454689 18 7.3129603 -0.53495274E-01 2.4028189 2.0801115 Mean for G = 9.3180116 Mean for L = 5.0368304 For the above table NWD = 53 WT = -0.92694566 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. 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 1392.94535033751 Iteration stops - Relative parameter change < 4.000000189989805E-003 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-002 Number of residuals 289 Residual Standard error 0.243007209043561 Backforecasting not used in Estimation Autocorrelation Function Data - THE ESTIMATED RESIDUALS - MODEL 1 289 Observations Original Series Mean of the Series 1.954374326686871E-004 St. Dev. of Series 0.239620103643486 Number of observations 289 S. E. of mean 1.411975001624438E-002 T value of mean (against zero) 1.384142300280400E-002 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 25- 36 0.04 -0.02 0.02 0.09 -0.12 0.06 -0.02 -0.05 0.11 0.02 0.03 0.06 St.E. 0.06 0.06 0.06 0.06 0.06 0.07 0.07 0.07 0.07 0.07 0.07 0.07 Mod. Q 28.0 28.1 28.2 31.0 35.8 37.1 37.3 38.2 42.3 42.5 42.7 44.0 Mean divided by St. Error (using N in S. D.) 1.386543242761841E-002 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-004 St. Dev. of Series 0.239620103643486 Number of observations 289 S. E. of mean 1.411975001624438E-002 T value of mean (against zero) 1.384142300280400E-002 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 25- 36 0.09 -0.01 0.06 0.07 -0.12 0.08 0.02 -0.09 0.11 -0.03 0.02 0.05 Cross Correlations Series 1 - PREWHITENED VAR=GASIN Series 2 - THE ESTIMATED RESIDUALS - MODEL 1 Mean Series 1 = -7.311710726643630E-004 ST. Dev. Series 1 = 0.189870576802632 Mean Series 2 = 1.954374326686871E-004 ST. Dev. Series 2 = 0.239620103643486 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 25 0.019 25 0.037 18.8 15.9 19.9 16.8 26 0.057 26 0.077 19.7 17.7 20.9 18.7 27 -0.071 27 0.022 21.2 17.8 22.5 18.8 28 -0.001 28 -0.071 21.2 19.2 22.5 20.4 29 0.037 29 0.045 21.6 19.8 22.9 21.1 30 -0.156 30 0.005 28.6 19.8 30.8 21.1 31 0.029 31 -0.014 28.9 19.9 31.1 21.1 32 0.033 32 0.080 29.2 21.7 31.4 23.2 33 -0.014 33 -0.003 29.2 21.7 31.5 23.2 34 0.014 34 -0.109 29.3 25.2 31.5 27.1 35 -0.039 35 0.068 29.7 26.5 32.1 28.6 36 0.029 36 -0.013 30.0 26.6 32.3 28.7 37 0.045 37 0.055 30.6 27.4 33.0 29.7 38 0.140 38 -0.094 36.2 30.0 39.5 32.6 39 0.035 39 0.023 36.6 30.1 39.9 32.8 40 -0.028 40 0.037 36.8 30.5 40.2 33.2 41 -0.073 41 -0.049 38.3 31.2 42.0 34.1 42 -0.007 42 0.061 38.3 32.3 42.0 35.3 43 0.009 43 0.090 38.4 34.6 42.0 38.1 44 -0.005 44 -0.053 38.4 35.5 42.0 39.0 45 0.034 45 0.017 38.7 35.5 42.4 39.1 46 -0.038 46 -0.017 39.1 35.6 42.9 39.2 47 -0.050 47 0.049 39.9 36.3 43.8 40.1 48 0.107 48 -0.013 43.1 36.4 47.7 40.1 49 0.030 49 0.028 43.4 36.6 48.0 40.4 50 0.023 50 -0.027 43.5 36.8 48.2 40.6 51 -0.017 51 0.037 43.6 37.2 48.3 41.1 52 -0.108 52 -0.024 47.0 37.4 52.4 41.3 53 -0.119 53 0.078 51.1 39.1 57.4 43.4 54 0.005 54 -0.015 51.1 39.2 57.4 43.5 Number of terms for Sum of Cross Correlations Squared 55 0.17673330E+00 0.13550980E+00 Haugh S Statistic - See JASA June 76 Page 382 S for left side 51.076 DF 55 Chi Prob 0.374700 S for right side 38.240 DF 54 Chi Prob 0.051568 S for both sides 89.316 DF 109 CHI Prob 0.084185 Test for feedback plus instantaneous causality S for right side 39.162 DF 55 Chi Prob 0.052581 Haugh Modified S Statistic - See JASA June 76 Page 383 S for left side 57.411 DF 55 Chi Prob 0.614081 S for right side 42.607 DF 54 Chi Prob 0.131546 S for both sides 100.02 DF 109 CHI Prob 0.280717 Test for feedback plus instantaneous causality S for right side 43.530 DF 55 Chi Prob 0.132270 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. Autocorrelation Function Data - CROSS CORRELATIONS SERIES # 1 55 Observations Original Series Mean of the Series -7.646620761639997E-003 St. Dev. of Series 5.616815725471709E-002 Number of observations 55 S. E. of mean 7.643518059247892E-003 T value of mean (against zero) -1.00040592595819 1- 12 0.11 -0.08 -0.03 -0.40 -0.06 0.21 -0.08 -0.01 0.02 -0.01 0.25 0.06 St.E. 0.13 0.14 0.14 0.14 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.17 Mod. Q 0.7 1.1 1.2 10.9 11.1 13.8 14.2 14.2 14.3 14.3 18.6 18.8 13- 24 -0.09 -0.05 -0.27 -0.10 0.09 -0.24 -0.07 0.06 -0.11 0.22 0.15 -0.08 St.E. 0.17 0.17 0.17 0.18 0.18 0.18 0.19 0.19 0.19 0.19 0.19 0.20 Mod. Q 19.4 19.6 25.3 26.2 26.9 31.7 32.1 32.5 33.5 38.2 40.5 41.2 25- 27 -0.03 -0.16 -0.07 St.E. 0.20 0.20 0.20 Mod. Q 41.3 44.0 44.6 Mean divided by St. Error (using N in S. D.) 1.00962645198951 Q Statistic 32.195 DF 27 Prob. 0.77508 Modified Q Statistic 44.621 DF 27 Prob. 0.98218 NOTE: In some cases degrees of freedom for Q and Modified Q Statistics may have to be adjusted. Autocorrelation Function Data - CROSS CORRELATIONS SERIES # 2 55 Observations Original Series Mean of the Series -1.634225543891596E-003 St. Dev. of Series 4.960991659704518E-002 Number of observations 55 S. E. of mean 6.751054546932840E-003 T value of mean (against zero) -0.242069669639103 1- 12 -0.19 -0.04 -0.07 -0.08 -0.05 0.16 0.00 0.15 -0.33 0.23 0.13 -0.07 St.E. 0.13 0.14 0.14 0.14 0.14 0.14 0.15 0.15 0.15 0.16 0.17 0.17 Mod. Q 2.2 2.2 2.5 2.9 3.0 4.7 4.8 6.2 13.7 17.5 18.8 19.1 13- 24 -0.16 0.15 -0.27 0.30 0.08 0.09 -0.19 -0.09 0.03 0.17 -0.04 0.08 St.E. 0.17 0.17 0.17 0.18 0.19 0.19 0.19 0.20 0.20 0.20 0.20 0.20 Mod. Q 21.1 22.9 28.4 35.8 36.3 36.9 40.0 40.8 40.9 43.7 43.9 44.5 25- 27 -0.11 -0.08 -0.02 St.E. 0.20 0.20 0.20 Mod. Q 45.7 46.4 46.5 Mean divided by St. Error (using N in S. D.) 0.244300773666364 Q Statistic 33.791 DF 27 Prob. 0.82779 Modified Q Statistic 46.464 DF 27 Prob. 0.98867 NOTE: In some cases degrees of freedom for Q and Modified Q Statistics may have to be adjusted. Test to determine whether Autocorrelations of Series # 2 are similar to Autocorrelations of Cross Correlations # terms for Chi square test for Spurious left hand CCF 27 1-12 0.350 1.235 1.314 6.518 6.518 6.771 7.168 7.219 7.590 7.728 9.380 9.436 13-24 9.503 9.828 10.792 11.032 11.849 13.369 13.425 13.517 13.759 14.300 14.718 14.859 25-27 14.957 15.438 15.632 # terms for Chi square test for Spurious right hand CCF 27 1-12 2.183 2.560 2.561 2.578 2.580 2.653 2.684 3.227 5.658 6.788 7.172 8.030 13-24 8.486 8.798 9.693 12.326 12.952 13.154 13.280 13.483 13.520 13.739 13.826 13.996 25-27 14.475 14.561 14.601 Test using Chi Square only for elements GE 2 SE in absolute value (either or both elements ) -- Series # 2 only For left hand cross correlations, # elements = 2, Chi Square= 5.45602 , only Series #2 Sig, #= 1, Chi= 0.252281 For right hand cross correlations, # elements = 2, Chi Square= 2.50426 , only Series #2 Sig, #= 1, Chi= 0.737324E-01 Test using Chi Square only for elements GE SE in absolute value (either or both elements ) -- Series # 2 only For left hand cross correlations, # elements = 11, Chi Square= 11.5121 , only Series #2 Sig, #= 8, Chi= 3.13658 For right hand cross correlations, # elements = 12, Chi Square= 11.7182 , only Series #2 Sig, #= 8, Chi= 5.22880 Autocorrelation Function Data - PREWHITENED VAR=GASIN 289 Observations Original Series Mean of the Series -7.311710726643630E-004 St. Dev. of Series 0.189870576802632 Number of observations 289 S. E. of mean 1.118823103374522E-002 T value of mean (against zero) -6.535180319918781E-002 1- 12 -0.04 0.07 0.06 -0.15 -0.01 0.06 0.02 0.00 -0.05 0.04 0.15 -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 2.8 9.1 9.1 10.2 10.3 10.3 11.1 11.5 17.9 20.0 13- 24 0.10 0.04 -0.08 0.02 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 25.4 26.6 27.6 29.6 29.7 29.8 30.1 30.6 30.6 25- 36 -0.01 0.00 0.07 -0.04 -0.06 0.00 0.01 0.00 0.08 0.05 0.05 -0.03 St.E. 0.06 0.06 0.06 0.06 0.06 0.07 0.07 0.07 0.07 0.07 0.07 0.07 Mod. Q 30.6 30.6 32.2 32.8 34.1 34.1 34.1 34.1 36.3 37.0 38.0 38.2 Mean divided by St. Error (using N in S. D.) 6.546516287362876E-002 Q Statistic 29.250 DF 21 Prob. 0.89188 Modified Q Statistic 30.552 DF 21 Prob. 0.91856 NOTE: In some cases degrees of freedom for Q and Modified Q Statistics may have to be adjusted. 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 25 -0.43693697E-05 0.31160646E-01 0.31165015E-01 -3.16149 -3.37582 26 -0.23684192E-05 0.60493194E-01 0.60495563E-01 -3.16149 -3.31533 27 -0.12838029E-05 -0.11418782 -0.11418653 -3.16149 -3.42951 28 -0.69588604E-06 0.45676876E-01 0.45677572E-01 -3.16149 -3.38384 29 -0.37720540E-06 0.50044427E-01 0.50044805E-01 -3.16149 -3.33379 30 -0.20446439E-06 -0.21646727 -0.21646706 -3.16149 -3.55026 31 -0.11083003E-06 0.12660376 0.12660387 -3.16149 -3.42366 32 -0.60075478E-07 0.11646853E-01 0.11646913E-01 -3.16149 -3.41201 33 -0.32563945E-07 -0.38508479E-01 -0.38508447E-01 -3.16149 -3.45052 34 -0.17651304E-07 0.27618832E-01 0.27618849E-01 -3.16149 -3.42290 35 -0.95678987E-08 -0.47205788E-01 -0.47205778E-01 -3.16149 -3.47010 36 -0.51862846E-08 0.57264903E-01 0.57264908E-01 -3.16149 -3.41284 37 -0.28112283E-08 0.32664675E-01 0.32664678E-01 -3.16149 -3.38017 38 -0.15238278E-08 0.15484277 0.15484277 -3.16149 -3.22533 39 -0.82599169E-09 -0.25127808E-01 -0.25127807E-01 -3.16149 -3.25046 40 -0.44772924E-09 -0.37200250E-01 -0.37200249E-01 -3.16149 -3.28766 41 -0.24269187E-09 -0.60394844E-01 -0.60394844E-01 -3.16149 -3.34805 42 -0.13155126E-09 0.33916552E-01 0.33916553E-01 -3.16149 -3.31414 43 -0.71307431E-10 0.10174950E-01 0.10174950E-01 -3.16149 -3.30396 44 -0.38652231E-10 -0.21604776E-01 -0.21604776E-01 -3.16149 -3.32557 45 -0.20951462E-10 0.40801590E-01 0.40801590E-01 -3.16149 -3.28477 46 -0.11356751E-10 -0.66886896E-01 -0.66886896E-01 -3.16149 -3.35165 47 -0.61559332E-11 -0.40304160E-01 -0.40304160E-01 -3.16149 -3.39196 48 -0.33368269E-11 0.16299007 0.16299007 -3.16149 -3.22897 49 -0.18087288E-11 -0.22617728E-01 -0.22617728E-01 -3.16149 -3.25159 50 -0.98042241E-12 0.16786983E-01 0.16786983E-01 -3.16149 -3.23480 51 -0.53143849E-12 -0.30016994E-01 -0.30016994E-01 -3.16149 -3.26482 52 -0.28806652E-12 -0.12198795 -0.12198795 -3.16149 -3.38680 53 -0.15614661E-12 -0.86914457E-01 -0.86914457E-01 -3.16149 -3.47372 54 -0.84639354E-13 0.58731889E-01 0.58731889E-01 -3.16149 -3.41499 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 X 25 XX 0.3116E-01 X 26 XXXX 0.6049E-01 X 27 XXXXXX -0.1142 X 28 XXX 0.4568E-01 X 29 XXX 0.5004E-01 X 30 XXXXXXXXXXX -0.2165 X 31 XXXXXXX 0.1266 X 32 XX 0.1165E-01 X 33 XXX -0.3851E-01 X 34 XX 0.2762E-01 X 35 XXX -0.4721E-01 X 36 XXXX 0.5726E-01 X 37 XX 0.3266E-01 X 38 XXXXXXXX 0.1548 X 39 XX -0.2513E-01 X 40 XXX -0.3720E-01 X 41 XXXX -0.6039E-01 X 42 XXX 0.3392E-01 X 43 X 0.1017E-01 X 44 XX -0.2160E-01 X 45 XXX 0.4080E-01 X 46 XXXX -0.6689E-01 X 47 XXX -0.4030E-01 X 48 XXXXXXXX 0.1630 X 49 XX -0.2262E-01 X 50 XX 0.1679E-01 X 51 XX -0.3002E-01 X 52 XXXXXXX -0.1220 X 53 XXXXX -0.8691E-01 X 54 XXXX 0.5873E-01 B34SI 8.11F (D:M:Y) 14/10/11 (H:M:S) 9:30:25 DATA STEP PAGE 17 Variable Label # Cases Mean Std. Dev. Variance Maximum Minimum TIME 1 296 148.500 85.5921 7326.00 296.000 1.00000 GASIN 2 Input gas rate in cu. ft / min 296 -0.568345E-01 1.07277 1.15083 2.83400 -2.71600 GASOUT 3 Percent CO2 in outlet gas 296 53.5091 3.20212 10.2536 60.5000 45.6000 CONSTANT 4 296 1.00000 0.00000 0.00000 1.00000 1.00000 Number of observations in data file 296 Current missing variable code 1.000000000000000E+031 B34SI 8.11F (D:M:Y) 14/10/11 (H:M:S) 9:30:26 PGMCALL STEP PAGE 18 OUTPUT FROM RATS * * Data passed from B34S(r) system to RATS * CALENDAR(IRREGULAR) ALLOCATE 296 OPEN DATA rats.dat DATA(FORMAT=FREE,ORG=OBS, $ MISSING= 0.1000000000000000E+32 ) / $ TIME $ GASIN $ GASOUT $ CONSTANT SET TREND = T TABLE Series Obs Mean Std Error Minimum Maximum TIME 296 148.50000000 85.59205571 1.00000000 296.00000000 GASIN 296 -0.05683446 1.07276550 -2.71600000 2.83400000 GASOUT 296 53.50912162 3.20212079 45.60000000 60.50000000 TREND 296 148.50000000 85.59205571 1.00000000 296.00000000 * * boxjenk(AR=||1,2,3||, iterations=200,define=bjeqtest, $ constant) gasin * * res Box-Jenkins - Estimation by LS Gauss-Newton Convergence in 3 Iterations. Final criterion was 0.0000000 <= 0.0000100 Dependent Variable GASIN Usable Observations 293 Degrees of Freedom 289 Centered R^2 0.9692584 R-Bar^2 0.9689393 Uncentered R^2 0.9693464 Mean of Dependent Variable -0.057651877 Std Error of Dependent Variable 1.078164861 Standard Error of Estimate 0.190016173 Sum of Squared Residuals 10.434676202 Regression F(3,289) 3037.3190 Significance Level of F 0.0000000 Log Likelihood 72.8341 Durbin-Watson Statistic 2.0840 Q(36-3) 38.5692 Significance Level of Q 0.2322539 Variable Coeff Std Error T-Stat Signif ************************************************************************************ 1. CONSTANT -0.068941307 0.198841155 -0.34672 0.72905739 2. AR{1} 1.974960749 0.055256961 35.74139 0.00000000 3. AR{2} -1.373235351 0.100144664 -13.71252 0.00000000 4. AR{3} 0.342442440 0.055280765 6.19460 0.00000000 boxjenk(diff=1,AR=||1,2,3||, iterations=200,define=bjeq, $ B34SI 8.11F (D:M:Y) 14/10/11 (H:M:S) 9:30:26 PGMCALL STEP PAGE 19 MA=||1,3||,constant) gasout * * res Box-Jenkins - Estimation by LS Gauss-Newton Convergence in 17 Iterations. Final criterion was 0.0000065 <= 0.0000100 Dependent Variable GASOUT Usable Observations 292 Degrees of Freedom 286 Centered R^2 0.9890390 R-Bar^2 0.9888474 Uncentered R^2 0.9999605 Mean of Dependent Variable 53.507876712 Std Error of Dependent Variable 3.224003553 Standard Error of Estimate 0.340473871 Sum of Squared Residuals 33.153822731 Log Likelihood -96.6931 Durbin-Watson Statistic 1.9939 Q(36-5) 38.8316 Significance Level of Q 0.1575627 Variable Coeff Std Error T-Stat Signif ************************************************************************************ 1. CONSTANT 0.009171236 0.067497970 0.13587 0.89201628 2. AR{1} 0.430498700 0.081808579 5.26227 0.00000028 3. AR{2} 0.662060149 0.080439160 8.23057 0.00000000 4. AR{3} -0.649813141 0.057578073 -11.28577 0.00000000 5. MA{1} 0.735133719 0.086657084 8.48325 0.00000000 6. MA{3} 0.167532982 0.061473205 2.72530 0.00682035 forecast 1 10 290 # BJEQ fgasout print * * fgasout ENTRY FGASOUT 290 57.4120871666 291 57.2006041973 292 56.6382906829 293 55.9935320542 294 55.4862140568 295 55.2114547464 296 55.1813795318 297 55.3212976129 298 55.5452734848 299 55.7589829721 source(noecho) d:\r\bjident.src @bjident res OPEN COPY myrun.por SMPL COPY(UNIT=COPY,FORMAT=PORTABLE) / RES B34SI 8.11F (D:M:Y) 14/10/11 (H:M:S) 9:30:26 DATA STEP PAGE 20 Variable # Cases Mean Std Deviation Variance Maximum Minimum OBSNUM 1 292 150.5000000 84.43735350 7129.666667 296.0000000 5.000000000 RES 2 292 0.1009726027E-02 0.3375346666 0.1139296512 1.672840000 -0.8676500000 CONSTANT 3 292 1.000000000 0.000000000 0.000000000 1.000000000 1.000000000 Number of observations in data file 292 Current missing variable code 1.000000000000000E+031 B34SI 8.11F (D:M:Y) 14/10/11 (H:M:S) 9:30:26 DATA STEP PAGE 21 B34S normal exit on Date (D:M:Y) 14/10/11 at Time (H:M:S) 9:30:26