B34S 8.10R (D:M:Y) 8/ 6/04 (H:M:S) 14:49:25 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+31 B34S(r) Matrix Command. Version February 2004. Date of Run d/m/y 8/ 6/04. Time of Run h:m:s 14:49:25. => CALL LOADDATA$ => ACF1=ACF(GASOUT,24,SE1,PACF1)$ => CALL GRAPH(ACF1,PACF1 :NOKEY :HEADING 'ACF & PACF of Gasout')$ => CALL GRAPH(ACF(DIF(GASOUT),24) :HEADING 'ACF of Gasout(1-B)')$ => CALL GRAPH(ACF(DIF(GASOUT,2,1),24) :HEADING 'ACF of Gasout(1-B)**2')$ => ACF2=ACF(GASIN,24,SE2,PACF2)$ => CALL GRAPH(ACF2,PACF2 :NOKEY :HEADING 'ACF & PACF of Gasin')$ => CALL GRAPH(ACF1,SE1 :NOKEY :HEADING 'ACF and SE of ACF of Gasout')$ => I=INTEGERS(24)$ => CALL TABULATE(I,ACF1,ACF2,SE1,SE2,PACF1,PACF2)$ Obs I ACF1 ACF2 SE1 SE2 PACF1 PACF2 1 1 0.9708 0.9525 0.5812E-01 0.5812E-01 0.9708 0.9525 2 2 0.8960 0.8341 0.9872E-01 0.9751E-01 -0.8039 -0.7880 3 3 0.7925 0.6819 0.1232 0.1192 0.1883 0.3390 4 4 0.6800 0.5312 0.1393 0.1317 0.2600 0.1212 5 5 0.5745 0.4075 0.1501 0.1388 0.5949E-01 0.5896E-01 6 6 0.4854 0.3182 0.1574 0.1428 -0.6258E-01 -0.1115 7 7 0.4161 0.2602 0.1624 0.1451 -0.1435E-01 0.4862E-01 8 8 0.3656 0.2275 0.1659 0.1467 0.5490E-01 0.9945E-01 9 9 0.3304 0.2131 0.1686 0.1479 0.5452E-02 0.1587E-01 10 10 0.3065 0.2083 0.1708 0.1489 0.3141E-01 -0.6973E-01 11 11 0.2880 0.2028 0.1726 0.1499 -0.1166 -0.9434E-01 12 12 0.2693 0.1893 0.1743 0.1508 -0.4302E-01 0.4141E-01 13 13 0.2473 0.1673 0.1757 0.1516 0.5110E-01 0.8801E-01 14 14 0.2215 0.1375 0.1768 0.1522 0.5381E-01 -0.1353 15 15 0.1930 0.1048 0.1778 0.1527 -0.4613E-01 0.5137E-01 16 16 0.1649 0.7541E-01 0.1785 0.1529 0.3394E-01 0.3276E-01 17 17 0.1398 0.5203E-01 0.1790 0.1530 -0.3344E-02 -0.2230E-01 18 18 0.1210 0.3705E-01 0.1794 0.1531 0.8548E-01 0.3398E-01 19 19 0.1103 0.3398E-01 0.1796 0.1531 0.1655E-01 0.9339E-01 20 20 0.1078 0.4236E-01 0.1799 0.1532 -0.2576E-01 -0.4077E-01 21 21 0.1112 0.5635E-01 0.1801 0.1532 -0.4925E-01 -0.9068E-01 22 22 0.1171 0.6939E-01 0.1803 0.1533 0.9711E-02 0.3797E-01 23 23 0.1228 0.7653E-01 0.1806 0.1534 0.4906E-01 0.3583E-01 24 24 0.1259 0.7611E-01 0.1808 0.1535 -0.1210E-02 0.6018E-02 => CALL PRINT('ACF, SE, PACF, Modified Q Prob Q for gasin':)$ ACF, SE, PACF, Modified Q Prob Q for gasin => ACF2=ACF(GASIN,24, SE2,PACF2,MQ2,PMQ2)$ => CALL TABULATE(ACF2,SE2,PACF2,MQ2,PMQ2)$ Obs ACF2 SE2 PACF2 MQ2 PMQ2 1 0.9525 0.5812E-01 0.9525 271.3 1.000 2 0.8341 0.9751E-01 -0.7880 480.0 1.000 3 0.6819 0.1192 0.3390 620.0 1.000 4 0.5312 0.1317 0.1212 705.2 1.000 5 0.4075 0.1388 0.5896E-01 755.6 1.000 6 0.3182 0.1428 -0.1115 786.3 1.000 7 0.2602 0.1451 0.4862E-01 807.0 1.000 8 0.2275 0.1467 0.9945E-01 822.9 1.000 9 0.2131 0.1479 0.1587E-01 836.8 1.000 10 0.2083 0.1489 -0.6973E-01 850.2 1.000 11 0.2028 0.1499 -0.9434E-01 862.9 1.000 12 0.1893 0.1508 0.4141E-01 874.1 1.000 13 0.1673 0.1516 0.8801E-01 882.8 1.000 14 0.1375 0.1522 -0.1353 888.7 1.000 15 0.1048 0.1527 0.5137E-01 892.2 1.000 16 0.7541E-01 0.1529 0.3276E-01 893.9 1.000 17 0.5203E-01 0.1530 -0.2230E-01 894.8 1.000 18 0.3705E-01 0.1531 0.3398E-01 895.2 1.000 19 0.3398E-01 0.1531 0.9339E-01 895.6 1.000 20 0.4236E-01 0.1532 -0.4077E-01 896.2 1.000 21 0.5635E-01 0.1532 -0.9068E-01 897.2 1.000 22 0.6939E-01 0.1533 0.3797E-01 898.7 1.000 23 0.7653E-01 0.1534 0.3583E-01 900.6 1.000 24 0.7611E-01 0.1535 0.6018E-02 902.5 1.000 => CALL GRAPH(ACF2,PMQ2)$ => CALL GRAPH(ACF2 SE2 :OVERLAY ACFPLOT => :HEADING 'Overlay plot of ACF of gasin')$ => CALL GRAPH(PACF2 SE2 :OVERLAY ACFPLOT3D => :HEADING '3D Overlay plot of PACF of gasin')$ => CALL GRAPH(ACF2 :OVERLAY ACFPLOT => :HEADING 'Just plot of ACF of gasin')$ => CALL GRAPH(GASIN GASOUT :HEADING 'Scaled Plot of gasin gasout' => :NOKEY :SCALE :PLOTTYPE OBSPLOT)$ => N=400$ => RR=RN(ARRAY(N:))$ => ACF1=ACF(RR,24,SE1)$ => ACF2=ACF(DIF(RR) ,24,SE2)$ => ACF3=ACF(DIF(RR,2,1),24,SE3)$ => CALL GRAPH(ACF1,SE1 :OVERLAY ACFPLOT => :HEADING 'ACF of Random series')$ => CALL GRAPH(ACF2,SE2 :OVERLAY ACFPLOT => :HEADING 'ACF of rn(1-B)')$ => CALL GRAPH(ACF3,SE3 :OVERLAY ACFPLOT => :HEADING 'ACF of rn(1-B)**2')$ B34S Matrix Command Ending. Last Command reached. Space available in allocator 2874697, peak space used 5824 Number variables used 22, peak number used 23 Number temp variables used 63, # user temp clean 0 Autocorrelation Function Data - VAR=GASIN 296 Observations 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 25- 36 0.07 0.06 0.05 0.05 0.06 0.07 0.10 0.12 0.14 0.14 0.13 0.10 St.E. 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.16 0.16 0.16 Mod. Q 904.1 905.4 906.3 907.2 908.2 910.0 913.1 918.1 924.6 931.2 936.5 939.8 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. Partial Autocorrelations Data - VAR=GASIN 296 Observations 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 25- 36 0.00 -0.03 0.06 0.08 0.08 -0.07 -0.02 0.01 -0.02 -0.05 -0.01 -0.01 B34S 8.10R (D:M:Y) 8/ 6/04 (H:M:S) 14:49:27 DATA 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 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+31 B34S(r) Matrix Command. Version February 2004. Date of Run d/m/y 8/ 6/04. Time of Run h:m:s 14:49:27. => CALL LOADDATA$ => CALL LOAD(ACF_PLOT)$ => CALL ACF_PLOT(GASOUT,24,NAMELIST(GASOUT))$ => ACF1=ACF(SERIES,NACF,SE1,PACF1)$ => CALL CHARACTER(CC,'ACF Plot for ')$ => => CALL CHARACTER(CC2,TITLE)$ => => CALL IALEN(CC2,II)$ => CALL EXPAND(CC,CC2,14,14+II)$ => CALL GRAPH(ACF1 SE1 :OVERLAY ACFPLOT => :HEADING CC => :PSPACEON => :PGYSCALERIGHT 'i' => :PGBORDER => :PGXSCALETOP 'i' => :HISTSCALE INTEGERS(0,NACF,2) => :FITSPLINE => :COLORS BLACK BBLUE BRED => )$ => CALL CHARACTER(CC,'PACF Plot for ')$ => CALL CHARACTER(CC2,TITLE)$ => => CALL EXPAND(CC,CC2,15,15+II)$ => CALL GRAPH(PACF1 SE1 :OVERLAY ACFPLOT => :HEADING CC => :PSPACEON => :PGYSCALERIGHT 'i' => :PGBORDER => :PGXSCALETOP 'i' => :HISTSCALE INTEGERS(0,NACF,2) => :FITSPLINE => :COLORS BLACK BBLUE BRED => )$ => RETURN$ B34S Matrix Command Ending. Last Command reached. Space available in allocator 2874961, peak space used 5629 Number variables used 8, peak number used 27 Number temp variables used 25, # user temp clean 0 B34S(r) Matrix Command. Version February 2004. Date of Run d/m/y 8/ 6/04. Time of Run h:m:s 14:49:27. => N=3$ => X=MATRIX(N,N:INTEGERS(1,N*N))$ => CALL PRINT(X)$ X = Matrix of 3 by 3 elements 1 2 3 1 1.00000 2.00000 3.00000 2 4.00000 5.00000 6.00000 3 7.00000 8.00000 9.00000 => TEST=X$ => CALL ADDCOL(TEST)$ => CALL PRINT('We add at the right',TEST)$ We add at the right TEST = Matrix of 3 by 4 elements 1 2 3 4 1 1.00000 2.00000 3.00000 0.00000 2 4.00000 5.00000 6.00000 0.00000 3 7.00000 8.00000 9.00000 0.00000 => TEST=X$ => CALL ADDROW(TEST,2,4)$ => CALL PRINT('We add 4 cols after 1 and before old 2',TEST)$ We add 4 cols after 1 and before old 2 TEST = Matrix of 7 by 3 elements 1 2 3 1 1.00000 2.00000 3.00000 2 0.00000 0.00000 0.00000 3 0.00000 0.00000 0.00000 4 0.00000 0.00000 0.00000 5 0.00000 0.00000 0.00000 6 4.00000 5.00000 6.00000 7 7.00000 8.00000 9.00000 B34S Matrix Command Ending. Last Command reached. Space available in allocator 2874905, peak space used 229 Number variables used 7, peak number used 7 Number temp variables used 9, # user temp clean 0 B34S(r) Matrix Command. Version February 2004. Date of Run d/m/y 8/ 6/04. Time of Run h:m:s 14:49:27. => N=3$ => X=MATRIX(N,N:INTEGERS(1,N*N))$ => CALL PRINT(X)$ X = Matrix of 3 by 3 elements 1 2 3 1 1.00000 2.00000 3.00000 2 4.00000 5.00000 6.00000 3 7.00000 8.00000 9.00000 => TEST=X$ => CALL ADDROW(TEST)$ => CALL PRINT('We add at the end',TEST)$ We add at the end TEST = Matrix of 4 by 3 elements 1 2 3 1 1.00000 2.00000 3.00000 2 4.00000 5.00000 6.00000 3 7.00000 8.00000 9.00000 4 0.00000 0.00000 0.00000 => TEST=X$ => CALL ADDROW(TEST,2,4)$ => CALL PRINT('We add 4 rows after 2 and before old 3',TEST)$ We add 4 rows after 2 and before old 3 TEST = Matrix of 7 by 3 elements 1 2 3 1 1.00000 2.00000 3.00000 2 0.00000 0.00000 0.00000 3 0.00000 0.00000 0.00000 4 0.00000 0.00000 0.00000 5 0.00000 0.00000 0.00000 6 4.00000 5.00000 6.00000 7 7.00000 8.00000 9.00000 B34S Matrix Command Ending. Last Command reached. Space available in allocator 2874905, peak space used 229 Number variables used 7, peak number used 7 Number temp variables used 9, # user temp clean 0 B34S(r) Matrix Command. Version February 2004. Date of Run d/m/y 8/ 6/04. Time of Run h:m:s 14:49:27. => X=MATRIX(3,3:)$ => CALL PRINT(X)$ X = Matrix of 3 by 3 elements 1 2 3 1 0.00000 0.00000 0.00000 2 0.00000 0.00000 0.00000 3 0.00000 0.00000 0.00000 => X1=MATRIX(3,3:1 2 3 4 5 6 7 8 9)$ => CALL PRINT(X1)$ X1 = Matrix of 3 by 3 elements 1 2 3 1 1.00000 2.00000 3.00000 2 4.00000 5.00000 6.00000 3 7.00000 8.00000 9.00000 => V=VECTOR(4:1 2 3 4)$ => XX=MATRIX(2,2:V)$ => CALL PRINT(XX)$ XX = Matrix of 2 by 2 elements 1 2 1 1.00000 2.00000 2 3.00000 4.00000 => AX=AFAM(X)$ => CALL PRINT(AX)$ AX = Array of 3 by 3 elements 1 2 3 1 0.00000 0.00000 0.00000 2 0.00000 0.00000 0.00000 3 0.00000 0.00000 0.00000 => AV=AFAM(V)$ => CALL PRINT(V)$ V = Vector of 4 elements 1.00000 2.00000 3.00000 4.00000 B34S Matrix Command Ending. Last Command reached. Space available in allocator 2874889, peak space used 540 Number variables used 18, peak number used 18 Number temp variables used 26, # user temp clean 0 B34S(r) Matrix Command. Version February 2004. Date of Run d/m/y 8/ 6/04. Time of Run h:m:s 14:49:27. => ID=10.$ => X=20.1$ => CALL AGGDATA(ID,X,NEWX,NEWID)$ => CALL PRINT(ID,X,NEWX,NEWID,%NELM,%NNZERO,%VARX)$ ID = 10.000000 X = 20.100000 NEWX = 20.100000 NEWID = 10.000000 %NELM = 1.0000000 %NNZERO = 1.0000000 %VARX = 0.0000000 => ID=ARRAY(6:10. 10. 11. 11. 11. 12.)$ => X= ARRAY(6:1 2 3 4 5 6)$ => CALL TABULATE(ID,X)$ Obs ID X 1 10.00 1.000 2 10.00 2.000 3 11.00 3.000 4 11.00 4.000 5 11.00 5.000 6 12.00 6.000 => CALL AGGDATA(ID,X,NEWX,NEWID)$ => CALL TABULATE(NEWX,NEWID,%NELM,%NNZERO,%VARX)$ Obs NEWX NEWID %NELM %NNZERO %VARX 1 1.500 10.00 2.000 2.000 0.5000 2 4.000 11.00 3.000 3.000 1.000 3 6.000 12.00 1.000 1.000 0.000 B34S Matrix Command Ending. Last Command reached. Space available in allocator 2874905, peak space used 590 Number variables used 21, peak number used 21 Number temp variables used 18, # user temp clean 0 B34S(r) Matrix Command. Version February 2004. Date of Run d/m/y 8/ 6/04. Time of Run h:m:s 14:49:27. => N=10$ => X=RN(ARRAY(N:))$ => Y=RN(X)$ => CALL TABULATE(X,Y)$ Obs X Y 1 2.052 0.3074 2 1.083 -1.548 3 0.8256E-01 1.498 4 1.278 -0.1682 5 -1.226 0.4985 6 0.3385 1.268 7 -1.320 0.7414 8 -1.524 -0.1872 9 -0.4592 0.4092 10 -0.6056 1.063 => I=INTEGERS(1,N,2)$ => X(I)=MISSING()$ => CALL TABULATE(X,Y)$ Obs X Y 1 Missing 0.3074 2 1.083 -1.548 3 Missing 1.498 4 1.278 -0.1682 5 Missing 0.4985 6 0.3385 1.268 7 Missing 0.7414 8 -1.524 -0.1872 9 Missing 0.4092 10 -0.6056 1.063 => CALL ALIGN(X,Y)$ => CALL TABULATE(X,Y)$ Obs X Y 1 1.083 -1.548 2 1.278 -0.1682 3 0.3385 1.268 4 -1.524 -0.1872 5 -0.6056 1.063 B34S Matrix Command Ending. Last Command reached. Space available in allocator 2874905, peak space used 282 Number variables used 9, peak number used 9 Number temp variables used 11, # user temp clean 0 B34S 8.10R (D:M:Y) 8/ 6/04 (H:M:S) 14:49:27 DATA STEP PAGE 3 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+31 B34S(r) Matrix Command. Version February 2004. Date of Run d/m/y 8/ 6/04. Time of Run h:m:s 14:49:27. => CALL LOADDATA$ => * :NAR 3 :NMA 1 WILL FAIL AS TOO COMPLEX $ => CALL ARMA(GASIN :NAR 2 :NMA 1 => :FORECAST 296 24 => :PRINT)$ Results from DNSPE/DN2PE WMEAN = -5.683445945945951E-02 CONST = -5.269910230604669E-03 AVAR = 3.442787624576694E-02 PAR 1 2 1.540 -0.633 PMA -0.5041 ---------------------------------------------------------------------- Final Results, Iteration 7 Parameter Estimate Std. Error t-ratio WMEAN -0.1194827 0.0991693 -1.2048351 PAR 1 1.5960363 0.0515433 30.9649475 2 -0.6852169 0.0510981 -13.4098341 PMA 1 -0.3304481 0.0669340 -4.9369245 CONST = -0.0106555 AVAR = 0.0368414 Residual SS (including backcasts) = 10.7576793 Number of residuals = 305 Residual SS (excluding backcasts) = 10.7542727 Number of residuals = 294 ARIMA Model Estimated Dependent variable GASIN Sum of Squared Residuals 10.75427270141248 Sum of Absolute Error 39.56438195979493 Maximum absolute Error 0.9951851443619938 Large Sample Residual Variance 3.656635945406302E-02 Large Sample Residual SD 0.1912233235096154 Number of Residuals 294 => CALL GRAPH(%RES)$ => CALL GRAPH(%Y,%YHAT)$ => ACF1=ACF(%RES)$ => CALL GRAPH(ACF1)$ => CALL PRINT(ACF1)$ ACF1 = Vector of 73 elements 0.322213E-01 0.108107 -0.224255E-01 -0.170263 -0.248257E-01 0.608782E-01 0.461781E-01 0.374529E-01 -0.929795E-02 0.588224E-01 0.163471 -0.390983E-01 0.108795 0.411835E-01 -0.528133E-01 0.188115E-01 0.542316E-01 -0.454501E-01 -0.683428E-01 0.207103E-01 0.281867E-01 0.472772E-01 0.524726E-01 0.458416E-02 0.290472E-02 -0.314129E-02 0.712904E-01 -0.381912E-01 -0.646232E-01 -0.195171E-01 0.364578E-02 0.106071E-01 0.952020E-01 0.479452E-01 0.631545E-01 -0.197455E-01 -0.708553E-02 0.181842E-01 -0.661427E-01 -0.105038E-01 -0.196025E-01 -0.301302E-01 0.223402E-01 0.570214E-01 -0.388360E-02 0.167747E-01 -0.340203E-01 0.993886E-02 -0.847250E-01 -0.147708E-02 -0.435802E-01 -0.307107E-02 -0.213938E-01 -0.821441E-01 -0.252478E-01 -0.268044E-01 0.270451E-01 0.124093 -0.957132E-01 -0.430459E-01 -0.565824E-01 -0.999564E-01 0.679217E-02 0.372712E-01 0.173810E-01 0.203390E-01 0.399198E-01 -0.220402E-01 0.214289E-01 -0.986536E-01 0.788816E-02 -0.750628E-01 -0.948407E-03 => CALL ARMA(DIF(GASIN) :NAR 3 => :FORECAST 295 24 => :PRINT)$ Results from DNSPE/DN2PE WMEAN = -5.186440677966073E-04 CONST = -2.264852495596987E-04 AVAR = 3.697645665732224E-02 PAR 1 2 3 1.000 -0.248 -0.189 (PMA is not printed since NPMA = 0.) ---------------------------------------------------------------------- Final Results, Iteration 2 Parameter Estimate Std. Error t-ratio WMEAN -0.0007581 0.0261592 -0.0289798 PAR 1 0.9990771 0.0576311 17.3357311 2 -0.2478935 0.0811311 -3.0554703 3 -0.1882008 0.0578075 -3.2556502 CONST = -0.0003313 AVAR = 0.0373159 Residual SS (including backcasts) = 10.8589226 Number of residuals = 304 Residual SS (excluding backcasts) = 10.8532188 Number of residuals = 292 ARIMA Model Estimated Dependent variable ##52 Sum of Squared Residuals 10.85321879192414 Sum of Absolute Error 39.46269793083010 Maximum absolute Error 0.9867135775372824 Large Sample Residual Variance 3.716837312421799E-02 Large Sample Residual SD 0.1927910089299239 Number of Residuals 292 => CALL GRAPH(%RES)$ => CALL GRAPH(%Y,%YHAT)$ => ACF1 = ACF(%RES)$ => ACF2 = ACF(DIF(GASIN))$ => ACFRAW = ACF(GASIN)$ => CALL GRAPH(ACF1,ACF2)$ => CALL TABULATE(ACF1,ACF2,ACFRAW)$ Obs ACF1 ACF2 ACFRAW 1 -0.1988E-01 0.7472 0.9525 2 -0.3348E-01 0.3582 0.8341 3 0.7364E-01 -0.1593E-01 0.6819 4 -0.1411 -0.2829 0.5312 5 -0.2466E-01 -0.3622 0.4075 6 0.4307E-01 -0.3300 0.3182 7 -0.3603E-01 -0.2681 0.2602 8 -0.9158E-01 -0.1940 0.2275 9 -0.1510 -0.1048 0.2131 10 -0.9763E-02 0.5832E-02 0.2083 11 0.9382E-01 0.8386E-01 0.2028 12 -0.1238 0.8826E-01 0.1893 13 0.6393E-01 0.8428E-01 0.1673 14 0.3053E-01 0.3411E-01 0.1375 15 -0.1191 -0.3249E-01 0.1048 16 0.4408E-02 -0.6292E-01 0.7541E-01 17 0.7769E-01 -0.8894E-01 0.5203E-01 18 -0.7008E-01 -0.1259 0.3705E-01 19 -0.1036 -0.1209 0.3398E-01 20 0.1276E-01 -0.5936E-01 0.4236E-01 21 0.1063E-01 0.9290E-02 0.5635E-01 22 0.1703E-01 0.6070E-01 0.6939E-01 23 0.2903E-01 0.7775E-01 0.7653E-01 24 -0.1713E-01 0.5834E-01 0.7611E-01 25 -0.3984E-01 0.2645E-01 0.7011E-01 26 -0.1356E-01 -0.5276E-02 0.6169E-01 27 0.8288E-01 -0.4137E-01 0.5396E-01 28 -0.3964E-01 -0.9630E-01 0.5036E-01 29 -0.7492E-01 -0.1153 0.5623E-01 30 0.7706E-02 -0.7426E-01 0.7329E-01 31 0.1148E-01 -0.4381E-03 0.9759E-01 32 0.1031E-02 0.8282E-01 0.1220 33 0.7618E-01 0.1527 0.1385 34 0.4316E-01 0.1667 0.1401 35 0.4714E-01 0.1308 0.1256 36 -0.3014E-01 0.6110E-01 0.9867E-01 37 0.9581E-02 0.2265E-03 0.6633E-01 38 0.4388E-01 -0.4979E-01 0.3422E-01 39 -0.5732E-01 -0.9126E-01 0.6864E-02 40 -0.3618E-03 -0.9182E-01 -0.1195E-01 41 -0.2509E-02 -0.6705E-01 -0.2221E-01 42 -0.4597E-01 -0.2285E-01 -0.2610E-01 43 0.1811E-01 0.4046E-01 -0.2757E-01 44 0.5877E-01 0.8391E-01 -0.3279E-01 45 -0.8381E-02 0.8522E-01 -0.4601E-01 46 0.4870E-02 0.6367E-01 -0.6767E-01 47 -0.8532E-02 0.2280E-01 -0.9580E-01 48 0.2152E-01 -0.1960E-01 -0.1265 49 -0.6947E-01 -0.6449E-01 -0.1555 50 -0.4296E-02 -0.7958E-01 -0.1783 51 -0.3634E-01 -0.8651E-01 -0.1934 52 0.1242E-01 -0.8458E-01 -0.2002 53 -0.9144E-02 -0.8685E-01 -0.1991 54 -0.7321E-01 -0.7547E-01 -0.1898 55 -0.1970E-01 -0.3067E-01 -0.1737 56 -0.5082E-01 0.2671E-01 -0.1551 57 0.3534E-01 0.7756E-01 -0.1391 58 0.1379 0.7500E-01 -0.1304 59 -0.1011 -0.6749E-02 -0.1289 60 -0.2510E-01 -0.6964E-01 -0.1267 61 0.4343E-03 -0.9768E-01 -0.1177 62 -0.7386E-01 -0.7965E-01 -0.9924E-01 63 0.4150E-01 -0.5522E-02 -0.7299E-01 64 0.6922E-01 0.6966E-01 -0.4593E-01 65 0.1048E-01 0.1135 -0.2515E-01 66 0.2240E-01 0.1287 -0.1509E-01 67 0.4830E-01 0.1150 -0.1735E-01 68 0.1539E-01 0.7104E-01 -0.3077E-01 69 0.4535E-01 0.1876E-01 -0.5137E-01 70 -0.5470E-01 -0.3607E-01 -0.7410E-01 71 0.3462E-01 -0.5140E-01 -0.9349E-01 72 -0.6020E-01 -0.5293E-01 -0.1080 73 -0.8838E-02 -0.2467E-01 -0.1173 74 NA NA -0.1242 => CALL DF(GASIN,DF)$ => CALL PP(GASIN,PP)$ => CALL PRINT(DF,PP)$ DF = -2.6648230 PP = -2.6648230 B34S Matrix Command Ending. Last Command reached. Space available in allocator 2874789, peak space used 15322 Number variables used 75, peak number used 77 Number temp variables used 102, # user temp clean 0 B34S 8.10R (D:M:Y) 8/ 6/04 (H:M:S) 14:49:28 DATA STEP PAGE 4 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+31 B34S(r) Matrix Command. Version February 2004. Date of Run d/m/y 8/ 6/04. Time of Run h:m:s 14:49:28. => * MODEL DISCUSSED IN BOX-JENKINS AND IN STOKES (1997)$ => CALL LOADDATA$ => CALL ARMA(GASOUT :MAXIT 2000 :RELERR 0.0 => :NAR 8 => :NMA 0 => :FORECAST 296 24 => :PRINT)$ Results from DNSPE/DN2PE WMEAN = 53.50912162162156 CONST = 1.624317434716489 AVAR = 0.1853827493331597 PAR 1 2 3 4 5 6 7 8 1.842 -0.807 -0.280 0.089 0.178 0.008 -0.115 0.055 (PMA is not printed since NPMA = 0.) ---------------------------------------------------------------------- Final Results, Iteration 12 Parameter Estimate Std. Error t-ratio WMEAN 53.8569708 0.3688376 146.0181196 PAR 1 2.1227771 0.0585524 36.2543079 2 -1.3037109 0.1374415 -9.4855683 3 -0.1708674 0.1573593 -1.0858423 4 0.3514054 0.1580872 2.2228583 5 -0.0052628 0.1585091 -0.0332018 6 0.1299818 0.1584179 0.8204996 7 -0.2669701 0.1378545 -1.9366083 8 0.1215229 0.0585085 2.0770126 CONST = 1.1376663 AVAR = 0.1050682 Residual SS (including backcasts) = 30.1545752 Number of residuals = 299 Residual SS (excluding backcasts) = 30.1146929 Number of residuals = 288 ARIMA Model Estimated Dependent variable GASOUT Sum of Squared Residuals 30.11469289839501 Sum of Absolute Error 67.86412539358780 Maximum absolute Error 1.570147779511230 Large Sample Residual Variance 0.1044463351149811 Large Sample Residual SD 0.3231815822644927 Number of Residuals 288 => CALL NAMES(INFO)$ # Name Kind Klass Nrows Ncols Level Begin Add End Add. Size Address Location 1 TIME 8 5 296 1 100 1211 1532 322 101227 2 2 GASIN 8 5 296 1 100 1533 1854 322 101549 3 3 GASOUT 8 5 296 1 100 1855 2176 322 101871 4 4 CONSTANT 8 5 296 1 100 2177 2498 322 102193 5 5 %YVAR -8 0 1 1 100 2634 2660 27 102650 11 6 %ARPARMS 8 1 8 1 100 2661 2694 34 102677 12 7 %ARORDER -4 1 8 1 100 2695 2724 30 205421 13 8 %MAPARMS 8 1 1 1 100 2725 2751 27 102741 14 9 %COEF 8 1 9 1 100 3291 3325 35 103307 29 10 %NRES -4 0 1 1 100 3326 3352 27 206683 30 11 %RESOBS -4 1 286 1 100 3353 3521 169 206737 31 12 %AVAR 8 0 1 1 100 3522 3548 27 103538 32 13 %SERIESM 8 0 1 1 100 3549 3575 27 103565 33 14 %CONST 8 0 1 1 100 3576 3602 27 103592 34 15 %RSS 8 0 1 1 100 3603 3629 27 103619 35 16 %SUMABS 8 0 1 1 100 3915 3941 27 103931 36 17 %MAXABS 8 0 1 1 100 4227 4253 27 104243 37 18 %SE 8 1 9 1 100 5074 5108 35 105090 44 19 %T 8 1 9 1 100 5109 5143 35 105125 45 20 %COV 8 2 9 9 100 5144 5250 107 105160 46 21 %CNAME -8 1 9 1 100 10334 10368 35 110350 59 22 %CORDER -4 1 9 1 100 10369 10399 31 220769 60 23 %RES 8 1 288 1 100 10400 10713 314 110416 61 24 %Y 8 1 288 1 100 10714 11027 314 110730 62 25 %YHAT 8 1 288 1 100 11028 11341 314 111044 63 26 %FCAST 8 1 24 1 100 11342 11391 50 111358 64 27 %FCONF 8 1 24 1 100 11392 11441 50 111408 65 28 %FPSI 8 1 24 1 100 11442 11491 50 111458 66 29 %FOREOBS -4 1 24 1 100 11492 11529 38 223015 67 Space available 2874841 , used 11529 , peak used 11744 # Temp varibles 43 , peak # used 71 => CALL PRINT(%ARPARMS,%MAPARMS)$ %ARPARMS= Vector of 8 elements 2.12278 -1.30371 -0.170867 0.351405 -0.526278E-02 0.129982 -0.266970 0.121523 %MAPARMS= Vector of 1 elements 0.00000 => CALL PRINT(%RSS,%CONST)$ %RSS = 30.114693 %CONST = 1.6243174 => CALL TABULATE(%RESOBS,%Y,%RES,%YHAT)$ Obs %RESOBS %Y %RES %YHAT 1 11 52.20 -0.2792E-01 52.23 2 12 52.00 -0.6166E-01 52.06 3 13 52.00 -0.5887E-01 52.06 4 14 52.40 -0.2547E-01 52.43 5 15 53.00 0.3942E-02 53.00 6 16 54.00 0.1995E-01 53.98 7 17 54.90 0.9128E-02 54.89 8 18 56.00 -0.1650 56.17 9 19 56.80 -0.2030 57.00 10 20 56.80 -0.7328E-01 56.87 11 21 56.40 0.5328E-01 56.35 12 22 55.70 -0.5842E-01 55.76 13 23 55.00 -0.1908 55.19 14 24 54.30 0.8586E-01 54.21 15 25 53.20 0.3066 52.89 16 26 52.30 0.7603E-01 52.22 17 27 51.60 0.3617 51.24 18 28 51.20 -0.1700E-01 51.22 19 29 50.80 0.4472 50.35 20 30 50.50 0.1856E-01 50.48 21 31 50.00 -0.4677 50.47 22 32 49.20 0.8098E-01 49.12 23 33 48.40 -0.3343E-01 48.43 24 34 47.90 0.3276E-01 47.87 25 35 47.60 -0.1823 47.78 26 36 47.50 -0.6076 48.11 27 37 47.50 0.1190 47.38 28 38 47.60 -0.2713E-01 47.63 29 39 48.10 -0.7598E-01 48.18 30 40 49.00 -0.3577 49.36 31 41 50.00 -0.1500 50.15 32 42 51.10 -0.3206 51.42 33 43 51.80 -0.4734 52.27 34 44 51.90 -0.1554 52.06 35 45 51.70 -0.7821E-02 51.71 36 46 51.20 -0.2217 51.42 37 47 50.00 -0.2141 50.21 38 48 48.30 -0.1680 48.47 39 49 47.00 -0.7114E-01 47.07 40 50 45.80 0.2535 45.55 41 51 45.60 0.2046 45.40 42 52 46.00 -0.3472E-01 46.03 43 53 46.90 0.1598 46.74 44 54 47.80 -0.1832 47.98 45 55 48.20 -0.2786 48.48 46 56 48.30 0.2467E-01 48.28 47 57 47.90 -0.1777 48.08 48 58 47.20 -0.7507 47.95 49 59 47.20 -0.6062 47.81 50 60 48.10 0.2046 47.90 51 61 49.40 -0.4423 49.84 52 62 50.60 0.3064 50.29 53 63 51.50 -0.6508E-01 51.57 54 64 51.60 0.1471E-01 51.59 55 65 51.20 -0.1323 51.33 56 66 50.50 -0.4762 50.98 57 67 50.10 -0.2426E-01 50.12 58 68 49.80 -0.4118 50.21 59 69 49.60 -0.3351 49.94 60 70 49.40 0.5248 48.88 61 71 49.30 0.4855 48.81 62 72 49.20 -0.2466E-01 49.22 63 73 49.30 -0.1826 49.48 64 74 49.70 0.4504E-01 49.65 65 75 50.30 -0.3231 50.62 66 76 51.30 -0.1474 51.45 67 77 52.80 -0.1609 52.96 68 78 54.40 0.1820 54.22 69 79 56.00 -0.1985 56.20 70 80 56.90 -0.2163 57.12 71 81 57.50 -0.1258 57.63 72 82 57.30 -0.7085E-02 57.31 73 83 56.60 -0.1144 56.71 74 84 56.00 0.1580E-01 55.98 75 85 55.40 0.1426 55.26 76 86 55.40 0.3534E-01 55.36 77 87 56.40 0.3439 56.06 78 88 57.20 0.5200 56.68 79 89 58.00 0.2126 57.79 80 90 58.40 0.3063 58.09 81 91 58.40 -0.2093 58.61 82 92 58.10 0.3343 57.77 83 93 57.70 -0.2654 57.97 84 94 57.00 -0.1596 57.16 85 95 56.00 0.3313 55.67 86 96 54.70 -0.1110 54.81 87 97 53.20 0.4500 52.75 88 98 52.10 0.7780 51.32 89 99 51.60 -0.3633 51.96 90 100 51.00 0.2145 50.79 91 101 50.50 0.4240E-01 50.46 92 102 50.40 0.2442E-01 50.38 93 103 51.00 0.1947E-01 50.98 94 104 51.80 -0.9332E-02 51.81 95 105 52.40 -0.2247 52.62 96 106 53.00 -0.3213 53.32 97 107 53.40 -0.3097 53.71 98 108 53.60 -0.3249 53.92 99 109 53.70 0.1279 53.57 100 110 53.80 0.1049 53.70 101 111 53.80 -0.6519 54.45 102 112 53.80 -0.2061 54.01 103 113 53.30 0.2534 53.05 104 114 53.00 0.4506 52.55 105 115 52.90 -0.1301 53.03 106 116 53.40 -0.3371 53.74 107 117 54.60 0.2454 54.35 108 118 56.40 0.4490E-01 56.36 109 119 58.00 -0.4500E-01 58.04 110 120 59.40 0.3892E-02 59.40 111 121 60.20 0.8137E-01 60.12 112 122 60.00 -0.4110E-01 60.04 113 123 59.40 0.2316E-01 59.38 114 124 58.40 -0.4586 58.86 115 125 57.60 0.2761 57.32 116 126 56.90 0.1534 56.75 117 127 56.40 0.3785 56.02 118 128 56.00 0.5257 55.47 119 129 55.70 0.5038 55.20 120 130 55.30 0.3124E-01 55.27 121 131 55.00 0.3158 54.68 122 132 54.40 0.1120 54.29 123 133 53.70 -0.3691 54.07 124 134 52.80 0.1746 52.63 125 135 51.60 -0.1337 51.73 126 136 50.60 0.2256 50.37 127 137 49.40 -0.8144E-01 49.48 128 138 48.80 -0.2421E-01 48.82 129 139 48.50 0.5575E-02 48.49 130 140 48.70 -0.1354E-01 48.71 131 141 49.20 -0.1477 49.35 132 142 49.80 0.2385E-01 49.78 133 143 50.40 -0.3752 50.78 134 144 50.70 -0.1823 50.88 135 145 50.90 -0.2873 51.19 136 146 50.70 -0.4957 51.20 137 147 50.50 -0.1150E-01 50.51 138 148 50.40 -0.5955 51.00 139 149 50.20 0.2022 50.00 140 150 50.40 -0.1752 50.58 141 151 51.20 0.2243E-01 51.18 142 152 52.30 0.2144E-01 52.28 143 153 53.20 -0.1069 53.31 144 154 53.90 0.4251E-01 53.86 145 155 54.10 -0.2562 54.36 146 156 54.00 0.4170E-01 53.96 147 157 53.60 -0.3306 53.93 148 158 53.20 0.2312E-01 53.18 149 159 53.00 0.5004E-01 52.95 150 160 52.80 -0.2799 53.08 151 161 52.30 0.2997 52.00 152 162 51.90 0.4478 51.45 153 163 51.60 0.1531 51.45 154 164 51.60 -0.1867 51.79 155 165 51.40 0.8613E-01 51.31 156 166 51.20 -0.9499E-01 51.29 157 167 50.70 -0.2737E-02 50.70 158 168 50.00 -0.1469 50.15 159 169 49.40 0.1108E-01 49.39 160 170 49.30 0.1345 49.17 161 171 49.70 -0.1790 49.88 162 172 50.60 -0.3920 50.99 163 173 51.80 0.9429E-01 51.71 164 174 53.00 0.2654E-01 52.97 165 175 54.00 0.8304E-01 53.92 166 176 55.30 -0.4340 55.73 167 177 55.90 -0.1015 56.00 168 178 55.90 -0.2985 56.20 169 179 54.60 -0.2908 54.89 170 180 53.50 -0.2761E-01 53.53 171 181 52.40 0.1858 52.21 172 182 52.10 0.1333 51.97 173 183 52.30 0.1673 52.13 174 184 53.00 0.2042 52.80 175 185 53.80 0.1124 53.69 176 186 54.60 0.9406E-01 54.51 177 187 55.40 0.6645 54.74 178 188 55.90 -0.4091 56.31 179 189 55.90 -0.2305 56.13 180 190 55.20 -0.8355 56.04 181 191 54.40 0.5301 53.87 182 192 53.70 -0.8916E-01 53.79 183 193 53.60 0.2450 53.35 184 194 53.60 0.6418E-01 53.54 185 195 53.20 0.1425 53.06 186 196 52.50 0.1428 52.36 187 197 52.00 0.8692E-01 51.91 188 198 51.40 0.2867 51.11 189 199 51.00 -0.9778E-01 51.10 190 200 50.90 -0.2294 51.13 191 201 52.40 -0.4189 52.82 192 202 53.50 0.1342 53.37 193 203 55.60 0.7285E-01 55.53 194 204 58.00 0.3112 57.69 195 205 59.50 -0.2284 59.73 196 206 60.00 -0.5647 60.56 197 207 60.40 -0.1607 60.56 198 208 60.50 0.2523 60.25 199 209 60.20 -0.3053 60.51 200 210 59.70 -0.1392 59.84 201 211 59.00 0.4453E-01 58.96 202 212 57.60 1.369 56.23 203 213 56.40 -0.7215 57.12 204 214 55.20 1.046 54.15 205 215 54.50 0.7412 53.76 206 216 54.10 -0.5028 54.60 207 217 54.10 -0.9875E-01 54.20 208 218 54.40 0.7003 53.70 209 219 55.50 0.2966 55.20 210 220 56.20 -0.2848 56.48 211 221 57.00 -0.2026E-02 57.00 212 222 57.30 0.3796E-01 57.26 213 223 57.40 -0.5684 57.97 214 224 57.00 0.2106 56.79 215 225 56.40 -0.1797 56.58 216 226 55.90 0.1244 55.78 217 227 55.50 -0.9816E-01 55.60 218 228 55.30 0.4159E-01 55.26 219 229 55.20 0.1717 55.03 220 230 55.40 0.6735 54.73 221 231 56.00 -0.4278 56.43 222 232 56.50 0.2859 56.21 223 233 57.10 -0.1062 57.21 224 234 57.30 0.1128 57.19 225 235 56.80 -0.2022 57.00 226 236 55.60 -0.1118 55.71 227 237 55.00 0.2225 54.78 228 238 54.10 -0.5105E-01 54.15 229 239 54.30 0.7428E-01 54.23 230 240 55.30 -0.2947E-01 55.33 231 241 56.40 0.2685 56.13 232 242 57.20 0.3764 56.82 233 243 57.80 -0.1320 57.93 234 244 58.30 0.2485 58.05 235 245 58.60 -0.1616 58.76 236 246 58.80 -0.4201 59.22 237 247 58.80 -0.3964 59.20 238 248 58.60 0.7126 57.89 239 249 58.00 -0.5599 58.56 240 250 57.40 0.7227 56.68 241 251 57.00 0.5148 56.49 242 252 56.40 -0.1510 56.55 243 253 56.30 -0.3692E-01 56.34 244 254 56.40 0.2132 56.19 245 255 56.40 0.4227 55.98 246 256 56.00 0.5605E-02 55.99 247 257 55.20 0.8060E-01 55.12 248 258 54.00 0.2564E-01 53.97 249 259 53.00 0.3326E-01 52.97 250 260 52.00 -0.2089 52.21 251 261 51.60 0.1333 51.47 252 262 51.60 0.2132 51.39 253 263 51.10 -0.3588 51.46 254 264 50.40 0.4176 49.98 255 265 50.00 0.8864E-01 49.91 256 266 50.00 -0.1945 50.19 257 267 52.00 -0.3304 52.33 258 268 54.00 -0.2675 54.27 259 269 55.10 -0.2823 55.38 260 270 54.50 0.5567E-01 54.44 261 271 52.80 -0.3489 53.15 262 272 51.40 0.1830 51.22 263 273 50.80 0.1482E-01 50.79 264 274 51.20 -0.8352 52.04 265 275 52.00 -0.2050 52.21 266 276 52.80 0.2712 52.53 267 277 53.80 0.1290 53.67 268 278 54.50 1.570 52.93 269 279 54.90 -0.4857 55.39 270 280 54.90 -0.7733 55.67 271 281 54.80 -0.8038 55.60 272 282 54.40 -0.2313 54.63 273 283 53.70 0.6692 53.03 274 284 53.30 0.1349 53.17 275 285 52.80 0.1835 52.62 276 286 52.60 -0.1449 52.74 277 287 52.60 -0.1258E-01 52.61 278 288 53.00 0.5311 52.47 279 289 54.30 -0.5469E-01 54.35 280 290 56.00 -0.6843E-01 56.07 281 291 57.00 -0.1530 57.15 282 292 58.00 0.1166 57.88 283 293 58.60 -0.1825 58.78 284 294 58.50 -0.3143 58.81 285 295 58.30 0.3139 57.99 286 296 57.80 -0.2694 58.07 287 NA 57.30 0.1127 57.19 288 NA 57.00 0.2529E-01 56.97 => CALL PRINT(%YVAR,%ARORDER,%ARPARMS)$ %YVAR = GASOUT %ARORDER= Vector of 8 elements 1 2 3 4 5 6 7 8 %ARPARMS= Vector of 8 elements 2.12278 -1.30371 -0.170867 0.351405 -0.526278E-02 0.129982 -0.266970 0.121523 => CALL GRAPH(%RES)$ => CALL GRAPH(%Y,%YHAT)$ => CALL GRAPH(ACF(%RES))$ => CALL TABULATE(%FOREOBS,%FCAST,%FCONF,%FPSI)$ Obs %FOREOBS %FCAST %FCONF %FPSI 1 297 57.28 0.6353 2.123 2 298 58.13 1.491 3.202 3 299 59.52 2.522 3.860 4 300 61.18 3.518 4.007 5 301 62.90 4.342 3.668 6 302 64.48 4.928 3.146 7 303 65.84 5.318 2.561 8 304 66.96 5.561 2.066 9 305 67.86 5.714 1.683 10 306 68.60 5.813 1.407 11 307 69.20 5.881 1.199 12 308 69.69 5.930 1.052 13 309 70.12 5.968 0.9493 14 310 70.49 5.998 0.8917 15 311 70.85 6.025 0.8676 16 312 71.20 6.050 0.8650 17 313 71.55 6.075 0.8655 18 314 71.91 6.100 0.8574 19 315 72.26 6.124 0.8323 20 316 72.61 6.147 0.7908 21 317 72.94 6.168 0.7368 22 318 73.25 6.185 0.6768 23 319 73.54 6.200 0.6159 24 320 73.80 6.213 0.5582 B34S Matrix Command Ending. Last Command reached. Space available in allocator 2874841, peak space used 12805 Number variables used 67, peak number used 71 Number temp variables used 50, # user temp clean 0 B34S 8.10R (D:M:Y) 8/ 6/04 (H:M:S) 14:49:29 DATA STEP Stokes-Neuburger RES 79 PAGE 5 Variable Label # Cases Mean Std. Dev. Variance Maximum Minimum FMS 1 MONEY STOCK M1 : FRIEDMAN 372 177.016 62.0064 3844.80 337.400 109.700 FMSCOM 2 MONEY STOCK M2 : FRIEDMAN 372 334.358 204.474 41809.5 888.300 143.200 FYAAC 3 MONETARY RATES : AA NEW CORPORATE BOND 372 5.39742 2.23559 4.99785 10.4400 2.48000 FYCP 4 MONETARY RATES : COMMERCIAL PAPER 372 4.17392 2.25080 5.06610 11.7200 1.00000 PC 5 CONSUMER PRICE INDEX : ALL ITEMS 372 101.501 29.9450 896.705 186.900 64.3000 FYGM3 6 MARKET YIELD ON 3 MONTH TREASURY 372 3.50927 2.00188 4.00754 8.96000 0.380000 FYGN3 7 NEW ISSUE RATE ON 3 MONTH TR 372 3.52967 2.00428 4.01714 8.74400 0.376000 M1DP 8 M1 / PC 372 1.71876 0.126372 0.159700E-01 2.01644 1.52078 M2DP 9 M2 / PC 372 3.04266 0.926131 0.857718 4.75281 1.99483 PCM1 10 PERCENT CHANGE M1 372 0.303525E-02 0.334316E-02 0.111767E-04 0.161699E-01 -0.530035E-02 PCM2 11 PERCENT CHANGE M2 372 0.493333E-02 0.392165E-02 0.153793E-04 0.167106E-01 -0.661603E-02 PCRM1 12 PERCENT CHANGE REAL M1 372 0.171943E-03 0.468067E-02 0.219087E-04 0.112360E-01 -0.197522E-01 PCRM2 13 PERCENT CHANGE REAL M2 372 0.206419E-02 0.502895E-02 0.252903E-04 0.150076E-01 -0.185707E-01 PCAA 14 PERCENT CHANGE AA CORP RATE 372 0.399916E-02 0.369309E-01 0.136389E-02 0.138191 -0.153846 PCCPIN 15 PERCENT CHANGE COMMERCIAL PAPER 372 0.699893E-02 0.617652E-01 0.381494E-02 0.494898 -0.246418 PCCMYTB 16 PERCENT CHANGE THREE MONTH TREASURY 372 0.117791E-01 0.966819E-01 0.934739E-02 0.857143 -0.368852 PCCNYTB 17 PERCENT CHANGE THREE MONTH NEW ISSUES 372 0.117452E-01 0.944909E-01 0.892853E-02 0.752599 -0.398768 CONSTANT 18 372 1.00000 0.00000 0.00000 1.00000 1.00000 Number of observations in data file 372 Current missing variable code 1.000000000000000E+31 Data begins on (D:M:Y) 1: 2:1947 ends 1: 1:1978. Frequency is 12 B34S(r) Matrix Command. Version February 2004. Date of Run d/m/y 8/ 6/04. Time of Run h:m:s 14:49:29. => CALL LOADDATA$ => DIFF2RM=DIF(DLOG(FMSCOM),2,1)$ => CALL GRAPH(DIFF2RM)$ => CALL ARMA(DIFF2RM :NAR 3 :MAXIT 8000 => :ITPRINT => :PRINT)$ Results from DNSPE/DN2PE WMEAN = 8.509593191055823E-06 CONST = 1.595923576379668E-05 AVAR = 7.038624877596445E-06 PAR 1 2 3 -0.4728 -0.3200 -0.0826 (PMA is not printed since NPMA = 0.) ---------------------------------------------------------------------- Iteration 1 WMEAN = 0.61931083559E-05 PAR 1 2 3 -0.4720 -0.3136 -0.0825 PMA Residual SS (including backcasts) = 0.2587232172038852E-02 Number of residuals = 372 Number of backcasts = 5 ---------------------------------------------------------------------- Final Results, Iteration 2 Parameter Estimate Std. Error t-ratio WMEAN 0.0000062 0.0000746 0.0828430 PAR 1 -0.4719792 0.0522130 -9.0394917 2 -0.3136279 0.0554807 -5.6529197 3 -0.0824996 0.0524344 -1.5733886 CONST = 0.0000115 AVAR = 0.0000071 Residual SS (including backcasts) = 0.0025872 Number of residuals = 372 Residual SS (excluding backcasts) = 0.0025871 Number of residuals = 367 ARIMA Model Estimated Dependent variable DIFF2RM Sum of Squared Residuals 2.587119852770780E-03 Sum of Absolute Error 0.7273894172891342 Maximum absolute Error 1.205085286576660E-02 Large Sample Residual Variance 7.049372625226297E-06 Large Sample Residual SD 2.655065465337210E-03 Number of Residuals 367 => CALL GRAPH(%RES)$ => CALL GRAPH(%Y,%YHAT)$ => ACFRES=ACF(%RES,30)$ => ACFY =ACF(%Y,30)$ => CALL GRAPH(ACFY,ACFRES :NOKEY)$ => CALL TABULATE(ACFRES,ACFY)$ Obs ACFRES ACFY 1 -0.8724E-02 -0.3519 2 -0.3166E-01 -0.1241 3 -0.3540E-01 0.9125E-01 4 -0.7296E-01 -0.5785E-01 5 0.2769E-01 0.1565E-01 6 0.3755E-01 0.9610E-01 7 -0.1429 -0.1414 8 -0.5888E-01 -0.4157E-02 9 -0.1834E-02 0.2516E-01 10 -0.2419E-01 -0.2463E-01 11 0.2405E-01 0.6055E-01 12 -0.9820E-01 -0.5876E-01 13 -0.9349E-01 -0.4513E-01 14 -0.2444E-01 0.2369E-01 15 -0.1847E-01 -0.1815E-01 16 0.6085E-03 -0.2418E-01 17 0.8936E-01 0.1012 18 -0.5467E-01 -0.8008E-01 19 0.7381E-02 0.4194E-02 20 0.2669E-01 0.3872E-01 21 -0.3957E-02 -0.4351E-01 22 0.5712E-01 0.6110E-01 23 -0.4437E-01 -0.8305E-02 24 -0.8547E-01 -0.4274E-01 25 -0.9738E-01 -0.6422E-01 26 0.2345E-01 0.4763E-01 27 0.3620E-01 0.4957E-02 28 0.5469E-01 0.1790E-01 29 0.1400E-01 -0.1222E-01 30 0.6316E-01 0.7515E-01 => * RESTRICTED MODEL $ => CALL ARMA(DIFF2RM :NAR 1 :MAXIT 8000 => :MAORDER IDINT(ARRAY(:3,4,7)) => :ITPRINT => :PRINT)$ ---------------------------------------------------------------------- Iteration 1 WMEAN = 0.10412325118E-04 PAR -0.3348 PMA 1 2 3 -0.0416 0.0011 0.1072 Residual SS (including backcasts) = 0.2705015031165270E-02 Number of residuals = 378 Number of backcasts = 9 ---------------------------------------------------------------------- Iteration 2 WMEAN = 0.83162180813E-05 PAR -0.3453 PMA 1 2 3 -0.0215 0.0112 0.1495 Residual SS (including backcasts) = 0.2676986824871369E-02 Number of residuals = 379 Number of backcasts = 10 ---------------------------------------------------------------------- Iteration 3 WMEAN = 0.64478794105E-06 PAR -0.3443 PMA 1 2 3 -0.0307 0.0111 0.1515 Residual SS (including backcasts) = 0.2676696355010378E-02 Number of residuals = 379 Number of backcasts = 10 ---------------------------------------------------------------------- Iteration 4 WMEAN = 0.52073965472E-06 PAR -0.3444 PMA 1 2 3 -0.0307 0.0109 0.1521 Residual SS (including backcasts) = 0.2676695118422025E-02 Number of residuals = 379 Number of backcasts = 10 ---------------------------------------------------------------------- Iteration 5 WMEAN = 0.52414262268E-06 PAR -0.3444 PMA 1 2 3 -0.0308 0.0109 0.1521 Residual SS (including backcasts) = 0.2676695098004272E-02 Number of residuals = 379 Number of backcasts = 10 ---------------------------------------------------------------------- Iteration 6 WMEAN = 0.52320188732E-06 PAR -0.3444 PMA 1 2 3 -0.0308 0.0108 0.1521 Residual SS (including backcasts) = 0.2676695097529253E-02 Number of residuals = 379 Number of backcasts = 10 ---------------------------------------------------------------------- Iteration 7 WMEAN = 0.52314972862E-06 PAR -0.3444 PMA 1 2 3 -0.0308 0.0108 0.1521 Residual SS (including backcasts) = 0.2676695097516672E-02 Number of residuals = 379 Number of backcasts = 10 ---------------------------------------------------------------------- Final Results, Iteration 8 Parameter Estimate Std. Error t-ratio WMEAN 0.0000005 0.0000925 0.0056575 PAR 1 -0.3444449 0.0493768 -6.9758494 PMA 1 -0.0307630 0.0521041 -0.5904141 2 0.0108463 0.0518210 0.2093025 3 0.1520981 0.0518393 2.9340296 CONST = 0.0000007 AVAR = 0.0000073 Residual SS (including backcasts) = 0.0026767 Number of residuals = 379 Residual SS (excluding backcasts) = 0.0026762 Number of residuals = 369 ARIMA Model Estimated Dependent variable DIFF2RM Sum of Squared Residuals 2.676170103080284E-03 Sum of Absolute Error 0.7286305195038206 Maximum absolute Error 1.271568799816998E-02 Large Sample Residual Variance 7.252493466639205E-06 Large Sample Residual SD 2.693045388893252E-03 Number of Residuals 369 => CALL GRAPH(%RES)$ => CALL GRAPH(%Y,%YHAT)$ => CALL GRAPH(ACF(%RES))$ => CALL GRAPH(%RES)$ => CALL GRAPH(%Y,%YHAT)$ => ACFRES=ACF(%RES,30)$ => ACFY =ACF(%Y,30)$ => CALL GRAPH(ACFY,ACFRES :NOKEY)$ => CALL TABULATE(ACFRES,ACFY)$ Obs ACFRES ACFY 1 -0.8731E-01 -0.3500 2 -0.2541 -0.1248 3 -0.4967E-02 0.8967E-01 4 -0.5130E-02 -0.5600E-01 5 0.9184E-02 0.1596E-01 6 0.2697E-01 0.9658E-01 7 -0.1709E-02 -0.1406 8 -0.5861E-01 -0.4158E-02 9 -0.2538E-01 0.2808E-01 10 0.2505E-01 -0.2368E-01 11 0.5320E-01 0.5932E-01 12 -0.1104 -0.5955E-01 13 -0.5971E-01 -0.4622E-01 14 0.9893E-02 0.2309E-01 15 -0.2137E-01 -0.1723E-01 16 0.1187E-01 -0.2325E-01 17 0.6777E-01 0.1014 18 -0.6303E-01 -0.7937E-01 19 -0.1690E-01 0.4212E-02 20 0.1278E-01 0.3780E-01 21 -0.1619E-02 -0.4403E-01 22 0.6883E-01 0.6045E-01 23 0.3719E-02 -0.9166E-02 24 -0.8814E-01 -0.4181E-01 25 -0.1096 -0.6295E-01 26 0.5020E-01 0.4789E-01 27 0.5992E-01 0.4973E-02 28 0.1352E-01 0.1730E-01 29 0.1804E-01 -0.1279E-01 30 0.3697E-01 0.7448E-01 B34S Matrix Command Ending. Last Command reached. Space available in allocator 2874753, peak space used 31092 Number variables used 88, peak number used 89 Number temp variables used 94, # user temp clean 0 B34S(r) Matrix Command. Version February 2004. Date of Run d/m/y 8/ 6/04. Time of Run h:m:s 14:49:30. => * WE GENERATE A SERIES AND USE METHOD OF MOMENTS TO GET COEF$ => N=10000$ => NACF=30$ => CALL FREE(MA)$ => AR= ARRAY(:-.9 )$ => NN=100$ => START=ARRAY(:.1)$ => TEST1=GENARMA(AR,MA,1.0,START,.1,N,NN)$ => CALL GRAPH(TEST1)$ => CALL ARMA(TEST1 :NAR 1 MAXIT 8000 => :ITPRINT => :PRINT)$ Results from DNSPE/DN2PE WMEAN = 0.5238836267526759 CONST = 0.9959172179274979 AVAR = 0.1009289557269621 PAR -0.9010 (PMA is not printed since NPMA = 0.) ---------------------------------------------------------------------- Final Results, Iteration 1 Parameter Estimate Std. Error t-ratio WMEAN 0.5238620 0.0016707 313.5625798 PAR 1 -0.9010381 0.0043382 -207.6974218 CONST = 0.9958817 AVAR = 0.1006616 Residual SS (including backcasts) = 1006.4146058 Number of residuals = 10019 Residual SS (excluding backcasts) = 1006.3060986 Number of residuals = 9999 ARIMA Model Estimated Dependent variable TEST1 Sum of Squared Residuals 1006.306098634042 Sum of Absolute Error 2527.391071004215 Maximum absolute Error 1.261610741524308 Large Sample Residual Variance 0.1006406737313452 Large Sample Residual SD 0.3172391428108222 Number of Residuals 9999 => CALL GRAPH(%RES)$ => CALL GRAPH(%Y,%YHAT)$ => ACFRES = ACF(%RES,NACF)$ => ACFY = ACF(%Y, NACF)$ => CALL GRAPH(ACFY,ACFRES :NOKEY)$ => CALL TABULATE(ACFRES,ACFY)$ Obs ACFRES ACFY 1 0.7733E-02 -0.9010 2 0.1247E-01 0.8135 3 -0.5970E-02 -0.7321 4 -0.3258E-02 0.6575 5 0.2161E-02 -0.5908 6 -0.1001E-01 0.5310 7 -0.2354E-02 -0.4789 8 0.1383E-01 0.4315 9 0.1541E-02 -0.3858 10 -0.1142E-01 0.3446 11 0.9663E-02 -0.3096 12 0.2485E-01 0.2800 13 0.1365E-01 -0.2482 14 0.9746E-03 0.2221 15 0.2194E-01 -0.1982 16 0.1511E-02 0.1808 17 0.8394E-02 -0.1651 18 -0.4419E-02 0.1529 19 0.2156E-01 -0.1433 20 0.2000E-01 0.1399 21 -0.1521E-01 -0.1338 22 0.1993E-02 0.1261 23 -0.1186E-01 -0.1194 24 0.8073E-02 0.1115 25 -0.3405E-02 -0.1033 26 0.3438E-02 0.9547E-01 27 -0.4475E-02 -0.8786E-01 28 0.5889E-02 0.8038E-01 29 0.1278E-01 -0.7242E-01 30 -0.1896E-02 0.6765E-01 B34S Matrix Command Ending. Last Command reached. Space available in allocator 2874833, peak space used 197040 Number variables used 61, peak number used 61 Number temp variables used 56, # user temp clean 0 B34S(r) Matrix Command. Version February 2004. Date of Run d/m/y 8/ 6/04. Time of Run h:m:s 14:49:31. => * WE GENERATE A SERIES AND USE METHOD OF MOMENTS TO GET COEF$ => N=10000$ => NACF=30$ => CALL FREE(MA)$ => AR= ARRAY(:-.9 )$ => NN=100$ => START=ARRAY(:.1)$ => TEST1=GENARMA(AR,MA,1.0,START,.1,N,NN)$ => CALL GRAPH(TEST1)$ => CALL ARMA(TEST1 :NAR 4 MAXIT 8000 => :ITPRINT :REFINE 2. => :PRINT)$ Results from DNSPE/DN2PE WMEAN = 0.5238836267526759 CONST = 0.9821867519239629 AVAR = 0.1008995338628706 PAR 1 2 3 4 -0.8930 0.0202 0.0057 -0.0076 (PMA is not printed since NPMA = 0.) ---------------------------------------------------------------------- Iteration 1 WMEAN = 0.52386584695 PAR 1 2 3 4 -0.8931 0.0200 0.0056 -0.0076 PMA Residual SS (including backcasts) = 1006.135737287712 Number of residuals = 10016 Number of backcasts = 20 ---------------------------------------------------------------------- Iteration 2 WMEAN = 0.52386241811 PAR 1 2 3 4 -0.8932 0.0198 0.0055 -0.0076 PMA Residual SS (including backcasts) = 1006.135657365871 Number of residuals = 10016 Number of backcasts = 20 ---------------------------------------------------------------------- Iteration 3 WMEAN = 0.52386191828 PAR 1 2 3 4 -0.8932 0.0197 0.0054 -0.0076 PMA Residual SS (including backcasts) = 1006.135611447726 Number of residuals = 10016 Number of backcasts = 20 ---------------------------------------------------------------------- Final Results, Iteration 4 Parameter Estimate Std. Error t-ratio WMEAN 0.5238619 0.0016927 309.4846724 PAR 1 -0.8933312 0.0100023 -89.3121801 2 0.0194629 0.0134122 1.4511301 3 0.0051936 0.0134113 0.3872524 4 -0.0076607 0.0100007 -0.7660174 CONST = 0.9829406 AVAR = 0.1006639 Residual SS (including backcasts) = 1006.1355737 Number of residuals = 10016 Residual SS (excluding backcasts) = 1006.0255721 Number of residuals = 9996 Revised Model ************* AR orders 1 ---------------------------------------------------------------------- Iteration 1 WMEAN = 0.52386171151 PAR -0.9010 PMA Residual SS (including backcasts) = 1006.414606861928 Number of residuals = 10019 Number of backcasts = 20 ---------------------------------------------------------------------- Final Results, Iteration 2 Parameter Estimate Std. Error t-ratio WMEAN 0.5238620 0.0016707 313.5625779 PAR 1 -0.9010381 0.0043382 -207.6974193 CONST = 0.9958817 AVAR = 0.1006616 Residual SS (including backcasts) = 1006.4146058 Number of residuals = 10019 Residual SS (excluding backcasts) = 1006.3060986 Number of residuals = 9999 ARIMA Model Estimated Dependent variable TEST1 Sum of Squared Residuals 1006.306098628913 Sum of Absolute Error 2527.391071233673 Maximum absolute Error 1.261610731979675 Large Sample Residual Variance 0.1006406737308313 Large Sample Residual SD 0.3172391428100121 Number of Residuals 9999 => CALL GRAPH(%RES)$ => CALL GRAPH(%Y,%YHAT)$ => ACFRES = ACF(%RES,NACF)$ => ACFY = ACF(%Y, NACF)$ => CALL GRAPH(ACFY,ACFRES :NOKEY)$ => CALL TABULATE(ACFRES,ACFY)$ Obs ACFRES ACFY 1 0.7733E-02 -0.9010 2 0.1247E-01 0.8135 3 -0.5970E-02 -0.7321 4 -0.3258E-02 0.6575 5 0.2161E-02 -0.5908 6 -0.1001E-01 0.5310 7 -0.2354E-02 -0.4789 8 0.1383E-01 0.4315 9 0.1541E-02 -0.3858 10 -0.1142E-01 0.3446 11 0.9663E-02 -0.3096 12 0.2485E-01 0.2800 13 0.1365E-01 -0.2482 14 0.9747E-03 0.2221 15 0.2194E-01 -0.1982 16 0.1511E-02 0.1808 17 0.8394E-02 -0.1651 18 -0.4419E-02 0.1529 19 0.2156E-01 -0.1433 20 0.2000E-01 0.1399 21 -0.1521E-01 -0.1338 22 0.1993E-02 0.1261 23 -0.1186E-01 -0.1194 24 0.8073E-02 0.1115 25 -0.3405E-02 -0.1033 26 0.3438E-02 0.9547E-01 27 -0.4475E-02 -0.8786E-01 28 0.5889E-02 0.8038E-01 29 0.1278E-01 -0.7242E-01 30 -0.1896E-02 0.6765E-01 B34S Matrix Command Ending. Last Command reached. Space available in allocator 2874833, peak space used 337699 Number variables used 74, peak number used 74 Number temp variables used 71, # user temp clean 0 B34S(r) Matrix Command. Version February 2004. Date of Run d/m/y 8/ 6/04. Time of Run h:m:s 14:49:32. => * WE GENERATE SERIES AND USE METHOD OF MOMENTS TO GET COEF$ => * MM GETS A GOOD STARTING VALUES FOR UNRESTRICTED MODELS $ => PROGRAM TESTIT$ => N=10000$ => NACF=30$ => * MODEL IS WAY TOO BIG !!!! $ => * REFINE REMOVES EXCESS PARAMATERS $ => NAR=9$ => NMA=0$ => CALL FREE(MA)$ => CALL FREE(AR)$ => IF(NAR.GT.0)AR= ARRAY(: .70, -.43 )$ => IF(NMA.GT.0)MA= ARRAY(:-.6 )$ => START=ARRAY(:.1 .1)$ => CALL TESTIT$ => NN=100$ => TEST1=GENARMA(AR,MA,1.0,START,.1,N,NN)$ => CALL GRAPH(TEST1)$ => CALL ARMA(TEST1 :NAR NAR :MAXIT 8000 => :NMA NMA :REFINE 2. => :PRINT)$ Results from DNSPE/DN2PE WMEAN = 1.363516793214166 CONST = 1.000503541758781 AVAR = 0.1008055400300905 PAR 1 2 3 4 5 6 7 8 0.7070 -0.4210 -0.0140 0.0079 0.0002 -0.0116 0.0036 0.0108 9 -0.0166 (PMA is not printed since NPMA = 0.) ---------------------------------------------------------------------- Final Results, Iteration 2 Parameter Estimate Std. Error t-ratio WMEAN 1.3635420 0.0043320 314.7604223 PAR 1 0.7063954 0.0100035 70.6150514 2 -0.4208022 0.0122483 -34.3560096 3 -0.0141510 0.0129512 -1.0926429 4 0.0085148 0.0129516 0.6574312 5 0.0002812 0.0129531 0.0217110 6 -0.0116603 0.0129536 -0.9001586 7 0.0041421 0.0129534 0.3197658 8 0.0105804 0.0122518 0.8635748 9 -0.0164736 0.0100043 -1.6466440 CONST = 0.9997125 AVAR = 0.1007531 Residual SS (including backcasts) = 1006.5235225 Number of residuals = 10003 Residual SS (excluding backcasts) = 1006.4316066 Number of residuals = 9991 Revised Model ************* AR orders 1 2 ---------------------------------------------------------------------- Final Results, Iteration 1 Parameter Estimate Std. Error t-ratio WMEAN 1.3634199 0.0044178 308.6213444 PAR 1 0.7097023 0.0090357 78.5446756 2 -0.4285743 0.0090371 -47.4237146 CONST = 0.9801244 AVAR = 0.1007786 Residual SS (including backcasts) = 1007.4835791 Number of residuals = 10006 Residual SS (excluding backcasts) = 1007.3896609 Number of residuals = 9998 ARIMA Model Estimated Dependent variable TEST1 Sum of Squared Residuals 1007.389660901021 Sum of Absolute Error 2530.302979747414 Maximum absolute Error 1.261231382883444 Large Sample Residual Variance 0.1007591174050590 Large Sample Residual SD 0.3174257667629693 Number of Residuals 9998 => CALL GRAPH(%RES)$ => CALL GRAPH(%Y,%YHAT)$ => ACFRES = ACF(%RES,NACF)$ => ACFY = ACF(%Y, NACF)$ => CALL GRAPH(ACFY,ACFRES :NOKEY)$ => CALL TABULATE(ACFRES,ACFY)$ Obs ACFRES ACFY 1 -0.3098E-02 0.4972 2 0.5239E-02 -0.7524E-01 3 -0.9028E-02 -0.2711 4 -0.1807E-03 -0.1608 5 0.3959E-02 -0.7747E-03 6 -0.8488E-02 0.6418E-01 7 -0.3712E-02 0.5026E-01 8 0.1392E-01 0.1240E-01 9 0.1093E-02 -0.2171E-01 10 -0.1135E-01 -0.2520E-01 11 0.9212E-02 0.6035E-02 12 0.2508E-01 0.3366E-01 13 0.1309E-01 0.3137E-01 14 0.1303E-02 0.1692E-01 15 0.2107E-01 0.8978E-02 16 0.1004E-02 -0.3120E-02 17 0.7465E-02 -0.4316E-02 18 -0.4726E-02 0.7986E-02 19 0.2177E-01 0.2975E-01 20 0.2032E-01 0.2459E-01 21 -0.1544E-01 -0.4893E-02 22 0.1635E-02 -0.1684E-01 23 -0.1176E-01 -0.1347E-01 24 0.8113E-02 0.1113E-02 25 -0.3129E-02 0.3761E-02 26 0.3814E-02 0.1219E-02 27 -0.5133E-02 -0.5592E-03 28 0.6472E-02 0.7018E-02 29 0.1219E-01 0.1114E-01 30 -0.2266E-02 0.5422E-02 => RETURN$ => * CORRECT MODEL $ => NAR=2$ => NMA=1$ => CALL FREE(MA)$ => CALL FREE(AR)$ => IF(NAR.GT.0)AR= ARRAY(: .70, -.43 )$ => IF(NMA.GT.0)MA= ARRAY(: .2 )$ => START=ARRAY(:.1 .1)$ => CALL TESTIT$ => NN=100$ => TEST1=GENARMA(AR,MA,1.0,START,.1,N,NN)$ => CALL GRAPH(TEST1)$ => CALL ARMA(TEST1 :NAR NAR :MAXIT 8000 => :NMA NMA :REFINE 2. => :PRINT)$ Results from DNSPE/DN2PE WMEAN = 1.376126011948332 CONST = 0.9895602935219522 AVAR = 9.780111150512678E-02 PAR 1 2 0.7062 -0.4253 PMA 0.2125 ---------------------------------------------------------------------- Final Results, Iteration 5 Parameter Estimate Std. Error t-ratio WMEAN 1.3761624 0.0034160 402.8537053 PAR 1 0.7110002 0.0240203 29.5999859 2 -0.4271122 0.0114332 -37.3570956 PMA 1 0.2178894 0.0264240 8.2458890 CONST = 0.9854865 AVAR = 0.0977633 Residual SS (including backcasts) = 977.2415726 Number of residuals = 10004 Residual SS (excluding backcasts) = 977.2131765 Number of residuals = 9998 ARIMA Model Estimated Dependent variable TEST1 Sum of Squared Residuals 977.2131765024377 Sum of Absolute Error 2492.926644236500 Maximum absolute Error 1.159847267926922 Large Sample Residual Variance 9.774086581860532E-02 Large Sample Residual SD 0.3126353559957756 Number of Residuals 9998 => CALL GRAPH(%RES)$ => CALL GRAPH(%Y,%YHAT)$ => ACFRES = ACF(%RES,NACF)$ => ACFY = ACF(%Y, NACF)$ => CALL GRAPH(ACFY,ACFRES :NOKEY)$ => CALL TABULATE(ACFRES,ACFY)$ Obs ACFRES ACFY 1 0.4791E-03 0.3850 2 -0.1855E-02 -0.1534 3 -0.1874E-02 -0.2721 4 0.2531E-02 -0.1287 5 -0.8320E-02 0.1746E-01 6 -0.4398E-02 0.6460E-01 7 -0.1348E-01 0.3662E-01 8 0.6247E-02 0.1588E-02 9 -0.8590E-02 -0.3056E-01 10 -0.1956E-01 -0.3551E-01 11 0.3963E-02 -0.7803E-02 12 0.3532E-02 0.1396E-01 13 0.6061E-02 0.2313E-01 14 0.1869E-01 0.1947E-01 15 0.8417E-03 -0.7621E-03 16 0.3657E-02 -0.6687E-02 17 0.7015E-03 0.4037E-02 18 0.1827E-01 0.2035E-01 19 0.1019E-01 0.9959E-02 20 -0.1872E-01 -0.1161E-01 21 0.2863E-02 -0.4046E-02 22 0.8717E-03 0.7200E-03 23 -0.6506E-02 -0.7341E-02 24 -0.2247E-01 -0.1519E-01 25 0.6073E-02 -0.5191E-02 26 -0.1145E-01 -0.1097E-01 27 -0.1263E-01 -0.1055E-01 28 -0.1142E-03 0.3020E-02 29 0.5264E-02 0.9703E-02 30 0.4201E-03 -0.8623E-03 => RETURN$ => * RESTRICTED MODEL $ => CALL ARMA(TEST1 :ARORDER IDINT(ARRAY(:1 2 4)) => :MAXIT 8000 => :MAORDER IDINT(ARRAY(:2) ) => :REFINE 2. => :PRINT)$ ---------------------------------------------------------------------- Final Results, Iteration 4 Parameter Estimate Std. Error t-ratio WMEAN 1.3761630 0.0034808 395.3597476 PAR 1 0.4960955 0.0099354 49.9320362 2 -0.4397101 0.0171809 -25.5929363 3 -0.0596208 0.0094102 -6.3357372 PMA 1 -0.1161967 0.0209078 -5.5575778 CONST = 1.3806154 AVAR = 0.0978108 Residual SS (including backcasts) = 977.6186384 Number of residuals = 10002 Residual SS (excluding backcasts) = 977.5930166 Number of residuals = 9996 ARIMA Model Estimated Dependent variable TEST1 Sum of Squared Residuals 977.5930165697005 Sum of Absolute Error 2493.547591114221 Maximum absolute Error 1.153844935464828 Large Sample Residual Variance 9.779842101526251E-02 Large Sample Residual SD 0.3127273908938303 Number of Residuals 9996 => CALL TABULATE(%CNAME,%CORDER,%COEF,%SE,%T)$ Obs %CNAME %CORDER %COEF %SE %T 1 Const 0 1.381 0.3481E-02 396.6 2 AR 1 0.4961 0.9935E-02 49.93 3 AR 2 -0.4397 0.1718E-01 -25.59 4 AR 4 -0.5962E-01 0.9410E-02 -6.336 5 MA 2 -0.1162 0.2091E-01 -5.558 => CALL GRAPH(%RES)$ => CALL GRAPH(%Y,%YHAT)$ => ACFRES = ACF(%RES,NACF)$ => ACFY = ACF(%Y, NACF)$ => CALL GRAPH(ACFY,ACFRES :NOKEY)$ => CALL TABULATE(ACFRES,ACFY)$ Obs ACFRES ACFY 1 -0.2461E-02 0.3851 2 0.6457E-03 -0.1534 3 -0.1171E-01 -0.2722 4 0.4314E-02 -0.1287 5 -0.1452E-01 0.1746E-01 6 -0.1041E-01 0.6462E-01 7 -0.1379E-01 0.3641E-01 8 0.8687E-02 0.1356E-02 9 -0.6881E-02 -0.3091E-01 10 -0.1917E-01 -0.3605E-01 11 0.3167E-02 -0.7937E-02 12 0.3052E-02 0.1404E-01 13 0.5921E-02 0.2325E-01 14 0.1881E-01 0.1978E-01 15 0.9291E-03 -0.5195E-03 16 0.3617E-02 -0.6615E-02 17 0.6344E-03 0.3935E-02 18 0.1816E-01 0.2042E-01 19 0.1002E-01 0.1012E-01 20 -0.1872E-01 -0.1157E-01 21 0.3142E-02 -0.4289E-02 22 0.7251E-03 0.5103E-03 23 -0.6285E-02 -0.7362E-02 24 -0.2261E-01 -0.1517E-01 25 0.6269E-02 -0.5175E-02 26 -0.1124E-01 -0.1112E-01 27 -0.1240E-01 -0.1056E-01 28 -0.2913E-03 0.3290E-02 29 0.5599E-02 0.1001E-01 30 0.4420E-03 -0.8388E-03 B34S Matrix Command Ending. Last Command reached. Space available in allocator 2874529, peak space used 598830 Number variables used 87, peak number used 87 Number temp variables used 180, # user temp clean 0 B34S 8.10R (D:M:Y) 8/ 6/04 (H:M:S) 14:49:35 DATA STEP PAGE 6 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+31 B34S(r) Matrix Command. Version February 2004. Date of Run d/m/y 8/ 6/04. Time of Run h:m:s 14:49:35. => CALL LOADDATA$ => CALL LOAD(GARCH2P)$ => * THIS SETTING IS WAY TOO BIG BUT TESTS SOFTWARE $ => NAR=70$ => NMA=0$ => GNAR=1$ => GNMA=0$ => CALL GARCH2P(GASOUT,NAR,NMA,COEF1,SE1,T1,GNAR,GNMA,COEF2,SE2,T2, => RES1,RES2,2.0)$ => CALL PRINT('First Moment Model ***************')$ => First Moment Model *************** => MM=2000$ => CALL ARMA(DATA :NAR NAR :NMA NMA :PRINT :REFINE REFINE => :MAXIT MM )$ Results from DNSPE/DN2PE WMEAN = 53.50912162162156 CONST = 1.946650940499152 AVAR = 0.1593013192084598 PAR 1 2 3 4 5 6 7 8 9 10 1.832 -0.763 -0.309 0.076 0.155 0.041 -0.043 -0.003 -0.170 0.198 11 12 13 14 15 16 17 18 19 20 0.061 -0.085 -0.128 0.137 -0.050 0.119 -0.168 0.056 -0.033 0.092 21 22 23 24 25 26 27 28 29 30 0.006 -0.094 0.059 -0.058 0.053 0.019 0.015 -0.018 -0.117 0.062 31 32 33 34 35 36 37 38 39 40 0.031 -0.030 0.257 -0.343 0.059 0.100 -0.055 0.031 -0.002 -0.078 41 42 43 44 45 46 47 48 49 50 0.061 0.062 -0.036 -0.081 0.016 0.107 -0.037 -0.086 0.020 0.059 51 52 53 54 55 56 57 58 59 60 -0.072 0.083 -0.027 -0.100 0.049 0.096 -0.002 -0.104 -0.008 0.049 61 62 63 64 65 66 67 68 69 70 0.038 -0.158 0.272 -0.145 -0.030 -0.003 0.055 -0.041 0.005 0.008 (PMA is not printed since NPMA = 0.) ---------------------------------------------------------------------- Final Results, Iteration 28 Parameter Estimate Std. Error t-ratio WMEAN 53.3026622 0.7098511 75.0899157 PAR 1 2.1420832 0.0660185 32.4467190 2 -1.3304864 0.1558631 -8.5362496 3 -0.1744297 0.1778991 -0.9804978 4 0.3772310 0.1771267 2.1297238 5 -0.0672414 0.1776078 -0.3785947 6 0.2472858 0.1768329 1.3984148 7 -0.3065771 0.1775211 -1.7269896 8 -0.0545465 0.1793598 -0.3041176 9 0.1297477 0.1793423 0.7234643 10 0.2079562 0.1789209 1.1622801 11 -0.2562800 0.1810142 -1.4158001 12 0.0874515 0.1831124 0.4775837 13 -0.2023306 0.1876758 -1.0780856 14 0.3067033 0.1879930 1.6314610 15 -0.1289212 0.1898485 -0.6790742 16 0.0444284 0.1900934 0.2337187 17 -0.1473746 0.1907049 -0.7727887 18 0.2012363 0.1909804 1.0537011 19 -0.3177629 0.1889926 -1.6813509 20 0.4049283 0.1941364 2.0857929 21 -0.1336577 0.1957087 -0.6829422 22 -0.1216748 0.1950267 -0.6238881 23 0.0125595 0.1907691 0.0658363 24 -0.0245692 0.1921246 -0.1278814 25 0.2900444 0.1921384 1.5095599 26 -0.3025763 0.1947714 -1.5534945 27 0.1949485 0.1948858 1.0003217 28 -0.1864876 0.1970354 -0.9464676 29 -0.0532732 0.1964962 -0.2711159 30 0.4158509 0.1979161 2.1011474 31 -0.4134531 0.2009548 -2.0574433 32 0.0613388 0.2072072 0.2960263 33 0.2604525 0.2055193 1.2672895 34 -0.3353294 0.2056492 -1.6305897 35 0.2766261 0.2070192 1.3362339 36 -0.0994055 0.2069178 -0.4804107 37 -0.1467482 0.2050320 -0.7157328 38 0.1168166 0.2029475 0.5756001 39 0.0516900 0.2038930 0.2535155 40 -0.0103865 0.2033465 -0.0510780 41 -0.0566304 0.2019948 -0.2803556 42 -0.0081503 0.2033752 -0.0400753 43 -0.0131332 0.2039967 -0.0643793 44 0.2193165 0.2082052 1.0533672 45 -0.3633156 0.2055898 -1.7671868 46 0.3152946 0.2008324 1.5699392 47 -0.1710820 0.2042851 -0.8374665 48 -0.1139317 0.2053313 -0.5548674 49 0.3964971 0.2000483 1.9820071 50 -0.2956846 0.1996740 -1.4808370 51 -0.1001573 0.2033004 -0.4926567 52 0.2543899 0.2034240 1.2505401 53 -0.0961937 0.1971120 -0.4880154 54 -0.1578147 0.1954060 -0.8076248 55 0.2570112 0.2024404 1.2695648 56 -0.1219959 0.1984066 -0.6148783 57 0.1274885 0.1917401 0.6649023 58 -0.2326167 0.1951878 -1.1917584 59 0.1193741 0.1982764 0.6020589 60 -0.0351294 0.1997220 -0.1758916 61 0.0372767 0.2033729 0.1832925 62 -0.1588183 0.2043079 -0.7773480 63 0.4005085 0.2021841 1.9809102 64 -0.1575344 0.2015903 -0.7814584 65 -0.3176665 0.2033354 -1.5622786 66 0.4163956 0.2023093 2.0582126 67 -0.4427960 0.2024432 -2.1872606 68 0.5022338 0.2095462 2.3967684 69 -0.3469133 0.1875532 -1.8496795 70 0.1017223 0.0783594 1.2981506 CONST = 1.3959208 AVAR = 0.0919256 Residual SS (including backcasts) = 20.6832703 Number of residuals = 246 Residual SS (excluding backcasts) = 19.8182479 Number of residuals = 226 Revised Model ************* AR orders 1 2 4 20 30 31 66 67 68 ---------------------------------------------------------------------- Final Results, Iteration 15 Parameter Estimate Std. Error t-ratio WMEAN 53.7365159 0.9078036 59.1939897 PAR 1 2.0927046 0.0406610 51.4671400 2 -1.3224416 0.0560419 -23.5973854 3 0.2077907 0.0218259 9.5203838 4 -0.0010044 0.0068681 -0.1462426 5 0.0092184 0.0279256 0.3301054 6 -0.0029965 0.0278214 -0.1077039 7 0.0986707 0.0624672 1.5795617 8 -0.2079440 0.1180791 -1.7610572 9 0.1025690 0.0634385 1.6168249 CONST = 1.2592081 AVAR = 0.1015356 Residual SS (including backcasts) = 29.0391883 Number of residuals = 248 Residual SS (excluding backcasts) = 27.2373416 Number of residuals = 228 ARIMA Model Estimated Dependent variable DATA Sum of Squared Residuals 27.23734157792492 Sum of Absolute Error 57.95266594232466 Maximum absolute Error 1.511170319131435 Large Sample Residual Variance 0.1194060111785315 Large Sample Residual SD 0.3455517489154577 Number of Residuals 228 => CALL PRINT('Second Moment Model ***************')$ => Second Moment Model *************** => RES1=AFAM(%RES)$ => COEF1=%COEF$ => SE1=%SE$ => T1=%T$ => DATA2=RES1*RES1$ => CALL ARMA(DATA2 :NAR GNAR :NMA GNMA :PRINT :REFINE REFINE => :MAXIT MM )$ Results from DNSPE/DN2PE WMEAN = 0.1194620244645830 CONST = 0.1013059471536543 AVAR = 6.328870743494999E-02 PAR 0.1520 (PMA is not printed since NPMA = 0.) ---------------------------------------------------------------------- Final Results, Iteration 1 Parameter Estimate Std. Error t-ratio WMEAN 0.1198310 0.0198032 6.0511025 PAR 1 0.1524329 0.0657631 2.3179075 CONST = 0.1015648 AVAR = 0.0637783 Residual SS (including backcasts) = 14.4138869 Number of residuals = 229 Residual SS (excluding backcasts) = 14.4138777 Number of residuals = 227 ARIMA Model Estimated Dependent variable DATA2 Sum of Squared Residuals 14.41387768505192 Sum of Absolute Error 28.86029381896727 Maximum absolute Error 2.181483257761853 Large Sample Residual Variance 6.349725850130265E-02 Large Sample Residual SD 0.2519866236555081 Number of Residuals 227 => RES2=AFAM(%RES)$ => COEF2=%COEF$ => SE2=%SE$ => T2=%T$ => RETURN$ => CALL GRAPH(RES1)$ => CALL GRAPH(RES2)$ => ACF1=ACF(RES1)$ => CALL GRAPH(ACF1)$ => ACF2=ACF(RES2)$ => CALL GRAPH(ACF2)$ => CALL TABULATE(ACF1,ACF2)$ Obs ACF1 ACF2 1 0.1077E-01 -0.3683E-01 2 0.4089E-01 0.2215 3 -0.8873E-01 0.1196 4 -0.4776E-01 0.8176E-01 5 -0.7203E-01 -0.2729E-02 6 0.1559 0.5106E-01 7 0.4380E-01 0.5410E-02 8 -0.8511E-02 -0.5962E-01 9 -0.1408 0.6105E-02 10 0.1277E-01 -0.3262E-01 11 -0.2405E-01 0.1309E-01 12 0.5128E-01 -0.5307E-01 13 -0.5509E-01 -0.4820E-01 14 0.4352E-01 0.1009E-01 15 -0.9865E-01 -0.5383E-01 16 0.2896E-01 0.4396E-02 17 -0.8863E-01 -0.1586E-01 18 0.2445E-01 0.3909E-01 19 -0.1302 -0.2093E-02 20 -0.7245E-02 -0.4178E-01 21 -0.2416E-01 -0.3884E-01 22 0.2723E-01 0.1298E-01 23 -0.6770E-01 -0.1895E-01 24 -0.3405E-01 0.2553E-01 25 -0.1235E-01 0.2519E-01 26 -0.1782E-01 -0.1981E-01 27 0.9001E-01 0.1764E-01 28 0.1070 0.6763E-01 29 -0.5809E-01 -0.3223E-02 30 0.9735E-01 0.3895E-01 31 -0.2338E-01 0.3029E-01 32 -0.2736E-01 0.5383E-01 33 0.8027E-01 0.2509E-01 34 0.3993E-01 0.4683E-01 35 -0.1757E-01 0.2400E-01 36 0.5013E-01 0.9463E-01 37 -0.2488E-02 0.2571E-01 38 -0.3516E-01 0.3731E-02 39 0.1254E-01 -0.3224E-01 40 0.2812E-01 -0.1969E-01 41 0.9520E-03 -0.2940E-01 42 0.1299E-01 -0.6442E-02 43 0.4312E-01 -0.2604E-01 44 0.2433E-01 -0.1550E-01 45 -0.3753E-01 -0.5364E-01 46 0.3738E-01 -0.3130E-01 47 -0.1023E-01 -0.5975E-01 48 -0.8030E-01 0.4056E-01 49 -0.3928E-01 -0.6284E-01 50 -0.5275E-01 0.9925E-03 51 -0.5986E-01 0.1898E-01 52 -0.5276E-02 -0.4220E-01 53 0.2471E-01 -0.3463E-01 54 -0.7470E-01 -0.5159E-01 55 -0.3558E-01 0.1484E-01 56 -0.3551E-01 -0.2801E-01 57 0.4724E-01 NA B34S Matrix Command Ending. Last Command reached. Space available in allocator 2874869, peak space used 47692 Number variables used 74, peak number used 85 Number temp variables used 98, # user temp clean 0 B34S(r) Matrix Command. Version February 2004. Date of Run d/m/y 8/ 6/04. Time of Run h:m:s 14:49:36. => * TESTS ARMA COMMAND FOR VARIOUS ARMA(1,J) MODELS $ => CALL ECHOOFF$ B34S Matrix Command Ending. Last Command reached. Space available in allocator 2874661, peak space used 317608 Number variables used 91, peak number used 93 Number temp variables used 332, # user temp clean 0 B34S(r) Matrix Command. Version February 2004. Date of Run d/m/y 8/ 6/04. Time of Run h:m:s 14:49:38. => * WE GENERATE A SERIES AND FOLLOWING HINICH SHOW THAT$ => * COEF SE IS INVARIANT TO CHANGES IN INPUT VARIANCE $ => N=10000$ => CALL FREE(MA)$ => AR= ARRAY(:.7 )$ => NN=10000$ => START=ARRAY(:.1)$ => VARNOISE=1.$ => TEST1=GENARMA(AR,MA,0.0,START,VARNOISE,N,NN)$ => CALL PRINT('Variance of the series going in ',VARIANCE(TEST1))$ Variance of the series going in 1.8960118 => CALL ARMA(TEST1 :NAR 1 MAXIT 8000 => :ITPRINT => :PRINT)$ Results from DNSPE/DN2PE WMEAN = 5.391207071964162E-02 CONST = 1.643683512234748E-02 AVAR = 0.9797824619142662 PAR 0.6951 (PMA is not printed since NPMA = 0.) ---------------------------------------------------------------------- Final Results, Iteration 1 Parameter Estimate Std. Error t-ratio WMEAN 0.0546521 0.0324713 1.6830906 PAR 1 0.6951819 0.0071889 96.7027561 CONST = 0.0166589 AVAR = 0.9796205 Residual SS (including backcasts) = 9794.2461691 Number of residuals = 10009 Residual SS (excluding backcasts) = 9794.1271976 Number of residuals = 9999 ARIMA Model Estimated Dependent variable TEST1 Sum of Squared Residuals 9794.127197615737 Sum of Absolute Error 7891.723480039392 Maximum absolute Error 3.677202901994603 Large Sample Residual Variance 0.9795106646292879 Large Sample Residual SD 0.9897023111164730 Number of Residuals 9999 => VARNOISE=10.$ => TEST1=GENARMA(AR,MA,0.0,START,VARNOISE,N,NN)$ => CALL PRINT('Variance of the series going in ',VARIANCE(TEST1))$ Variance of the series going in 18.901501 => CALL ARMA(TEST1 :NAR 1 MAXIT 8000 => :ITPRINT => :PRINT)$ Results from DNSPE/DN2PE WMEAN = 9.651022194312027E-04 CONST = 2.949856811677808E-04 AVAR = 9.787753567766003 PAR 0.6943 (PMA is not printed since NPMA = 0.) ---------------------------------------------------------------------- Final Results, Iteration 1 Parameter Estimate Std. Error t-ratio WMEAN -0.0023620 0.1023505 -0.0230774 PAR 1 0.6945875 0.0071879 96.6330059 CONST = -0.0007214 AVAR = 9.7661129 Residual SS (including backcasts) = 97641.5969146 Number of residuals = 10014 Residual SS (excluding backcasts) = 97607.1660605 Number of residuals = 9999 ARIMA Model Estimated Dependent variable TEST1 Sum of Squared Residuals 97607.16606050235 Sum of Absolute Error 24944.39053622673 Maximum absolute Error 13.13174893998882 Large Sample Residual Variance 9.761691000845886 Large Sample Residual SD 3.124370496731443 Number of Residuals 9999 B34S Matrix Command Ending. Last Command reached. Space available in allocator 2874825, peak space used 267034 Number variables used 61, peak number used 64 Number temp variables used 86, # user temp clean 0 B34S(r) Matrix Command. Version February 2004. Date of Run d/m/y 8/ 6/04. Time of Run h:m:s 14:49:38. => * USES NELSON (1976) FORMULA GET R**2 AS A F OF ACF $ => * NEEDS LARGE SAMPLES$ => N=10000$ => CALL FREE(MA)$ => AR= ARRAY(:-.8,.1 )$ => NN=1000$ => START=ARRAY(:.1,.1)$ => AR2=GENARMA(AR,MA,0.0,START,.1,N,NN)$ => AACFAR2=ACF(AR2)$ => CALL GRAPH(AR2)$ => CALL ARMA(AR2 :NAR 2 MAXIT 8000 => :ITPRINT => :PRINT)$ Results from DNSPE/DN2PE WMEAN = -3.424530515597316E-03 CONST = -5.816095120527240E-03 AVAR = 0.1003799217492655 PAR 1 2 -0.7996 0.1013 (PMA is not printed since NPMA = 0.) ---------------------------------------------------------------------- Iteration 1 WMEAN = -0.32330652971E-02 PAR 1 2 -0.7999 0.1013 PMA Residual SS (including backcasts) = 1002.179007499801 Number of residuals = 10018 Number of backcasts = 20 ---------------------------------------------------------------------- Final Results, Iteration 2 Parameter Estimate Std. Error t-ratio WMEAN -0.0032331 0.0018660 -1.7326590 PAR 1 -0.7998755 0.0099499 -80.3905375 2 0.1013063 0.0099488 10.1827252 CONST = -0.0054916 AVAR = 0.1002480 Residual SS (including backcasts) = 1002.1790075 Number of residuals = 10018 Residual SS (excluding backcasts) = 1001.6568885 Number of residuals = 9998 ARIMA Model Estimated Dependent variable AR2 Sum of Squared Residuals 1001.656888453753 Sum of Absolute Error 2519.573077140092 Maximum absolute Error 1.260726021866051 Large Sample Residual Variance 0.1001857254430606 Large Sample Residual SD 0.3165212875037959 Number of Residuals 9998 => GAMMA=MATRIX(2,2:1.0,AACFAR2(1),AACFAR2(1),1.0)$ => PP=VECTOR(2:AACFAR2(1),AACFAR2(2))$ => CALL PRINT(PP,GAMMA,%COEF)$ PP = Vector of 2 elements -0.889770 0.812790 GAMMA = Matrix of 2 by 2 elements 1 2 1 1.00000 -0.889770 2 -0.889770 1.00000 %COEF = Vector of 3 elements -0.549159E-02 -0.799875 0.101306 => RSQ1=PP*INV(GAMMA)*PP$ => TESTRSQ=1.0-(VARIANCE(%RES)/VARIANCE(%Y))$ => CALL PRINT(RSQ1,TESTRSQ)$ RSQ1 = 0.79382801 TESTRSQ = 0.79421016 B34S Matrix Command Ending. Last Command reached. Space available in allocator 2874825, peak space used 208884 Number variables used 61, peak number used 61 Number temp variables used 75, # user temp clean 0 B34S(r) Matrix Command. Version February 2004. Date of Run d/m/y 8/ 6/04. Time of Run h:m:s 14:49:39. => X=ARRAY(3,3:)$ => X=RN(X)$ => CALL PRINT(X)$ X = Array of 3 by 3 elements 1 2 3 1 2.05157 1.27773 -1.32010 2 1.08325 -1.22596 -1.52445 3 0.825589E-01 0.338525 -0.459242 => XFROMI_4=ARRAY(2,2:1 2 3 4)$ => XFROMR_8=ARRAY(2,2:1. 2. 3. 4.)$ => XD1=ARRAY(3:)$ => XD1=RN(XD1)$ => CALL PRINT(XD1,XFROMI_4,XFROMR_8)$ XD1 = Array of 3 elements -0.605638 0.307389 -1.54789 XFROMI_4= Array of 2 by 2 elements 1 2 1 1.00000 2.00000 2 3.00000 4.00000 XFROMR_8= Array of 2 by 2 elements 1 2 1 1.00000 2.00000 2 3.00000 4.00000 => CALL CHARACTER(CC,'abcdefghi')$ => CX =ARRAY(3,3:CC)$ => * PLACE CHARACTER*1 IN CHARACTER*1 WITH DIFFERENT DIMENSIONS$ => CX1 =C1ARRAY(3,3:CC)$ => * PLACE CHARACTER*1 IN CHARACTER*8 $ => CALL CHARACTER(CC,'1234567812345678abcdefghABCDEFGH')$ => CX8 =C8ARRAY(2,2:CC)$ => CALL PRINT(CX,CX1,CX8)$ abc def ghi abc def ghi CX8 = Array of 2 by 2 elements 1 2 1 12345678 12345678 2 abcdefgh ABCDEFGH => * RECODE CX8 INTO ONE ROW AND CHARACTER*1 $ => * TWO WAYS TO DO THE SAME THING $ => NEWCX8 = ARRAY(4:CX8)$ => NEWCX8_1=C8ARRAY(4:CX8)$ => * PLACE CHARACTER*8 INTO CHARACTER*1 $ => NEWCX8_2=C1ARRAY(32:CX8)$ => * RECODE A CHARACTER*1 ARRAY$ => NEWCH1=C1ARRAY(NOROWS(CC),1:CC)$ => CALL PRINT(NEWCX8,NEWCX8_1,NEWCX8_2,NEWCH1)$ NEWCX8 = Array of 4 elements 12345678 abcdefgh 12345678 ABCDEFGH NEWCX8_1= Array of 4 elements 12345678 abcdefgh 12345678 ABCDEFGH NEWCX8_2= 12345678abcdefgh12345678ABCDEFGH 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 a b c d e f g h A B C D E F G H => CALL NAMES(ALL)$ # Name Kind Klass Nrows Ncols Level Begin Add End Add. Size Address Location 1 X 8 6 3 3 100 90 124 35 100104 4 2 XFROMI_4 8 6 2 2 100 236 265 30 100250 9 3 XFROMR_8 8 6 2 2 100 266 295 30 100280 10 4 XD1 8 5 3 1 100 296 324 29 100310 11 5 CX -1 6 3 3 100 353 380 28 100367 13 6 CX1 -1 6 3 3 100 381 408 28 100395 14 7 CC -1 5 32 1 100 409 438 30 100423 15 8 CX8 -8 6 2 2 100 469 498 30 100483 17 9 NEWCX8 -8 5 4 1 100 499 528 30 100513 18 10 NEWCX8_1 -8 5 4 1 100 529 558 30 100543 19 11 NEWCX8_2 -1 5 32 1 100 559 588 30 100573 20 12 NEWCH1 -1 6 32 1 100 589 618 30 100603 21 Space available 2874753 , used 618 , peak used 618 # Temp varibles 39 , peak # used 21 B34S Matrix Command Ending. Last Command reached. Space available in allocator 2874753, peak space used 618 Number variables used 21, peak number used 21 Number temp variables used 39, # user temp clean 0 B34S 8.10R (D:M:Y) 8/ 6/04 (H:M:S) 14:49:39 DATA STEP PAGE 7 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+31 B34S(r) Matrix Command. Version February 2004. Date of Run d/m/y 8/ 6/04. Time of Run h:m:s 14:49:39. => CALL LOADDATA$ => CALL LOAD(RTEST)$ => CALL AUTOBJ(GASOUT :PRINT :NAC 24 :NPAC 24 :NODIF => :AUTOBUILD )$ Time Series Parameter Estimation for Model 1 Data - Z = VAR= GASOUT Observations 296 Differencing on Z - None Transformations Examined - None. Univariate Model Parameters. Parameter Beginning # Type Order Value 1 Mean 53.51 2 Autoregressive 1 1 1.685 3 Autoregressive 1 2 -0.7187 4 Moving average 1 1 -0.4125 5 Moving average 1 2 -0.3325 6 Moving average 1 5 0.2043 7 Moving average 2 4 0.1988 Output at each iteration has been suppressed. Residual output has been suppressed. Initial sum of Squares 32.05175329997294 Iteration stops - Relative parameter change < 4.000000000000000E-03 Correlation Matrix of the Parameters. 1/Cond = 0.7053E-04 1 2 3 4 5 6 7 1 1.0000 2 -0.0175 1.0000 3 0.0202 -0.9855 1.0000 4 -0.0073 0.5729 -0.5723 1.0000 5 -0.0074 0.5374 -0.5192 0.5113 1.0000 6 0.0069 0.0592 -0.0297 0.0563 -0.0907 1.0000 7 0.0056 0.2389 -0.1728 0.0235 0.2401 0.0156 1.0000 End of Estimation for Model 1 Summary of model 1 Data - Z = VAR= GASOUT 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 53.62 52.19 75.41 55.04 0.7110 2 Autoregressive 1 1 1.685 1.575 30.75 1.794 0.5479E-01 3 Autoregressive 1 2 -0.7187 -0.8258 -13.43 -0.6117 0.5351E-01 4 Moving average 1 1 -0.4124 -0.5480 -6.081 -0.2768 0.6781E-01 5 Moving average 1 2 -0.3324 -0.4661 -4.974 -0.1988 0.6682E-01 6 Moving average 1 5 0.2042 0.9589E-01 3.771 0.3124 0.5414E-01 7 Moving average 2 4 0.1990 0.6701E-01 3.016 0.3309 0.6598E-01 Other Information and results. Residual Sum of Squares 32.049219 287 D.F. Residual Mean Square 0.1116697513762220 Number of residuals 294 Residual Standard error 0.3341702431040531 Backforecasting not used in Estimation Autocorrelation Function Data - THE ESTIMATED RESIDUALS - MODEL 1 294 Observations Original Series Mean of the Series -4.816676483364075E-04 St. Dev. of Series 0.3301677085487052 Number of observations 294 S. E. of mean 1.928860348664975E-02 T value of mean (against zero) -2.497161853473658E-02 1- 12 0.02 0.01 0.02 -0.01 -0.04 -0.06 -0.04 0.04 -0.09 0.05 0.04 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 0.2 0.3 0.4 0.8 1.7 2.1 2.6 4.9 5.8 6.4 9.4 13- 24 0.01 0.07 -0.03 0.03 -0.01 0.02 -0.11 0.00 0.01 0.09 0.03 -0.05 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 9.4 10.8 11.2 11.5 11.6 11.7 15.8 15.8 15.9 18.5 18.8 19.4 Mean divided by St. Error (using N in S. D.) 2.501419592036013E-02 Partial Autocorrelations Data - THE ESTIMATED RESIDUALS - MODEL 1 294 Observations Original Series Mean of the Series -4.816676483364075E-04 St. Dev. of Series 0.3301677085487052 Number of observations 294 S. E. of mean 1.928860348664975E-02 T value of mean (against zero) -2.497161853473658E-02 1- 12 0.02 0.01 0.01 -0.01 -0.04 -0.05 -0.03 0.04 -0.09 0.06 0.04 0.10 13- 24 0.00 0.06 -0.04 0.04 0.01 0.03 -0.11 0.00 0.02 0.09 0.03 -0.08 => CALL RTEST(%RES,GASOUT,48)$ => CALL ECHOOFF$ Residual Sum of Squares is: 32.04921864497570 ******************************************************* ** Diagnostics/Summary Stats for Dependent Var: ******************************************************* Print--> Describe Dependent Var: Summary data for series Y Mean 53.50912162162156 Standard Deviation 3.202120786435257 Skewness -5.173145345413963E-02 Kurtosis -0.6089697605545719 6-th order cumulant 2.113810959374490 Maximim 60.50000000000000 Minimum 45.60000000000000 Median 53.50000000000000 Q1 51.20000000000000 Q3 56.00000000000000 Number of Observations 296 Print--> ACF,Std.Err,PACF,Q-Stat,Prob.Q Obs ACFY SEY PACFY MQY PMQY 1 0.9708 0.5812E-01 0.9708 281.8 0.000 2 0.8960 0.9872E-01 -0.8039 522.7 0.000 3 0.7925 0.1232 0.1883 711.8 0.000 4 0.6800 0.1393 0.2600 851.4 0.000 5 0.5745 0.1501 0.5949E-01 951.5 0.000 6 0.4854 0.1574 -0.6258E-01 1023. 0.000 7 0.4161 0.1624 -0.1435E-01 1076. 0.000 8 0.3656 0.1659 0.5490E-01 1117. 0.000 9 0.3304 0.1686 0.5452E-02 1150. 0.000 10 0.3065 0.1708 0.3141E-01 1179. 0.000 11 0.2880 0.1726 -0.1166 1205. 0.000 12 0.2693 0.1743 -0.4302E-01 1228. 0.000 13 0.2473 0.1757 0.5110E-01 1247. 0.000 14 0.2215 0.1768 0.5381E-01 1262. 0.000 15 0.1930 0.1778 -0.4613E-01 1274. 0.000 16 0.1649 0.1785 0.3394E-01 1282. 0.000 17 0.1398 0.1790 -0.3344E-02 1288. 0.000 18 0.1210 0.1794 0.8548E-01 1293. 0.000 19 0.1103 0.1796 0.1655E-01 1297. 0.000 20 0.1078 0.1799 -0.2576E-01 1301. 0.000 21 0.1112 0.1801 -0.4925E-01 1305. 0.000 22 0.1171 0.1803 0.9711E-02 1309. 0.000 23 0.1228 0.1806 0.4906E-01 1314. 0.000 24 0.1259 0.1808 -0.1210E-02 1319. 0.000 25 0.1259 0.1811 0.4331E-02 1324. 0.000 26 0.1224 0.1814 -0.5242E-01 1329. 0.000 27 0.1156 0.1817 0.8768E-02 1334. 0.000 28 0.1064 0.1820 0.2992E-01 1337. 0.000 29 0.9688E-01 0.1822 0.5418E-01 1340. 0.000 30 0.9081E-01 0.1824 0.8003E-01 1343. 0.000 31 0.9019E-01 0.1825 -0.5487E-01 1346. 0.000 32 0.9484E-01 0.1827 -0.5673E-01 1349. 0.000 33 0.1019 0.1828 -0.3483E-01 1352. 0.000 34 0.1054 0.1830 -0.1153 1356. 0.000 35 0.1026 0.1832 0.1173 1360. 0.000 36 0.9244E-01 0.1834 0.6625E-02 1362. 0.000 37 0.7630E-01 0.1836 -0.3389E-01 1364. 0.000 38 0.5757E-01 0.1837 0.2546E-01 1366. 0.000 39 0.3900E-01 0.1837 -0.1561E-01 1366. 0.000 40 0.2235E-01 0.1838 -0.2580E-01 1366. 0.000 41 0.8799E-02 0.1838 -0.3820E-02 1366. 0.000 42 -0.2339E-02 0.1838 -0.5406E-01 1366. 0.000 43 -0.1247E-01 0.1838 -0.6314E-01 1366. 0.000 44 -0.2359E-01 0.1838 -0.1761E-01 1367. 0.000 45 -0.3762E-01 0.1838 -0.5409E-02 1367. 0.000 46 -0.5579E-01 0.1838 -0.5364E-01 1368. 0.000 47 -0.7881E-01 0.1839 -0.6159E-01 1370. 0.000 48 -0.1062 0.1840 -0.3451E-02 1374. 0.000 ******************************************************* ** Diagnostics of standardized residuals ******************************************************* Print--> Describe standardized resid. series Summary data for series RESA Mean -1.456374368131765E-03 Standard Deviation 1.000000000000000 Skewness 0.7290812382504048 Kurtosis 2.773998941497093 6-th order cumulant 21.82011739718559 Maximim 4.848275330811776 Minimum -2.719320286024572 Median 2.525523074603715E-02 Q1 -0.6392286349784683 Q3 0.5305269216261558 Number of Observations 294 Print--> Engle LM Test for standardized res1 series Obs LAG LMVALUE PROB 1 1 5.772 0.9837 2 2 15.30 0.9995 Print--> ACF, Std.Err, PACF, Q-Stat, Prob.Q Obs ACFA SEA PACFA MQA PMQA 1 0.2458E-01 0.5832E-01 0.2458E-01 0.1794 0.6719 2 0.1497E-01 0.5836E-01 0.1437E-01 0.2462 0.8842 3 0.1540E-01 0.5837E-01 0.1469E-01 0.3171 0.9568 4 -0.1170E-01 0.5838E-01 -0.1266E-01 0.3582 0.9858 5 -0.3895E-01 0.5839E-01 -0.3885E-01 0.8150 0.9761 6 -0.5554E-01 0.5848E-01 -0.5370E-01 1.747 0.9414 7 -0.3617E-01 0.5866E-01 -0.3236E-01 2.144 0.9514 8 0.3722E-01 0.5873E-01 0.4160E-01 2.566 0.9586 9 -0.8830E-01 0.5881E-01 -0.8884E-01 4.946 0.8390 10 0.5411E-01 0.5926E-01 0.5640E-01 5.843 0.8282 11 0.4302E-01 0.5943E-01 0.3696E-01 6.413 0.8445 12 0.9863E-01 0.5954E-01 0.9506E-01 9.415 0.6672 13 0.5541E-02 0.6009E-01 -0.4814E-02 9.424 0.7402 14 0.6732E-01 0.6009E-01 0.6354E-01 10.83 0.6991 15 -0.3267E-01 0.6035E-01 -0.4257E-01 11.17 0.7408 16 0.3347E-01 0.6041E-01 0.3918E-01 11.52 0.7765 17 -0.1113E-01 0.6047E-01 0.5859E-02 11.56 0.8263 18 0.2205E-01 0.6048E-01 0.2635E-01 11.71 0.8619 19 -0.1142 0.6051E-01 -0.1057 15.84 0.6681 20 -0.4423E-02 0.6123E-01 0.4198E-02 15.84 0.7263 21 0.8234E-02 0.6124E-01 0.2313E-01 15.86 0.7772 22 0.9144E-01 0.6124E-01 0.8524E-01 18.54 0.6735 23 0.2658E-01 0.6170E-01 0.2851E-01 18.77 0.7147 24 -0.4550E-01 0.6174E-01 -0.8138E-01 19.43 0.7284 25 0.7552E-01 0.6186E-01 0.7380E-01 21.28 0.6769 26 -0.1189E-01 0.6217E-01 -0.3625E-01 21.33 0.7250 27 0.3563E-01 0.6218E-01 0.7189E-01 21.74 0.7505 28 0.6902E-01 0.6225E-01 0.3862E-01 23.30 0.7180 29 -0.1496 0.6251E-01 -0.1432 30.64 0.3824 30 0.5552E-01 0.6371E-01 0.5789E-01 31.66 0.3835 31 -0.2558E-01 0.6388E-01 0.1053E-01 31.88 0.4228 32 -0.5007E-01 0.6391E-01 -0.4390E-01 32.71 0.4320 33 0.9689E-01 0.6404E-01 0.9788E-01 35.84 0.3367 34 0.1399E-02 0.6454E-01 -0.2073E-01 35.84 0.3822 35 0.2529E-01 0.6454E-01 0.1027E-01 36.05 0.4190 36 0.7053E-01 0.6457E-01 0.7750E-01 37.73 0.3900 37 -0.7613E-02 0.6484E-01 -0.5403E-02 37.75 0.4348 38 -0.1221E-01 0.6484E-01 -0.5779E-01 37.80 0.4785 39 -0.1503E-01 0.6485E-01 -0.1670E-01 37.88 0.5209 40 -0.3528E-01 0.6486E-01 -0.2206E-01 38.31 0.5467 41 -0.2004E-01 0.6492E-01 0.5586E-02 38.44 0.5848 42 -0.1036E-01 0.6494E-01 0.1990E-01 38.48 0.6262 43 -0.1228E-01 0.6495E-01 -0.2686E-01 38.53 0.6652 44 0.3625E-01 0.6496E-01 0.2057E-01 38.99 0.6858 45 0.3882E-02 0.6503E-01 -0.7668E-03 39.00 0.7232 46 0.2973E-01 0.6503E-01 0.4405E-01 39.31 0.7468 47 0.2782E-01 0.6507E-01 0.1111E-01 39.58 0.7704 48 -0.2692E-01 0.6511E-01 -0.7959E-01 39.84 0.7930 ******************************************************* ** Diagnostic testing of squared standardized residuals ******************************************************* Print--> ACF, Std.Err, PACF, Q-Stat, Prob.Q Obs ACFB SEB PACFB MQB PMQB 1 0.1403 0.5832E-01 0.1403 5.844 0.1563E-01 2 0.1989 0.5946E-01 0.1828 17.63 0.1483E-03 3 0.1432 0.6168E-01 0.1000 23.77 0.2794E-04 4 0.5261E-01 0.6280E-01 -0.9908E-02 24.60 0.6060E-04 5 -0.8048E-02 0.6295E-01 -0.6039E-01 24.62 0.1651E-03 6 -0.5601E-02 0.6295E-01 -0.2240E-01 24.63 0.4003E-03 7 -0.1798E-01 0.6295E-01 -0.7788E-02 24.72 0.8489E-03 8 -0.5671E-01 0.6297E-01 -0.4238E-01 25.70 0.1180E-02 9 -0.5717E-01 0.6315E-01 -0.3916E-01 26.70 0.1567E-02 10 -0.3091E-01 0.6332E-01 -0.7612E-03 26.99 0.2610E-02 11 -0.1209E-01 0.6337E-01 0.2156E-01 27.04 0.4533E-02 12 -0.4915E-01 0.6338E-01 -0.3366E-01 27.78 0.5948E-02 13 -0.7296E-01 0.6351E-01 -0.6986E-01 29.43 0.5680E-02 14 -0.1742E-01 0.6379E-01 0.4762E-02 29.53 0.8860E-02 15 -0.5004E-01 0.6381E-01 -0.1902E-01 30.31 0.1086E-01 16 -0.3218E-02 0.6394E-01 0.2248E-01 30.31 0.1645E-01 17 -0.1335E-01 0.6394E-01 -0.5903E-02 30.37 0.2381E-01 18 0.3596E-01 0.6395E-01 0.3754E-01 30.78 0.3056E-01 19 -0.2905E-02 0.6402E-01 -0.1025E-01 30.78 0.4269E-01 20 -0.4469E-01 0.6402E-01 -0.6631E-01 31.41 0.4998E-01 21 -0.3821E-01 0.6413E-01 -0.4865E-01 31.88 0.6024E-01 22 0.1608 0.6421E-01 0.1959 40.15 0.1039E-01 23 0.3040E-02 0.6556E-01 -0.7649E-03 40.15 0.1478E-01 24 0.4722E-01 0.6556E-01 -0.6200E-02 40.87 0.1721E-01 25 0.4957E-01 0.6568E-01 -0.5193E-02 41.67 0.1952E-01 26 -0.2197E-01 0.6581E-01 -0.5021E-01 41.82 0.2561E-01 27 0.5601E-02 0.6583E-01 0.8189E-02 41.83 0.3419E-01 28 0.5983E-01 0.6583E-01 0.6666E-01 43.00 0.3478E-01 29 0.1992E-01 0.6602E-01 0.1149E-01 43.13 0.4425E-01 30 0.7824E-01 0.6604E-01 0.8054E-01 45.15 0.3737E-01 31 -0.9479E-02 0.6635E-01 -0.3032E-01 45.18 0.4803E-01 32 0.2100E-01 0.6636E-01 -0.1562E-01 45.33 0.5946E-01 33 0.1346E-01 0.6638E-01 -0.8133E-02 45.39 0.7392E-01 34 0.1213E-01 0.6639E-01 0.1760E-01 45.44 0.9091E-01 35 0.1112E-02 0.6640E-01 0.2076E-01 45.44 0.1113 36 0.8593E-01 0.6640E-01 0.9647E-01 47.93 0.8824E-01 37 0.7469E-02 0.6677E-01 0.1088E-01 47.95 0.1073 38 0.5998E-02 0.6678E-01 -0.2379E-01 47.96 0.1291 39 -0.1811E-02 0.6678E-01 -0.3138E-01 47.96 0.1538 40 -0.1348E-02 0.6678E-01 -0.2536E-01 47.96 0.1813 41 -0.3924E-01 0.6678E-01 -0.2956E-01 48.49 0.1965 42 -0.4146E-01 0.6686E-01 0.1020E-01 49.08 0.2104 43 -0.3908E-01 0.6694E-01 0.1742E-01 49.61 0.2264 44 -0.3574E-01 0.6702E-01 -0.3509E-01 50.06 0.2455 45 -0.6552E-01 0.6709E-01 -0.4118E-01 51.56 0.2327 46 -0.5540E-01 0.6730E-01 -0.6670E-01 52.64 0.2327 47 -0.5587E-01 0.6746E-01 -0.4637E-01 53.74 0.2320 48 0.3264E-01 0.6762E-01 0.1124 54.11 0.2525 ******************************************************* ** Display graphics for Dependent Variable ******************************************************* ******************************************************* ** Display graphics for 1st Moment Residuals ******************************************************* ******************************************************* ** Display graphs for Squared Standardized Residuals ******************************************************* Time Series Parameter Estimation for Model 1 Data - Z = VAR= GASOUT Observations 296 Differencing on Z - 1) 1 of order 1 Transformations Examined - None. Univariate Model Parameters. Parameter Beginning # Type Order Value 1 Autoregressive 1 1 0.6801 2 Moving average 1 1 -0.4604 3 Moving average 1 2 -0.3399 4 Moving average 1 5 0.2148 5 Moving average 1 9 0.8567E-01 6 Moving average 2 4 0.2520 Output at each iteration has been suppressed. Residual output has been suppressed. Initial sum of Squares 33.42264826889216 Iteration stops - Relative parameter change < 4.000000000000000E-03 Correlation Matrix of the Parameters. 1/Cond = 0.1119 1 2 3 4 5 6 1 1.0000 2 0.6120 1.0000 3 0.5608 0.5573 1.0000 4 0.0729 0.0416 -0.0749 1.0000 5 -0.0909 -0.1308 -0.0274 0.0203 1.0000 6 0.2726 0.0867 0.2482 -0.0388 -0.0079 1.0000 End of Estimation for Model 1 Summary of model 1 Data - Z = VAR= GASOUT Observations 296 Differencing on Z - 1) 1 of order 1 Univariate Model Parameters. Parameter Estimated 95 Per Cent # Type Order Value Lower Limit t Upper Limit Std. Error 1 Autoregressive 1 1 0.6801 0.5607 11.39 0.7996 0.5971E-01 2 Moving average 1 1 -0.4603 -0.5990 -6.640 -0.3217 0.6933E-01 3 Moving average 1 2 -0.3399 -0.4736 -5.082 -0.2061 0.6687E-01 4 Moving average 1 5 0.2147 0.1106 4.125 0.3189 0.5206E-01 5 Moving average 1 9 0.8557E-01 -0.2018E-01 1.618 0.1913 0.5287E-01 6 Moving average 2 4 0.2520 0.1310 4.165 0.3730 0.6050E-01 Other Information and results. Residual Sum of Squares 33.422648 288 D.F. Residual Mean Square 0.1160508610784690 Number of residuals 294 Residual Standard error 0.3406623857699423 Backforecasting not used in Estimation Autocorrelation Function Data - THE ESTIMATED RESIDUALS - MODEL 1 294 Observations Original Series Mean of the Series 4.017589613275743E-03 St. Dev. of Series 0.3371443832131860 Number of observations 294 S. E. of mean 1.969618517248465E-02 T value of mean (against zero) 0.2039780585982849 1- 12 0.03 0.03 0.00 0.00 -0.07 -0.13 -0.09 0.00 -0.06 -0.03 -0.01 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 0.2 0.5 0.5 0.5 2.1 6.8 9.3 9.3 10.4 10.7 10.8 12.6 13- 24 -0.02 0.05 -0.09 0.01 -0.04 -0.01 -0.13 -0.04 0.00 0.07 0.01 -0.05 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 12.8 13.7 16.2 16.2 16.8 16.8 21.9 22.4 22.4 24.0 24.1 24.9 Mean divided by St. Error (using N in S. D.) 0.2043258475270483 Partial Autocorrelations Data - THE ESTIMATED RESIDUALS - MODEL 1 294 Observations Original Series Mean of the Series 4.017589613275743E-03 St. Dev. of Series 0.3371443832131860 Number of observations 294 S. E. of mean 1.969618517248465E-02 T value of mean (against zero) 0.2039780585982849 1- 12 0.03 0.03 0.00 -0.01 -0.07 -0.12 -0.08 0.01 -0.06 -0.03 -0.03 0.05 13- 24 -0.05 0.04 -0.11 0.00 -0.04 0.00 -0.13 -0.05 -0.01 0.05 0.00 -0.10 Residual Sum of Squares is: 33.42264799059907 ******************************************************* ** Diagnostics/Summary Stats for Dependent Var: ******************************************************* Print--> Describe Dependent Var: Summary data for series Y Mean 53.50912162162156 Standard Deviation 3.202120786435257 Skewness -5.173145345413963E-02 Kurtosis -0.6089697605545719 6-th order cumulant 2.113810959374490 Maximim 60.50000000000000 Minimum 45.60000000000000 Median 53.50000000000000 Q1 51.20000000000000 Q3 56.00000000000000 Number of Observations 296 Print--> ACF,Std.Err,PACF,Q-Stat,Prob.Q Obs ACFY SEY PACFY MQY PMQY 1 0.9708 0.5812E-01 0.9708 281.8 0.000 2 0.8960 0.9872E-01 -0.8039 522.7 0.000 3 0.7925 0.1232 0.1883 711.8 0.000 4 0.6800 0.1393 0.2600 851.4 0.000 5 0.5745 0.1501 0.5949E-01 951.5 0.000 6 0.4854 0.1574 -0.6258E-01 1023. 0.000 7 0.4161 0.1624 -0.1435E-01 1076. 0.000 8 0.3656 0.1659 0.5490E-01 1117. 0.000 9 0.3304 0.1686 0.5452E-02 1150. 0.000 10 0.3065 0.1708 0.3141E-01 1179. 0.000 11 0.2880 0.1726 -0.1166 1205. 0.000 12 0.2693 0.1743 -0.4302E-01 1228. 0.000 13 0.2473 0.1757 0.5110E-01 1247. 0.000 14 0.2215 0.1768 0.5381E-01 1262. 0.000 15 0.1930 0.1778 -0.4613E-01 1274. 0.000 16 0.1649 0.1785 0.3394E-01 1282. 0.000 17 0.1398 0.1790 -0.3344E-02 1288. 0.000 18 0.1210 0.1794 0.8548E-01 1293. 0.000 19 0.1103 0.1796 0.1655E-01 1297. 0.000 20 0.1078 0.1799 -0.2576E-01 1301. 0.000 21 0.1112 0.1801 -0.4925E-01 1305. 0.000 22 0.1171 0.1803 0.9711E-02 1309. 0.000 23 0.1228 0.1806 0.4906E-01 1314. 0.000 24 0.1259 0.1808 -0.1210E-02 1319. 0.000 25 0.1259 0.1811 0.4331E-02 1324. 0.000 26 0.1224 0.1814 -0.5242E-01 1329. 0.000 27 0.1156 0.1817 0.8768E-02 1334. 0.000 28 0.1064 0.1820 0.2992E-01 1337. 0.000 29 0.9688E-01 0.1822 0.5418E-01 1340. 0.000 30 0.9081E-01 0.1824 0.8003E-01 1343. 0.000 31 0.9019E-01 0.1825 -0.5487E-01 1346. 0.000 32 0.9484E-01 0.1827 -0.5673E-01 1349. 0.000 33 0.1019 0.1828 -0.3483E-01 1352. 0.000 34 0.1054 0.1830 -0.1153 1356. 0.000 35 0.1026 0.1832 0.1173 1360. 0.000 36 0.9244E-01 0.1834 0.6625E-02 1362. 0.000 37 0.7630E-01 0.1836 -0.3389E-01 1364. 0.000 38 0.5757E-01 0.1837 0.2546E-01 1366. 0.000 39 0.3900E-01 0.1837 -0.1561E-01 1366. 0.000 40 0.2235E-01 0.1838 -0.2580E-01 1366. 0.000 41 0.8799E-02 0.1838 -0.3820E-02 1366. 0.000 42 -0.2339E-02 0.1838 -0.5406E-01 1366. 0.000 43 -0.1247E-01 0.1838 -0.6314E-01 1366. 0.000 44 -0.2359E-01 0.1838 -0.1761E-01 1367. 0.000 45 -0.3762E-01 0.1838 -0.5409E-02 1367. 0.000 46 -0.5579E-01 0.1838 -0.5364E-01 1368. 0.000 47 -0.7881E-01 0.1839 -0.6159E-01 1370. 0.000 48 -0.1062 0.1840 -0.3451E-02 1374. 0.000 ******************************************************* ** Diagnostics of standardized residuals ******************************************************* Print--> Describe standardized resid. series Summary data for series RESA Mean 1.189624195926964E-02 Standard Deviation 1.000000000000000 Skewness 0.7154060341129300 Kurtosis 2.663208635762389 6-th order cumulant 25.80072379485283 Maximim 4.860336671871243 Minimum -2.659066142831283 Median -2.035111901564721E-02 Q1 -0.6310594093877364 Q3 0.5745386081031547 Number of Observations 294 Print--> Engle LM Test for standardized res1 series Obs LAG LMVALUE PROB 1 1 4.504 0.9662 2 2 12.78 0.9983 Print--> ACF, Std.Err, PACF, Q-Stat, Prob.Q Obs ACFA SEA PACFA MQA PMQA 1 0.2581E-01 0.5832E-01 0.2581E-01 0.1979 0.6564 2 0.3027E-01 0.5836E-01 0.2963E-01 0.4710 0.7902 3 0.3683E-02 0.5841E-01 0.2163E-02 0.4751 0.9243 4 -0.4209E-02 0.5841E-01 -0.5260E-02 0.4804 0.9754 5 -0.7264E-01 0.5842E-01 -0.7269E-01 2.069 0.8395 6 -0.1252 0.5872E-01 -0.1221 6.804 0.3393 7 -0.9069E-01 0.5962E-01 -0.8310E-01 9.298 0.2319 8 -0.4246E-02 0.6009E-01 0.5808E-02 9.304 0.3173 9 -0.6112E-01 0.6009E-01 -0.5726E-01 10.44 0.3157 10 -0.2889E-01 0.6030E-01 -0.3383E-01 10.70 0.3813 11 -0.1495E-01 0.6035E-01 -0.3053E-01 10.77 0.4628 12 0.7776E-01 0.6036E-01 0.5392E-01 12.64 0.3961 13 -0.2474E-01 0.6070E-01 -0.4789E-01 12.82 0.4614 14 0.5285E-01 0.6074E-01 0.3625E-01 13.69 0.4729 15 -0.8894E-01 0.6089E-01 -0.1115 16.16 0.3715 16 0.1474E-01 0.6133E-01 -0.4645E-02 16.23 0.4372 17 -0.4175E-01 0.6134E-01 -0.4357E-01 16.78 0.4697 18 -0.5754E-02 0.6144E-01 -0.6694E-05 16.79 0.5379 19 -0.1267 0.6144E-01 -0.1309 21.87 0.2909 20 -0.4058E-01 0.6233E-01 -0.5350E-01 22.39 0.3196 21 -0.1274E-02 0.6242E-01 -0.1174E-01 22.39 0.3772 22 0.7108E-01 0.6242E-01 0.5464E-01 24.01 0.3468 23 0.1139E-01 0.6269E-01 0.8405E-03 24.05 0.4010 24 -0.5086E-01 0.6270E-01 -0.1012 24.88 0.4121 25 0.6963E-01 0.6284E-01 0.3266E-01 26.45 0.3838 26 -0.1337E-01 0.6310E-01 -0.6555E-01 26.51 0.4353 27 0.2979E-01 0.6311E-01 0.4700E-01 26.80 0.4746 28 0.5361E-01 0.6316E-01 0.3587E-01 27.74 0.4783 29 -0.1555 0.6331E-01 -0.1721 35.68 0.1831 30 0.5197E-01 0.6460E-01 0.1950E-01 36.57 0.1900 31 -0.3154E-01 0.6474E-01 -0.8801E-02 36.90 0.2148 32 -0.4696E-01 0.6479E-01 -0.5373E-01 37.63 0.2270 33 0.8985E-01 0.6491E-01 0.1074 40.32 0.1780 34 0.5975E-02 0.6533E-01 -0.4289E-01 40.34 0.2104 35 0.3198E-01 0.6533E-01 -0.6119E-02 40.68 0.2345 36 0.7115E-01 0.6538E-01 0.6356E-01 42.39 0.2148 37 -0.7247E-03 0.6565E-01 -0.1133E-01 42.39 0.2499 38 -0.1844E-01 0.6565E-01 -0.4057E-01 42.50 0.2832 39 -0.8968E-02 0.6566E-01 -0.3644E-01 42.53 0.3216 40 -0.3624E-01 0.6567E-01 -0.2681E-01 42.98 0.3448 41 -0.2080E-01 0.6574E-01 0.1623E-01 43.13 0.3804 42 -0.6201E-02 0.6576E-01 0.1763E-01 43.14 0.4222 43 -0.2276E-01 0.6576E-01 -0.1743E-01 43.32 0.4576 44 0.4754E-01 0.6579E-01 0.2216E-01 44.11 0.4671 45 0.7379E-02 0.6590E-01 -0.6478E-02 44.13 0.5088 46 0.2697E-01 0.6591E-01 0.4542E-01 44.38 0.5402 47 0.2873E-01 0.6594E-01 0.2291E-01 44.67 0.5694 48 -0.2621E-01 0.6599E-01 -0.7444E-01 44.92 0.6000 ******************************************************* ** Diagnostic testing of squared standardized residuals ******************************************************* Print--> ACF, Std.Err, PACF, Q-Stat, Prob.Q Obs ACFB SEB PACFB MQB PMQB 1 0.1239 0.5832E-01 0.1239 4.560 0.3273E-01 2 0.1827 0.5921E-01 0.1699 14.51 0.7081E-03 3 0.1070 0.6110E-01 0.7022E-01 17.93 0.4549E-03 4 0.3493E-01 0.6173E-01 -0.1389E-01 18.30 0.1080E-02 5 -0.1078E-01 0.6180E-01 -0.4518E-01 18.33 0.2560E-02 6 -0.1094E-01 0.6180E-01 -0.1780E-01 18.37 0.5379E-02 7 -0.2207E-01 0.6181E-01 -0.1179E-01 18.51 0.9854E-02 8 -0.4564E-01 0.6184E-01 -0.3349E-01 19.15 0.1409E-01 9 -0.4405E-01 0.6195E-01 -0.2866E-01 19.74 0.1958E-01 10 -0.3593E-01 0.6206E-01 -0.1397E-01 20.14 0.2799E-01 11 0.1910E-01 0.6213E-01 0.4477E-01 20.25 0.4205E-01 12 -0.6390E-01 0.6215E-01 -0.5797E-01 21.51 0.4342E-01 13 -0.4761E-01 0.6237E-01 -0.4767E-01 22.21 0.5219E-01 14 -0.3741E-01 0.6250E-01 -0.1868E-01 22.65 0.6630E-01 15 -0.4402E-01 0.6257E-01 -0.1782E-01 23.25 0.7898E-01 16 -0.1612E-01 0.6268E-01 0.7702E-02 23.33 0.1052 17 -0.1310E-01 0.6269E-01 -0.1698E-02 23.38 0.1371 18 0.2433E-01 0.6270E-01 0.2938E-01 23.57 0.1696 19 0.3844E-02 0.6273E-01 0.3300E-03 23.58 0.2129 20 -0.4821E-01 0.6273E-01 -0.6599E-01 24.31 0.2289 21 -0.2249E-01 0.6286E-01 -0.2765E-01 24.48 0.2706 22 0.1647 0.6289E-01 0.1893 33.15 0.5976E-01 23 -0.1160E-01 0.6434E-01 -0.2588E-01 33.20 0.7772E-01 24 0.5876E-01 0.6434E-01 0.5418E-02 34.31 0.7933E-01 25 0.4629E-01 0.6453E-01 0.1059E-01 35.00 0.8817E-01 26 -0.1629E-01 0.6464E-01 -0.3925E-01 35.09 0.1098 27 0.1866E-01 0.6465E-01 0.1434E-01 35.20 0.1338 28 0.5248E-01 0.6467E-01 0.5465E-01 36.10 0.1400 29 0.4073E-01 0.6482E-01 0.2906E-01 36.65 0.1555 30 0.4012E-01 0.6490E-01 0.3064E-01 37.18 0.1720 31 -0.3572E-02 0.6499E-01 -0.1787E-01 37.18 0.2056 32 -0.5366E-02 0.6499E-01 -0.2255E-01 37.19 0.2422 33 0.4867E-02 0.6499E-01 -0.1053E-01 37.20 0.2817 34 0.7185E-02 0.6499E-01 0.3487E-01 37.22 0.3232 35 0.2544E-01 0.6499E-01 0.3740E-01 37.43 0.3580 36 0.6702E-01 0.6503E-01 0.7332E-01 38.95 0.3385 37 0.2019E-01 0.6526E-01 0.1775E-01 39.09 0.3762 38 0.9143E-02 0.6528E-01 -0.1927E-01 39.12 0.4195 39 -0.2089E-01 0.6529E-01 -0.4345E-01 39.26 0.4580 40 -0.1448E-01 0.6531E-01 -0.2919E-01 39.34 0.4999 41 -0.4747E-01 0.6532E-01 -0.3205E-01 40.11 0.5100 42 -0.4876E-01 0.6544E-01 0.9396E-02 40.93 0.5177 43 -0.3353E-01 0.6556E-01 0.1156E-01 41.32 0.5442 44 -0.4166E-01 0.6562E-01 -0.4514E-01 41.93 0.5609 45 -0.6070E-01 0.6571E-01 -0.3559E-01 43.21 0.5478 46 -0.5988E-01 0.6590E-01 -0.6858E-01 44.47 0.5364 47 -0.4348E-01 0.6609E-01 -0.3458E-01 45.14 0.5499 48 0.1672E-01 0.6618E-01 0.8467E-01 45.24 0.5867 ******************************************************* ** Display graphics for Dependent Variable ******************************************************* ******************************************************* ** Display graphics for 1st Moment Residuals ******************************************************* ******************************************************* ** Display graphs for Squared Standardized Residuals ******************************************************* B34S Matrix Command Ending. Last Command reached. Space available in allocator 2874913, peak space used 67851 Number variables used 64, peak number used 82 Number temp variables used 228, # user temp clean 0 B34S 8.10R (D:M:Y) 8/ 6/04 (H:M:S) 14:49:42 DATA STEP PAGE 8 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+31 Note: Initial value for Estimated Parameter 1 was zero. Reset to .10 Time Series Parameter Estimation for Model 1 Data - Z = VAR=GASOUT Observations 296 Differencing on Z - None Transformations Examined - None. Univariate Model Parameters. Parameter Beginning # Type Order Value 1 Mean 0.000 2 Autoregressive 1 1 0.1000 3 Autoregressive 1 2 0.1000 4 Autoregressive 1 3 0.1000 Output at each iteration has been suppressed. Residual output has been suppressed. Initial sum of Squares 411358.9221771438 Iteration stops - Relative parameter change < 4.000000189989805E-03 Correlation Matrix of the Parameters. 1/Cond = 0.2498E-04 1 2 3 4 1 1.0000 2 0.0116 1.0000 3 -0.0151 -0.9614 1.0000 4 0.0217 0.8557 -0.9612 1.0000 End of Estimation for Model 1 Summary of model 1 Data - Z = VAR=GASOUT 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 53.60 52.09 70.94 55.11 0.7555 2 Autoregressive 1 1 2.203 2.099 42.21 2.308 0.5220E-01 3 Autoregressive 1 2 -1.695 -1.891 -17.27 -1.499 0.9814E-01 4 Autoregressive 1 3 0.4651 0.3603 8.878 0.5698 0.5238E-01 Other Information and results. Residual Sum of Squares 34.279711 289 D.F. Residual Mean Square 0.1186149155112211 Number of residuals 293 Residual Standard error 0.3444051618533338 Backforecasting not used in Estimation Autocorrelation Function Data - THE ESTIMATED RESIDUALS - MODEL 1 293 Observations Original Series Mean of the Series 9.675911408848128E-10 St. Dev. of Series 0.3420461946265564 Number of observations 293 S. E. of mean 2.001673950658156E-02 T value of mean (against zero) 4.833909841144040E-08 1- 12 -0.10 0.19 -0.06 -0.04 -0.11 0.08 -0.02 0.04 -0.08 0.06 -0.01 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 2.9 14.0 15.0 15.5 18.9 21.1 21.2 21.8 23.6 24.7 24.7 28.0 13- 24 -0.05 0.10 -0.08 0.07 -0.06 0.04 -0.11 0.02 -0.01 0.07 0.01 -0.02 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 28.7 32.1 33.9 35.3 36.6 37.0 40.9 41.0 41.1 42.8 42.9 43.1 Mean divided by St. Error (using N in S. D.) 4.842180009450980E-08 Q Statistic 41.442 DF 20 Prob. 0.99673 Modified Q Statistic 43.055 DF 20 Prob. 0.99799 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 9.675911408848128E-10 St. Dev. of Series 0.3420461946265564 Number of observations 293 S. E. of mean 2.001673950658156E-02 T value of mean (against zero) 4.833909841144040E-08 1- 12 -0.10 0.19 -0.02 -0.09 -0.11 0.10 0.03 0.00 -0.09 0.05 0.06 0.09 13- 24 -0.06 0.05 -0.01 0.05 -0.04 -0.01 -0.08 -0.01 0.05 0.05 0.01 -0.09 Time Series Forecasting for Model 1 Data - Z = VAR=GASOUT Observations 296 Differencing on Z - None Transformations Examined - None. Univariate Model Parameters. Parameter Beginning # Type Order Value 1 Mean 53.60 2 Autoregressive 1 1 2.203 3 Autoregressive 1 2 -1.695 4 Autoregressive 1 3 0.4651 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 56.097846 56.772880 57.447914 298 54.915073 56.548448 58.181823 299 53.612865 56.299409 58.985953 300 52.360798 56.025491 59.690185 301 51.264834 55.739717 60.214599 302 50.368716 55.458544 60.548373 303 49.670796 55.196042 60.721289 304 49.143998 54.961362 60.778726 305 48.752239 54.758475 60.764711 306 48.460860 54.587165 60.713471 307 48.241412 54.444477 60.647542 308 48.072618 54.326112 60.579605 309 47.939431 54.227509 60.515587 310 47.831559 54.144532 60.457505 311 47.742120 54.073795 60.405471 312 47.666584 54.012734 60.358885 313 47.601990 53.959509 60.317029 314 47.546376 53.912842 60.279307 315 47.498385 53.871839 60.245294 316 47.456999 53.835850 60.214701 317 47.421385 53.804350 60.187314 318 47.390818 53.776881 60.162944 319 47.364638 53.753015 60.141391 320 47.342247 53.732341 60.122436 Weights used in calculating confidence limits J PS(J) 0 1.000000 1 2.203387 2 3.159810 3 3.692378 4 3.804243 5 3.592764 6 3.184850 7 2.696558 8 2.213770 9 1.787999 10 1.441152 11 1.174113 12 0.9756533 13 0.8297244 14 0.7204061 15 0.6346039 16 0.5629885 17 0.4997958 18 0.4420500 19 0.3886262 20 0.3394095 21 0.2946696 22 0.2546721 23 0.2194923 24 0.1889706 B34S(r) Matrix Command. Version February 2004. Date of Run d/m/y 8/ 6/04. Time of Run h:m:s 14:49:42. => CALL LOADDATA$ => CALL AUTOBJ(GASOUT => :SMODELN 'test.mod' => :AR INDEX(1 2 3 ) => :PRINT => :NAC 200 :NPAC 24 => :FORECAST INDEX(24 296) => )$ Time Series Parameter Estimation for Model 1 Data - Z = VAR= GASOUT Observations 296 Differencing on Z - None Transformations Examined - None. Univariate Model Parameters. Parameter Beginning # Type Order Value 1 Mean 53.51 2 Autoregressive 1 1 0.1000 3 Autoregressive 1 2 0.1000 4 Autoregressive 1 3 0.1000 Output at each iteration has been suppressed. Residual output has been suppressed. Initial sum of Squares 1676.328418568524 Iteration stops - Relative parameter change < 4.000000000000000E-03 Correlation Matrix of the Parameters. 1/Cond = 0.2496E-04 1 2 3 4 1 1.0000 2 0.0130 1.0000 3 -0.0164 -0.9614 1.0000 4 0.0231 0.8557 -0.9612 1.0000 End of Estimation for Model 1 Summary of model 1 Data - Z = VAR= GASOUT 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 53.60 52.09 70.94 55.11 0.7556 2 Autoregressive 1 1 2.203 2.099 42.21 2.308 0.5220E-01 3 Autoregressive 1 2 -1.695 -1.891 -17.27 -1.499 0.9814E-01 4 Autoregressive 1 3 0.4651 0.3603 8.878 0.5698 0.5238E-01 Other Information and results. Residual Sum of Squares 34.279711 289 D.F. Residual Mean Square 0.1186149155112211 Number of residuals 293 Residual Standard error 0.3444051618533338 Backforecasting not used in Estimation Autocorrelation Function Data - THE ESTIMATED RESIDUALS - MODEL 1 293 Observations Original Series Mean of the Series 4.174577815824520E-10 St. Dev. of Series 0.3420461946265565 Number of observations 293 S. E. of mean 2.001673950658156E-02 T value of mean (against zero) 2.085543359572575E-08 1- 12 -0.10 0.19 -0.06 -0.04 -0.11 0.08 -0.02 0.04 -0.08 0.06 -0.01 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 2.9 14.0 15.0 15.5 18.9 21.1 21.2 21.8 23.6 24.7 24.7 28.0 13- 24 -0.05 0.10 -0.08 0.07 -0.06 0.04 -0.11 0.02 -0.01 0.07 0.01 -0.02 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 28.7 32.1 33.9 35.3 36.6 37.0 40.9 41.0 41.1 42.8 42.9 43.1 25- 36 0.07 -0.03 0.03 0.09 -0.15 0.07 -0.04 -0.06 0.10 0.01 0.02 0.07 St.E. 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 Mod. Q 44.5 44.8 45.0 47.8 54.9 56.6 57.1 58.2 61.3 61.4 61.5 63.2 37- 48 -0.01 -0.02 -0.01 -0.03 -0.02 0.00 -0.01 0.04 -0.01 0.02 0.04 -0.05 St.E. 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 Mod. Q 63.2 63.4 63.4 63.7 63.8 63.8 63.9 64.5 64.5 64.7 65.2 65.9 49- 60 0.02 0.00 -0.05 -0.06 0.03 -0.12 -0.02 -0.02 0.03 0.03 0.02 -0.04 St.E. 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 Mod. Q 66.0 66.0 66.9 68.1 68.5 73.6 73.8 74.0 74.3 74.6 74.7 75.5 61- 72 0.00 -0.12 0.03 0.05 0.00 0.07 -0.03 0.03 -0.04 -0.02 0.02 -0.08 St.E. 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 Mod. Q 75.5 81.1 81.5 82.6 82.6 84.3 84.7 85.1 85.7 85.9 86.1 88.9 73- 84 0.04 0.01 0.00 -0.02 -0.02 -0.05 -0.03 0.01 0.02 -0.07 0.07 -0.08 St.E. 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 Mod. Q 89.6 89.7 89.7 89.9 90.0 90.9 91.2 91.2 91.4 93.7 95.7 98.6 85- 96 0.11 -0.04 0.05 -0.08 0.13 -0.05 0.08 0.02 -0.04 -0.03 -0.01 -0.01 St.E. 0.07 0.07 0.07 0.07 0.07 0.08 0.08 0.08 0.08 0.08 0.08 0.08 Mod. Q 103.7 104.3 105.3 107.8 115.4 116.4 119.3 119.5 120.1 120.5 120.6 120.6 97-108 0.04 -0.02 0.08 -0.05 0.10 0.01 0.05 -0.02 0.02 -0.04 -0.05 0.01 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 121.5 121.6 124.5 125.5 130.0 130.1 131.2 131.3 131.6 132.3 133.6 133.6 109-120 -0.04 0.02 -0.02 0.03 0.01 0.08 0.05 0.01 0.08 -0.11 -0.06 0.03 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 134.3 134.4 134.7 135.1 135.2 138.5 139.8 139.8 143.4 148.8 150.4 151.0 121-132 -0.04 0.06 0.02 0.06 0.01 0.02 0.03 -0.03 0.02 0.00 0.00 0.01 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 152.0 154.1 154.4 156.3 156.4 156.7 157.1 157.6 157.8 157.8 157.8 157.9 133-144 -0.01 0.07 -0.06 0.06 -0.06 0.02 -0.07 -0.01 0.04 0.05 -0.07 0.03 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 157.9 160.6 162.7 164.9 166.8 167.0 169.8 169.9 170.7 172.0 174.8 175.5 145-156 -0.06 -0.05 0.01 0.05 -0.07 0.07 -0.09 0.02 -0.08 -0.03 -0.04 0.01 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 177.3 178.6 178.7 180.2 182.8 185.9 190.9 191.2 195.1 195.6 196.7 196.7 157-168 -0.03 0.04 0.01 -0.03 -0.01 0.01 -0.01 0.05 -0.03 0.02 -0.02 0.00 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 197.3 198.4 198.5 199.0 199.1 199.1 199.2 200.9 201.4 201.6 201.9 201.9 169-180 -0.01 0.04 -0.07 0.00 -0.04 0.01 0.00 -0.08 -0.02 0.01 -0.06 0.06 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 201.9 203.1 206.5 206.5 207.6 207.8 207.8 212.2 212.4 212.5 215.6 218.8 181-192 -0.01 -0.07 -0.01 -0.08 0.00 0.04 -0.01 0.07 -0.02 0.02 0.02 -0.05 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 218.8 222.3 222.3 228.0 228.0 229.1 229.1 233.3 233.8 234.0 234.4 236.9 193-200 -0.04 -0.03 -0.03 -0.09 0.00 -0.03 -0.01 0.06 St.E. 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 Mod. Q 238.3 239.0 239.6 246.1 246.1 246.8 246.8 250.0 Mean divided by St. Error (using N in S. D.) 2.089111443207128E-08 Partial Autocorrelations Data - THE ESTIMATED RESIDUALS - MODEL 1 293 Observations Original Series Mean of the Series 4.174577815824520E-10 St. Dev. of Series 0.3420461946265565 Number of observations 293 S. E. of mean 2.001673950658156E-02 T value of mean (against zero) 2.085543359572575E-08 1- 12 -0.10 0.19 -0.02 -0.09 -0.11 0.10 0.03 0.00 -0.09 0.05 0.06 0.09 13- 24 -0.06 0.05 -0.01 0.05 -0.04 -0.01 -0.08 -0.01 0.05 0.05 0.01 -0.09 Time Series Forecasting for Model 1 Data - Z = VAR= GASOUT Observations 296 Differencing on Z - None Transformations Examined - None. Univariate Model Parameters. Parameter Beginning # Type Order Value 1 Mean 53.60 2 Autoregressive 1 1 2.203 3 Autoregressive 1 2 -1.695 4 Autoregressive 1 3 0.4651 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 56.097846 56.772880 57.447914 298 54.915073 56.548448 58.181823 299 53.612865 56.299409 58.985953 300 52.360798 56.025491 59.690185 301 51.264834 55.739717 60.214599 302 50.368716 55.458544 60.548373 303 49.670796 55.196042 60.721289 304 49.143998 54.961362 60.778726 305 48.752239 54.758475 60.764711 306 48.460860 54.587165 60.713471 307 48.241412 54.444477 60.647542 308 48.072619 54.326111 60.579604 309 47.939431 54.227509 60.515587 310 47.831559 54.144532 60.457505 311 47.742120 54.073795 60.405471 312 47.666584 54.012734 60.358885 313 47.601990 53.959509 60.317029 314 47.546376 53.912841 60.279307 315 47.498385 53.871839 60.245294 316 47.456999 53.835850 60.214701 317 47.421385 53.804350 60.187314 318 47.390818 53.776881 60.162944 319 47.364638 53.753015 60.141391 320 47.342247 53.732341 60.122436 Weights used in calculating confidence limits J PS(J) 0 1.000000 1 2.203387 2 3.159810 3 3.692378 4 3.804243 5 3.592764 6 3.184850 7 2.696558 8 2.213770 9 1.787999 10 1.441152 11 1.174113 12 0.9756532 13 0.8297244 14 0.7204060 15 0.6346039 16 0.5629885 17 0.4997958 18 0.4420500 19 0.3886262 20 0.3394095 21 0.2946695 22 0.2546721 23 0.2194923 24 0.1889706 B34S Matrix Command Ending. Last Command reached. Space available in allocator 2874913, peak space used 29970 Number variables used 42, peak number used 42 Number temp variables used 17, # user temp clean 0 B34S 8.10R (D:M:Y) 8/ 6/04 (H:M:S) 14:49:42 DATA STEP PAGE 9 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+31 B34S(r) Matrix Command. Version February 2004. Date of Run d/m/y 8/ 6/04. Time of Run h:m:s 14:49:42. => CALL LOADDATA$ => CALL AUTOBJ(GASOUT => :SMODELN 'test.mod' :NOEST => :PRINT => :FORECAST INDEX(24 296) => )$ Time Series Forecasting for Model 1 Data - Z = VAR= GASOUT Observations 296 Differencing on Z - None Transformations Examined - None. Univariate Model Parameters. Parameter Beginning # Type Order Value 1 Mean 53.60 2 Autoregressive 1 1 2.203 3 Autoregressive 1 2 -1.695 4 Autoregressive 1 3 0.4651 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 56.097846 56.772880 57.447914 298 54.915073 56.548448 58.181823 299 53.612865 56.299409 58.985953 300 52.360798 56.025491 59.690185 301 51.264834 55.739717 60.214599 302 50.368716 55.458544 60.548373 303 49.670796 55.196042 60.721289 304 49.143998 54.961362 60.778726 305 48.752239 54.758475 60.764711 306 48.460860 54.587165 60.713471 307 48.241412 54.444477 60.647542 308 48.072619 54.326111 60.579604 309 47.939431 54.227509 60.515587 310 47.831559 54.144532 60.457505 311 47.742120 54.073795 60.405471 312 47.666584 54.012734 60.358885 313 47.601990 53.959509 60.317029 314 47.546376 53.912841 60.279307 315 47.498385 53.871839 60.245294 316 47.456999 53.835850 60.214701 317 47.421385 53.804350 60.187314 318 47.390818 53.776881 60.162944 319 47.364638 53.753015 60.141391 320 47.342247 53.732341 60.122436 Weights used in calculating confidence limits J PS(J) 0 1.000000 1 2.203387 2 3.159810 3 3.692378 4 3.804243 5 3.592764 6 3.184850 7 2.696558 8 2.213770 9 1.787999 10 1.441152 11 1.174113 12 0.9756532 13 0.8297244 14 0.7204060 15 0.6346039 16 0.5629885 17 0.4997958 18 0.4420500 19 0.3886262 20 0.3394095 21 0.2946695 22 0.2546721 23 0.2194923 24 0.1889706 B34S Matrix Command Ending. Last Command reached. Space available in allocator 2874933, peak space used 28423 Number variables used 28, peak number used 28 Number temp variables used 11, # user temp clean 0 B34S 8.10R (D:M:Y) 8/ 6/04 (H:M:S) 14:49:42 DATA STEP PAGE 10 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+31 Note: Initial value for Estimated Parameter 1 was zero. Reset to .10 Time Series Parameter Estimation for Model 1 Data - Z = VAR=GASOUT Observations 296 Differencing on Z - None Transformations Examined - None. Univariate Model Parameters. Parameter Beginning # Type Order Value 1 Mean 0.000 2 Autoregressive 1 1 0.1000 3 Autoregressive 1 2 0.1000 4 Autoregressive 1 3 0.1000 Output at each iteration has been suppressed. Residual output has been suppressed. Initial sum of Squares 411358.9221771438 Iteration stops - Relative parameter change < 4.000000189989805E-03 Correlation Matrix of the Parameters. 1/Cond = 0.2498E-04 1 2 3 4 1 1.0000 2 0.0116 1.0000 3 -0.0151 -0.9614 1.0000 4 0.0217 0.8557 -0.9612 1.0000 End of Estimation for Model 1 Summary of model 1 Data - Z = VAR=GASOUT 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 53.60 52.09 70.94 55.11 0.7555 2 Autoregressive 1 1 2.203 2.099 42.21 2.308 0.5220E-01 3 Autoregressive 1 2 -1.695 -1.891 -17.27 -1.499 0.9814E-01 4 Autoregressive 1 3 0.4651 0.3603 8.878 0.5698 0.5238E-01 Other Information and results. Residual Sum of Squares 34.279711 289 D.F. Residual Mean Square 0.1186149155112211 Number of residuals 293 Residual Standard error 0.3444051618533338 Backforecasting not used in Estimation Autocorrelation Function Data - THE ESTIMATED RESIDUALS - MODEL 1 293 Observations Original Series Mean of the Series 9.675911408848128E-10 St. Dev. of Series 0.3420461946265564 Number of observations 293 S. E. of mean 2.001673950658156E-02 T value of mean (against zero) 4.833909841144040E-08 1- 12 -0.10 0.19 -0.06 -0.04 -0.11 0.08 -0.02 0.04 -0.08 0.06 -0.01 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 2.9 14.0 15.0 15.5 18.9 21.1 21.2 21.8 23.6 24.7 24.7 28.0 13- 24 -0.05 0.10 -0.08 0.07 -0.06 0.04 -0.11 0.02 -0.01 0.07 0.01 -0.02 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 28.7 32.1 33.9 35.3 36.6 37.0 40.9 41.0 41.1 42.8 42.9 43.1 Mean divided by St. Error (using N in S. D.) 4.842180009450980E-08 Q Statistic 41.442 DF 20 Prob. 0.99673 Modified Q Statistic 43.055 DF 20 Prob. 0.99799 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 9.675911408848128E-10 St. Dev. of Series 0.3420461946265564 Number of observations 293 S. E. of mean 2.001673950658156E-02 T value of mean (against zero) 4.833909841144040E-08 1- 12 -0.10 0.19 -0.02 -0.09 -0.11 0.10 0.03 0.00 -0.09 0.05 0.06 0.09 13- 24 -0.06 0.05 -0.01 0.05 -0.04 -0.01 -0.08 -0.01 0.05 0.05 0.01 -0.09 Time Series Forecasting for Model 1 Data - Z = VAR=GASOUT Observations 296 Differencing on Z - None Transformations Examined - None. Univariate Model Parameters. Parameter Beginning # Type Order Value 1 Mean 53.60 2 Autoregressive 1 1 2.203 3 Autoregressive 1 2 -1.695 4 Autoregressive 1 3 0.4651 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 56.097846 56.772880 57.447914 298 54.915073 56.548448 58.181823 299 53.612865 56.299409 58.985953 300 52.360798 56.025491 59.690185 301 51.264834 55.739717 60.214599 302 50.368716 55.458544 60.548373 303 49.670796 55.196042 60.721289 304 49.143998 54.961362 60.778726 305 48.752239 54.758475 60.764711 306 48.460860 54.587165 60.713471 307 48.241412 54.444477 60.647542 308 48.072618 54.326112 60.579605 309 47.939431 54.227509 60.515587 310 47.831559 54.144532 60.457505 311 47.742120 54.073795 60.405471 312 47.666584 54.012734 60.358885 313 47.601990 53.959509 60.317029 314 47.546376 53.912842 60.279307 315 47.498385 53.871839 60.245294 316 47.456999 53.835850 60.214701 317 47.421385 53.804350 60.187314 318 47.390818 53.776881 60.162944 319 47.364638 53.753015 60.141391 320 47.342247 53.732341 60.122436 Weights used in calculating confidence limits J PS(J) 0 1.000000 1 2.203387 2 3.159810 3 3.692378 4 3.804243 5 3.592764 6 3.184850 7 2.696558 8 2.213770 9 1.787999 10 1.441152 11 1.174113 12 0.9756533 13 0.8297244 14 0.7204061 15 0.6346039 16 0.5629885 17 0.4997958 18 0.4420500 19 0.3886262 20 0.3394095 21 0.2946696 22 0.2546721 23 0.2194923 24 0.1889706 B34S(r) Matrix Command. Version February 2004. Date of Run d/m/y 8/ 6/04. Time of Run h:m:s 14:49:42. => CALL LOADDATA$ => CALL LOAD(RTEST)$ => CALL AUTOBJ(GASOUT => :SMODELN 'test.mod' => :AR INDEX(1 2 3 ) => :PRINT => :NAC 24 :NPAC 12 => :FORECAST INDEX(24 296) => )$ Time Series Parameter Estimation for Model 1 Data - Z = VAR= GASOUT Observations 296 Differencing on Z - None Transformations Examined - None. Univariate Model Parameters. Parameter Beginning # Type Order Value 1 Mean 53.51 2 Autoregressive 1 1 0.1000 3 Autoregressive 1 2 0.1000 4 Autoregressive 1 3 0.1000 Output at each iteration has been suppressed. Residual output has been suppressed. Initial sum of Squares 1676.328418568524 Iteration stops - Relative parameter change < 4.000000000000000E-03 Correlation Matrix of the Parameters. 1/Cond = 0.2496E-04 1 2 3 4 1 1.0000 2 0.0130 1.0000 3 -0.0164 -0.9614 1.0000 4 0.0231 0.8557 -0.9612 1.0000 End of Estimation for Model 1 Summary of model 1 Data - Z = VAR= GASOUT 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 53.60 52.09 70.94 55.11 0.7556 2 Autoregressive 1 1 2.203 2.099 42.21 2.308 0.5220E-01 3 Autoregressive 1 2 -1.695 -1.891 -17.27 -1.499 0.9814E-01 4 Autoregressive 1 3 0.4651 0.3603 8.878 0.5698 0.5238E-01 Other Information and results. Residual Sum of Squares 34.279711 289 D.F. Residual Mean Square 0.1186149155112211 Number of residuals 293 Residual Standard error 0.3444051618533338 Backforecasting not used in Estimation Autocorrelation Function Data - THE ESTIMATED RESIDUALS - MODEL 1 293 Observations Original Series Mean of the Series 4.174577815824520E-10 St. Dev. of Series 0.3420461946265565 Number of observations 293 S. E. of mean 2.001673950658156E-02 T value of mean (against zero) 2.085543359572575E-08 1- 12 -0.10 0.19 -0.06 -0.04 -0.11 0.08 -0.02 0.04 -0.08 0.06 -0.01 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 2.9 14.0 15.0 15.5 18.9 21.1 21.2 21.8 23.6 24.7 24.7 28.0 13- 24 -0.05 0.10 -0.08 0.07 -0.06 0.04 -0.11 0.02 -0.01 0.07 0.01 -0.02 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 28.7 32.1 33.9 35.3 36.6 37.0 40.9 41.0 41.1 42.8 42.9 43.1 Mean divided by St. Error (using N in S. D.) 2.089111443207128E-08 Partial Autocorrelations Data - THE ESTIMATED RESIDUALS - MODEL 1 293 Observations Original Series Mean of the Series 4.174577815824520E-10 St. Dev. of Series 0.3420461946265565 Number of observations 293 S. E. of mean 2.001673950658156E-02 T value of mean (against zero) 2.085543359572575E-08 1- 12 -0.10 0.19 -0.02 -0.09 -0.11 0.10 0.03 0.00 -0.09 0.05 0.06 0.09 Time Series Forecasting for Model 1 Data - Z = VAR= GASOUT Observations 296 Differencing on Z - None Transformations Examined - None. Univariate Model Parameters. Parameter Beginning # Type Order Value 1 Mean 53.60 2 Autoregressive 1 1 2.203 3 Autoregressive 1 2 -1.695 4 Autoregressive 1 3 0.4651 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 56.097846 56.772880 57.447914 298 54.915073 56.548448 58.181823 299 53.612865 56.299409 58.985953 300 52.360798 56.025491 59.690185 301 51.264834 55.739717 60.214599 302 50.368716 55.458544 60.548373 303 49.670796 55.196042 60.721289 304 49.143998 54.961362 60.778726 305 48.752239 54.758475 60.764711 306 48.460860 54.587165 60.713471 307 48.241412 54.444477 60.647542 308 48.072619 54.326111 60.579604 309 47.939431 54.227509 60.515587 310 47.831559 54.144532 60.457505 311 47.742120 54.073795 60.405471 312 47.666584 54.012734 60.358885 313 47.601990 53.959509 60.317029 314 47.546376 53.912841 60.279307 315 47.498385 53.871839 60.245294 316 47.456999 53.835850 60.214701 317 47.421385 53.804350 60.187314 318 47.390818 53.776881 60.162944 319 47.364638 53.753015 60.141391 320 47.342247 53.732341 60.122436 Weights used in calculating confidence limits J PS(J) 0 1.000000 1 2.203387 2 3.159810 3 3.692378 4 3.804243 5 3.592764 6 3.184850 7 2.696558 8 2.213770 9 1.787999 10 1.441152 11 1.174113 12 0.9756532 13 0.8297244 14 0.7204060 15 0.6346039 16 0.5629885 17 0.4997958 18 0.4420500 19 0.3886262 20 0.3394095 21 0.2946695 22 0.2546721 23 0.2194923 24 0.1889706 => CALL TABULATE(%FCAST,%FOREOBS,%FSE %FPSI)$ Obs %FCAST %FOREOBS %FSE %FPSI 1 56.77 297.0 0.3444 2.203 2 56.55 298.0 0.8334 3.160 3 56.30 299.0 1.371 3.692 4 56.03 300.0 1.870 3.804 5 55.74 301.0 2.283 3.593 6 55.46 302.0 2.597 3.185 7 55.20 303.0 2.819 2.697 8 54.96 304.0 2.968 2.214 9 54.76 305.0 3.064 1.788 10 54.59 306.0 3.126 1.441 11 54.44 307.0 3.165 1.174 12 54.33 308.0 3.191 0.9757 13 54.23 309.0 3.208 0.8297 14 54.14 310.0 3.221 0.7204 15 54.07 311.0 3.230 0.6346 16 54.01 312.0 3.238 0.5630 17 53.96 313.0 3.244 0.4998 18 53.91 314.0 3.248 0.4420 19 53.87 315.0 3.252 0.3886 20 53.84 316.0 3.255 0.3394 21 53.80 317.0 3.257 0.2947 22 53.78 318.0 3.258 0.2547 23 53.75 319.0 3.259 0.2195 24 53.73 320.0 3.260 0.1890 => CALL RTEST(%RES,GASOUT,48)$ => CALL ECHOOFF$ Residual Sum of Squares is: 34.27971058274288 ******************************************************* ** Diagnostics/Summary Stats for Dependent Var: ******************************************************* Print--> Describe Dependent Var: Summary data for series Y Mean 53.50912162162156 Standard Deviation 3.202120786435257 Skewness -5.173145345413963E-02 Kurtosis -0.6089697605545719 6-th order cumulant 2.113810959374490 Maximim 60.50000000000000 Minimum 45.60000000000000 Median 53.50000000000000 Q1 51.20000000000000 Q3 56.00000000000000 Number of Observations 296 Print--> ACF,Std.Err,PACF,Q-Stat,Prob.Q Obs ACFY SEY PACFY MQY PMQY 1 0.9708 0.5812E-01 0.9708 281.8 0.000 2 0.8960 0.9872E-01 -0.8039 522.7 0.000 3 0.7925 0.1232 0.1883 711.8 0.000 4 0.6800 0.1393 0.2600 851.4 0.000 5 0.5745 0.1501 0.5949E-01 951.5 0.000 6 0.4854 0.1574 -0.6258E-01 1023. 0.000 7 0.4161 0.1624 -0.1435E-01 1076. 0.000 8 0.3656 0.1659 0.5490E-01 1117. 0.000 9 0.3304 0.1686 0.5452E-02 1150. 0.000 10 0.3065 0.1708 0.3141E-01 1179. 0.000 11 0.2880 0.1726 -0.1166 1205. 0.000 12 0.2693 0.1743 -0.4302E-01 1228. 0.000 13 0.2473 0.1757 0.5110E-01 1247. 0.000 14 0.2215 0.1768 0.5381E-01 1262. 0.000 15 0.1930 0.1778 -0.4613E-01 1274. 0.000 16 0.1649 0.1785 0.3394E-01 1282. 0.000 17 0.1398 0.1790 -0.3344E-02 1288. 0.000 18 0.1210 0.1794 0.8548E-01 1293. 0.000 19 0.1103 0.1796 0.1655E-01 1297. 0.000 20 0.1078 0.1799 -0.2576E-01 1301. 0.000 21 0.1112 0.1801 -0.4925E-01 1305. 0.000 22 0.1171 0.1803 0.9711E-02 1309. 0.000 23 0.1228 0.1806 0.4906E-01 1314. 0.000 24 0.1259 0.1808 -0.1210E-02 1319. 0.000 25 0.1259 0.1811 0.4331E-02 1324. 0.000 26 0.1224 0.1814 -0.5242E-01 1329. 0.000 27 0.1156 0.1817 0.8768E-02 1334. 0.000 28 0.1064 0.1820 0.2992E-01 1337. 0.000 29 0.9688E-01 0.1822 0.5418E-01 1340. 0.000 30 0.9081E-01 0.1824 0.8003E-01 1343. 0.000 31 0.9019E-01 0.1825 -0.5487E-01 1346. 0.000 32 0.9484E-01 0.1827 -0.5673E-01 1349. 0.000 33 0.1019 0.1828 -0.3483E-01 1352. 0.000 34 0.1054 0.1830 -0.1153 1356. 0.000 35 0.1026 0.1832 0.1173 1360. 0.000 36 0.9244E-01 0.1834 0.6625E-02 1362. 0.000 37 0.7630E-01 0.1836 -0.3389E-01 1364. 0.000 38 0.5757E-01 0.1837 0.2546E-01 1366. 0.000 39 0.3900E-01 0.1837 -0.1561E-01 1366. 0.000 40 0.2235E-01 0.1838 -0.2580E-01 1366. 0.000 41 0.8799E-02 0.1838 -0.3820E-02 1366. 0.000 42 -0.2339E-02 0.1838 -0.5406E-01 1366. 0.000 43 -0.1247E-01 0.1838 -0.6314E-01 1366. 0.000 44 -0.2359E-01 0.1838 -0.1761E-01 1367. 0.000 45 -0.3762E-01 0.1838 -0.5409E-02 1367. 0.000 46 -0.5579E-01 0.1838 -0.5364E-01 1368. 0.000 47 -0.7881E-01 0.1839 -0.6159E-01 1370. 0.000 48 -0.1062 0.1840 -0.3451E-02 1374. 0.000 ******************************************************* ** Diagnostics of standardized residuals ******************************************************* Print--> Describe standardized resid. series Summary data for series RESA Mean 1.218387462213835E-09 Standard Deviation 1.000000000000000 Skewness 0.8276125335855661 Kurtosis 3.372731709240366 6-th order cumulant 25.76851122382656 Maximim 5.014228901409124 Minimum -2.868756628955830 Median -3.682777115740194E-02 Q1 -0.6192949102491651 Q3 0.5248012395707291 Number of Observations 293 Print--> Engle LM Test for standardized res1 series Obs LAG LMVALUE PROB 1 1 6.961 0.9917 2 2 15.38 0.9995 Print--> ACF, Std.Err, PACF, Q-Stat, Prob.Q Obs ACFA SEA PACFA MQA PMQA 1 -0.9915E-01 0.5842E-01 -0.9915E-01 2.910 0.8802E-01 2 0.1935 0.5899E-01 0.1855 14.03 0.8986E-03 3 -0.5590E-01 0.6112E-01 -0.2289E-01 14.96 0.1851E-02 4 -0.4226E-01 0.6129E-01 -0.8825E-01 15.49 0.3778E-02 5 -0.1069 0.6139E-01 -0.1077 18.93 0.1984E-02 6 0.8498E-01 0.6203E-01 0.9759E-01 21.10 0.1759E-02 7 -0.1880E-01 0.6242E-01 0.3435E-01 21.21 0.3474E-02 8 0.4338E-01 0.6244E-01 -0.3352E-02 21.78 0.5343E-02 9 -0.7646E-01 0.6254E-01 -0.9370E-01 23.56 0.5058E-02 10 0.6187E-01 0.6286E-01 0.4876E-01 24.73 0.5887E-02 11 -0.8610E-02 0.6307E-01 0.5890E-01 24.75 0.9917E-02 12 0.1027 0.6307E-01 0.8559E-01 27.99 0.5547E-02 13 -0.4925E-01 0.6364E-01 -0.6190E-01 28.74 0.7123E-02 14 0.1043 0.6377E-01 0.5298E-01 32.11 0.3864E-02 15 -0.7542E-01 0.6435E-01 -0.1147E-01 33.88 0.3542E-02 16 0.6665E-01 0.6465E-01 0.4870E-01 35.26 0.3656E-02 17 -0.6462E-01 0.6489E-01 -0.3643E-01 36.57 0.3844E-02 18 0.3777E-01 0.6510E-01 -0.1224E-01 37.02 0.5208E-02 19 -0.1105 0.6518E-01 -0.7923E-01 40.87 0.2511E-02 20 0.2098E-01 0.6582E-01 -0.6375E-02 41.01 0.3714E-02 21 -0.1220E-01 0.6584E-01 0.4722E-01 41.06 0.5515E-02 22 0.7452E-01 0.6585E-01 0.5110E-01 42.83 0.4953E-02 23 0.1356E-01 0.6613E-01 0.1311E-01 42.89 0.7141E-02 24 -0.2280E-01 0.6614E-01 -0.9125E-01 43.05 0.9805E-02 25 0.6600E-01 0.6617E-01 0.9617E-01 44.46 0.9629E-02 26 -0.3004E-01 0.6639E-01 0.8934E-02 44.75 0.1253E-01 27 0.2560E-01 0.6644E-01 0.2331E-01 44.97 0.1640E-01 28 0.9244E-01 0.6647E-01 0.5690E-01 47.75 0.1139E-01 29 -0.1480 0.6691E-01 -0.1472 54.92 0.2529E-02 30 0.7082E-01 0.6802E-01 0.4363E-01 56.57 0.2345E-02 31 -0.4037E-01 0.6827E-01 0.6196E-01 57.11 0.2912E-02 32 -0.5749E-01 0.6835E-01 -0.8877E-01 58.20 0.3108E-02 33 0.9718E-01 0.6852E-01 0.7797E-01 61.34 0.1955E-02 34 0.9410E-02 0.6899E-01 0.8874E-02 61.37 0.2743E-02 35 0.2176E-01 0.6899E-01 0.2033E-01 61.53 0.3676E-02 36 0.7105E-01 0.6901E-01 0.7611E-01 63.23 0.3350E-02 37 -0.6997E-02 0.6926E-01 -0.1522E-01 63.25 0.4585E-02 38 -0.1775E-01 0.6927E-01 -0.4727E-01 63.35 0.6068E-02 39 -0.5283E-02 0.6928E-01 -0.1903E-01 63.36 0.8115E-02 40 -0.3080E-01 0.6928E-01 0.2234E-02 63.69 0.1001E-01 41 -0.2012E-01 0.6933E-01 0.4602E-02 63.83 0.1274E-01 42 0.4822E-02 0.6935E-01 -0.4604E-02 63.83 0.1650E-01 43 -0.1297E-01 0.6935E-01 -0.2551E-01 63.89 0.2092E-01 44 0.4150E-01 0.6936E-01 0.3828E-01 64.49 0.2363E-01 45 -0.1235E-01 0.6944E-01 0.4505E-02 64.54 0.2950E-01 46 0.2289E-01 0.6945E-01 0.1877E-01 64.73 0.3560E-01 47 0.3602E-01 0.6948E-01 0.3513E-01 65.18 0.4062E-01 48 -0.4518E-01 0.6954E-01 -0.9286E-01 65.90 0.4404E-01 ******************************************************* ** Diagnostic testing of squared standardized residuals ******************************************************* Print--> ACF, Std.Err, PACF, Q-Stat, Prob.Q Obs ACFB SEB PACFB MQB PMQB 1 0.1543 0.5842E-01 0.1543 7.050 0.7927E-02 2 0.1922 0.5980E-01 0.1725 18.03 0.1219E-03 3 0.1163 0.6187E-01 0.6874E-01 22.05 0.6354E-04 4 0.6683E-01 0.6261E-01 0.1196E-01 23.39 0.1058E-03 5 -0.3230E-01 0.6285E-01 -0.7808E-01 23.70 0.2475E-03 6 -0.2353E-01 0.6291E-01 -0.3439E-01 23.87 0.5517E-03 7 -0.8344E-02 0.6294E-01 0.1139E-01 23.89 0.1191E-02 8 -0.6698E-01 0.6294E-01 -0.5043E-01 25.25 0.1409E-02 9 -0.3220E-01 0.6319E-01 -0.8556E-02 25.57 0.2404E-02 10 -0.3551E-01 0.6324E-01 -0.1207E-01 25.95 0.3805E-02 11 -0.2568E-01 0.6331E-01 -0.6327E-02 26.15 0.6154E-02 12 -0.5665E-01 0.6335E-01 -0.3981E-01 27.14 0.7372E-02 13 -0.6493E-01 0.6352E-01 -0.5323E-01 28.44 0.7845E-02 14 -0.7531E-02 0.6374E-01 0.2216E-01 28.46 0.1235E-01 15 -0.5584E-01 0.6375E-01 -0.3316E-01 29.43 0.1415E-01 16 -0.6047E-02 0.6391E-01 0.1145E-01 29.44 0.2112E-01 17 0.2579E-02 0.6392E-01 0.1412E-01 29.44 0.3065E-01 18 0.4562E-01 0.6392E-01 0.4229E-01 30.10 0.3650E-01 19 0.2813E-01 0.6403E-01 0.1676E-01 30.35 0.4754E-01 20 -0.2708E-01 0.6407E-01 -0.6296E-01 30.58 0.6099E-01 21 -0.2291E-02 0.6411E-01 -0.2042E-01 30.58 0.8091E-01 22 0.1110 0.6411E-01 0.1298 34.51 0.4352E-01 23 -0.1737E-01 0.6476E-01 -0.3809E-01 34.61 0.5683E-01 24 0.6598E-01 0.6478E-01 0.4417E-01 36.01 0.5477E-01 25 0.2189E-01 0.6501E-01 -0.1148E-01 36.16 0.6915E-01 26 -0.2632E-01 0.6503E-01 -0.5762E-01 36.39 0.8476E-01 27 -0.1068E-01 0.6507E-01 0.3912E-02 36.43 0.1063 28 0.1051 0.6507E-01 0.1202 40.03 0.6578E-01 29 0.1784E-01 0.6565E-01 0.6132E-02 40.13 0.8183E-01 30 0.4375E-01 0.6567E-01 0.2925E-01 40.76 0.9098E-01 31 0.2539E-01 0.6577E-01 -0.8676E-02 40.97 0.1086 32 0.3285E-01 0.6580E-01 0.9728E-02 41.33 0.1250 33 0.1140E-01 0.6586E-01 0.6615E-02 41.37 0.1503 34 0.3356E-01 0.6586E-01 0.3881E-01 41.75 0.1695 35 0.2618E-01 0.6592E-01 0.1917E-01 41.98 0.1941 36 0.1352 0.6596E-01 0.1400 48.13 0.8514E-01 37 0.3416E-01 0.6690E-01 0.1134E-01 48.52 0.9729E-01 38 0.3060E-01 0.6696E-01 -0.2608E-01 48.84 0.1119 39 -0.3059E-01 0.6700E-01 -0.6815E-01 49.16 0.1277 40 -0.2634E-01 0.6705E-01 -0.3368E-01 49.40 0.1466 41 -0.4883E-01 0.6709E-01 -0.1293E-01 50.21 0.1533 42 -0.3342E-01 0.6721E-01 0.2357E-01 50.60 0.1704 43 -0.4564E-01 0.6726E-01 -0.4565E-02 51.32 0.1799 44 -0.4599E-01 0.6737E-01 -0.2158E-01 52.05 0.1891 45 -0.5650E-01 0.6748E-01 -0.3022E-01 53.17 0.1886 46 -0.2240E-01 0.6764E-01 -0.3134E-01 53.34 0.2128 47 -0.4390E-01 0.6766E-01 -0.3459E-01 54.02 0.2240 48 0.1381E-01 0.6776E-01 0.7310E-01 54.09 0.2533 ******************************************************* ** Display graphics for Dependent Variable ******************************************************* ******************************************************* ** Display graphics for 1st Moment Residuals ******************************************************* ******************************************************* ** Display graphs for Squared Standardized Residuals ******************************************************* B34S Matrix Command Ending. Last Command reached. Space available in allocator 2874889, peak space used 36773 Number variables used 43, peak number used 77 Number temp variables used 122, # user temp clean 0 B34S 8.10R (D:M:Y) 8/ 6/04 (H:M:S) 14:49:44 DATA STEP Box-Jenkins Series A PAGE 11 Variable Label # Cases Mean Std. Dev. Variance Maximum Minimum Y 1 Chemical Process Concentration 197 17.0624 0.399247 0.159398 18.2000 16.1000 CONSTANT 2 197 1.00000 0.00000 0.00000 1.00000 1.00000 Number of observations in data file 197 Current missing variable code 1.000000000000000E+31 Time Series Parameter Estimation for Model 1 Data - Z = VAR=Y Observations 197 Differencing on Z - None Transformations Examined - None. Univariate Model Parameters. Parameter Beginning # Type Order Value 1 Mean 0.5000 2 Autoregressive 1 1 0.1000 3 Moving average 1 1 0.1000 Output at each iteration has been suppressed. Residual output has been suppressed. Initial sum of Squares 53742.74040824785 Iteration stops - Relative parameter change < 4.000000189989805E-03 Correlation Matrix of the Parameters. 1/Cond = 0.6024E-01 1 2 3 1 1.0000 2 0.1537 1.0000 3 0.1101 0.7404 1.0000 End of Estimation for Model 1 Summary of model 1 Data - Z = VAR=Y Observations 197 Differencing on Z - None Univariate Model Parameters. Parameter Estimated 95 Per Cent # Type Order Value Lower Limit t Upper Limit Std. Error 1 Mean 17.09 16.88 161.4 17.31 0.1059 2 Autoregressive 1 1 0.9067 0.8145 19.65 0.9990 0.4614E-01 3 Moving average 1 1 0.5693 0.3937 6.484 0.7449 0.8781E-01 Other Information and results. Residual Sum of Squares 19.268894 193 D.F. Residual Mean Square 9.983882648836834E-02 Number of residuals 196 Residual Standard error 0.3159728255536674 Backforecasting not used in Estimation Autocorrelation Function Data - THE ESTIMATED RESIDUALS - MODEL 1 196 Observations Original Series Mean of the Series -2.315255317133973E-03 St. Dev. of Series 0.3135367933397792 Number of observations 196 S. E. of mean 2.245283612692437E-02 T value of mean (against zero) -0.1031163860122610 1- 12 0.05 0.00 -0.09 -0.08 -0.09 0.02 0.17 0.04 0.06 0.02 -0.07 -0.09 St.E. 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.08 0.08 0.08 0.08 0.08 Mod. Q 0.4 0.4 2.1 3.5 5.1 5.2 11.0 11.3 12.2 12.2 13.3 15.0 13- 24 0.00 0.11 -0.11 0.01 0.06 0.09 -0.04 0.09 -0.08 -0.01 -0.04 0.05 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 15.0 17.5 20.0 20.0 20.8 22.6 22.9 24.9 26.4 26.4 26.9 27.4 Mean divided by St. Error (using N in S. D.) 0.1033804488928006 Q Statistic 25.482 DF 21 Prob. 0.77309 Modified Q Statistic 27.385 DF 21 Prob. 0.84153 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 1 196 Observations Original Series Mean of the Series -2.315255317133973E-03 St. Dev. of Series 0.3135367933397792 Number of observations 196 S. E. of mean 2.245283612692437E-02 T value of mean (against zero) -0.1031163860122610 1- 12 0.05 0.00 -0.09 -0.08 -0.08 0.02 0.16 0.01 0.05 0.04 -0.05 -0.05 13- 24 0.01 0.09 -0.14 -0.02 0.07 0.10 -0.03 0.09 -0.09 0.05 -0.04 0.03 Time Series Parameter Estimation for Model 1 Data - Z = VAR=Y Observations 197 Differencing on Z - 1) 1 of order 1 Transformations Examined - None. Univariate Model Parameters. Parameter Beginning # Type Order Value 1 Moving average 1 1 0.1000 Output at each iteration has been suppressed. Residual output has been suppressed. Initial sum of Squares 24.78602285620051 Iteration stops - Relative parameter change < 4.000000189989805E-03 Correlation Matrix of the Parameters. 1/Cond = 1.000 1 1 1.0000 End of Estimation for Model 1 Summary of model 1 Data - Z = VAR=Y Observations 197 Differencing on Z - 1) 1 of order 1 Univariate Model Parameters. Parameter Estimated 95 Per Cent # Type Order Value Lower Limit t Upper Limit Std. Error 1 Moving average 1 1 0.7024 0.6009 13.84 0.8039 0.5075E-01 Other Information and results. Residual Sum of Squares 19.885343 195 D.F. Residual Mean Square 0.1019761179568130 Number of residuals 196 Residual Standard error 0.3193369974757279 Backforecasting not used in Estimation Autocorrelation Function Data - THE ESTIMATED RESIDUALS - MODEL 1 196 Observations Original Series Mean of the Series 8.653804270120790E-03 St. Dev. of Series 0.3184037426167620 Number of observations 196 S. E. of mean 2.280136560376865E-02 T value of mean (against zero) 0.3795300869475324 1- 12 0.10 0.01 -0.11 -0.12 -0.13 -0.01 0.14 0.02 0.04 -0.01 -0.11 -0.12 St.E. 0.07 0.07 0.07 0.07 0.07 0.08 0.08 0.08 0.08 0.08 0.08 0.08 Mod. Q 2.2 2.2 4.7 7.7 10.9 11.0 14.9 15.0 15.2 15.3 17.6 20.9 13- 24 -0.04 0.06 -0.13 -0.01 0.04 0.08 -0.04 0.07 -0.10 -0.03 -0.06 0.03 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 21.2 22.1 25.8 25.9 26.3 27.5 27.9 29.0 31.1 31.4 32.3 32.5 Mean divided by St. Error (using N in S. D.) 0.3805019965720500 Q Statistic 30.448 DF 23 Prob. 0.86304 Modified Q Statistic 32.504 DF 23 Prob. 0.90988 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 1 196 Observations Original Series Mean of the Series 8.653804270120790E-03 St. Dev. of Series 0.3184037426167620 Number of observations 196 S. E. of mean 2.280136560376865E-02 T value of mean (against zero) 0.3795300869475324 1- 12 0.10 0.00 -0.11 -0.10 -0.11 0.00 0.12 -0.04 0.01 -0.01 -0.09 -0.08 13- 24 -0.02 0.04 -0.19 -0.04 0.04 0.07 -0.06 0.06 -0.12 0.02 -0.07 0.01 B34S(r) Matrix Command. Version February 2004. Date of Run d/m/y 8/ 6/04. Time of Run h:m:s 14:49:44. => CALL LOADDATA$ => CALL LOAD(RTEST)$ => CALL AUTOBJ(Y :AUTOBUILD :PRINT)$ Time Series Parameter Estimation for Model 1 Data - Z = VAR= Y Observations 197 Differencing on Z - None Transformations Examined - None. Univariate Model Parameters. Parameter Beginning # Type Order Value 1 Mean 17.06 2 Autoregressive 1 1 0.8392 3 Moving average 1 1 0.4787 4 Moving average 1 7 -0.1763 Output at each iteration has been suppressed. Residual output has been suppressed. Initial sum of Squares 18.58171499399077 Iteration stops - Relative parameter change < 4.000000000000000E-03 Correlation Matrix of the Parameters. 1/Cond = 0.7733E-01 1 2 3 4 1 1.0000 2 0.0259 1.0000 3 0.0343 0.7732 1.0000 4 -0.0064 0.4039 0.3515 1.0000 End of Estimation for Model 1 Summary of model 1 Data - Z = VAR= Y Observations 197 Differencing on Z - None Univariate Model Parameters. Parameter Estimated 95 Per Cent # Type Order Value Lower Limit t Upper Limit Std. Error 1 Mean 17.09 16.90 178.3 17.28 0.9582E-01 2 Autoregressive 1 1 0.8388 0.7108 13.11 0.9668 0.6399E-01 3 Moving average 1 1 0.4778 0.2833 4.913 0.6723 0.9725E-01 4 Moving average 1 7 -0.1765 -0.3201 -2.457 -0.3284E-01 0.7183E-01 Other Information and results. Residual Sum of Squares 18.574969 192 D.F. Residual Mean Square 9.674462830779887E-02 Number of residuals 196 Residual Standard error 0.3110379853133679 Backforecasting not used in Estimation B34S Matrix Command Ending. Last Command reached. Space available in allocator 2874961, peak space used 23510 Number variables used 31, peak number used 31 Number temp variables used 7, # user temp clean 0 B34S 8.10R (D:M:Y) 8/ 6/04 (H:M:S) 14:49:44 DATA STEP Box-Jenkins Series B PAGE 12 Variable Label # Cases Mean Std. Dev. Variance Maximum Minimum IBM 1 IBM COMMON STOCK CLOSING PRICES 369 478.469 84.2192 7092.88 603.000 306.000 CONSTANT 2 369 1.00000 0.00000 0.00000 1.00000 1.00000 Number of observations in data file 369 Current missing variable code 1.000000000000000E+31 Time Series Parameter Estimation for Model 1 Data - Z = VAR=IBM Observations 369 Differencing on Z - 1) 1 of order 1 Transformations Examined - None. Univariate Model Parameters. Parameter Beginning # Type Order Value 1 Moving average 1 1 0.1000 Output at each iteration has been suppressed. Residual output has been suppressed. Initial sum of Squares 19896.34467637599 Iteration stops - Relative parameter change < 4.000000189989805E-03 Correlation Matrix of the Parameters. 1/Cond = 1.000 1 1 1.0000 End of Estimation for Model 1 Summary of model 1 Data - Z = VAR=IBM Observations 369 Differencing on Z - 1) 1 of order 1 Univariate Model Parameters. Parameter Estimated 95 Per Cent # Type Order Value Lower Limit t Upper Limit Std. Error 1 Moving average 1 1 -0.8655E-01 -0.1906 -1.664 0.1749E-01 0.5202E-01 Other Information and results. Residual Sum of Squares 19216.604 367 D.F. Residual Mean Square 52.36131959384943 Number of residuals 368 Residual Standard error 7.236112187760042 Backforecasting not used in Estimation Autocorrelation Function Data - THE ESTIMATED RESIDUALS - MODEL 1 368 Observations Original Series Mean of the Series -0.2566378470485543 St. Dev. of Series 7.221715198951228 Number of observations 368 S. E. of mean 0.3769704648581590 T value of mean (against zero) -0.6807903296750802 1- 12 0.00 0.00 -0.05 -0.03 -0.03 0.12 0.05 0.04 -0.07 0.02 0.07 0.05 St.E. 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 Mod. Q 0.0 0.0 1.0 1.3 1.7 7.0 8.1 8.6 10.6 10.8 12.7 13.7 13- 24 -0.06 0.08 -0.08 0.12 0.11 0.04 0.04 0.07 -0.09 -0.03 0.06 0.02 St.E. 0.05 0.05 0.05 0.05 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 Mod. Q 15.0 17.3 20.0 25.2 30.0 30.6 31.2 33.2 36.4 36.7 38.3 38.5 Mean divided by St. Error (using N in S. D.) 0.6817172059786054 Q Statistic 36.878 DF 23 Prob. 0.96652 Modified Q Statistic 38.533 DF 23 Prob. 0.97769 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 1 368 Observations Original Series Mean of the Series -0.2566378470485543 St. Dev. of Series 7.221715198951228 Number of observations 368 S. E. of mean 0.3769704648581590 T value of mean (against zero) -0.6807903296750802 1- 12 0.00 0.00 -0.05 -0.03 -0.03 0.12 0.05 0.03 -0.06 0.03 0.09 0.04 13- 24 -0.07 0.07 -0.06 0.12 0.11 0.01 0.06 0.09 -0.06 -0.06 0.05 0.00 B34S(r) Matrix Command. Version February 2004. Date of Run d/m/y 8/ 6/04. Time of Run h:m:s 14:49:44. => CALL LOADDATA$ => CALL LOAD(RTEST)$ => CALL AUTOBJ(IBM :AUTOBUILD :PRINT)$ Time Series Parameter Estimation for Model 1 Data - Z = VAR= IBM Observations 369 Differencing on Z - 1) 1 of order 1 Transformations Examined - None. Univariate Model Parameters. Parameter Beginning # Type Order Value No Parameters in Model. Output at each iteration has been suppressed. Residual output has been suppressed. Initial sum of Squares 19363.00000000000 End of Estimation for Model 1 Summary of model 1 Data - Z = VAR= IBM Observations 369 Differencing on Z - 1) 1 of order 1 Univariate Model Parameters. Parameter Estimated 95 Per Cent # Type Order Value Lower Limit t Upper Limit Std. Error No Parameters in Model. Other Information and results. Residual Sum of Squares 19363.000 368 D.F. Residual Mean Square 52.61684782608696 Number of residuals 368 Residual Standard error 7.253747157579106 Backforecasting not used in Estimation B34S Matrix Command Ending. Last Command reached. Space available in allocator 2874961, peak space used 36613 Number variables used 39, peak number used 39 Number temp variables used 7, # user temp clean 0 B34S 8.10R (D:M:Y) 8/ 6/04 (H:M:S) 14:49:44 DATA STEP Box-Jenkins Series C PAGE 13 Variable Label # Cases Mean Std. Dev. Variance Maximum Minimum CHEM 1 Chemical Process Temperature 226 22.9739 2.05949 4.24149 27.1000 18.8000 CONSTANT 2 226 1.00000 0.00000 0.00000 1.00000 1.00000 Number of observations in data file 226 Current missing variable code 1.000000000000000E+31 Time Series Parameter Estimation for Model 1 Data - Z = VAR=CHEM Observations 226 Differencing on Z - 1) 1 of order 1 Transformations Examined - None. Univariate Model Parameters. Parameter Beginning # Type Order Value 1 Autoregressive 1 1 0.1000 Output at each iteration has been suppressed. Residual output has been suppressed. Initial sum of Squares 10.21800000000003 Iteration stops - Relative parameter change < 4.000000189989805E-03 Correlation Matrix of the Parameters. 1/Cond = 1.000 1 1 1.0000 End of Estimation for Model 1 Summary of model 1 Data - Z = VAR=CHEM Observations 226 Differencing on Z - 1) 1 of order 1 Univariate Model Parameters. Parameter Estimated 95 Per Cent # Type Order Value Lower Limit t Upper Limit Std. Error 1 Autoregressive 1 1 0.8131 0.7363 21.17 0.8899 0.3841E-01 Other Information and results. Residual Sum of Squares 4.0139016 223 D.F. Residual Mean Square 1.799955892082632E-02 Number of residuals 224 Residual Standard error 0.1341624348348908 Backforecasting not used in Estimation Autocorrelation Function Data - THE ESTIMATED RESIDUALS - MODEL 1 224 Observations Original Series Mean of the Series -9.019320867015703E-03 St. Dev. of Series 0.1335584351442110 Number of observations 224 S. E. of mean 8.943734334622080E-03 T value of mean (against zero) -1.008451339179544 1- 12 0.01 0.01 -0.05 -0.01 0.06 0.02 0.08 -0.02 -0.09 0.13 -0.09 0.08 St.E. 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 Mod. Q 0.0 0.0 0.7 0.7 1.5 1.6 3.0 3.1 4.9 8.9 11.0 12.7 13- 24 -0.06 0.04 0.01 -0.04 0.17 -0.08 0.00 -0.01 0.00 0.13 0.01 -0.01 St.E. 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 Mod. Q 13.5 13.9 13.9 14.3 21.4 22.9 22.9 23.0 23.0 27.1 27.2 27.2 Mean divided by St. Error (using N in S. D.) 1.010709911637248 Q Statistic 25.288 DF 23 Prob. 0.66437 Modified Q Statistic 27.219 DF 23 Prob. 0.75322 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 1 224 Observations Original Series Mean of the Series -9.019320867015703E-03 St. Dev. of Series 0.1335584351442110 Number of observations 224 S. E. of mean 8.943734334622080E-03 T value of mean (against zero) -1.008451339179544 1- 12 0.01 0.01 -0.05 -0.01 0.06 0.02 0.07 -0.02 -0.09 0.14 -0.10 0.07 13- 24 -0.05 0.04 0.00 -0.03 0.16 -0.09 0.01 -0.02 0.03 0.09 0.04 -0.06 B34S(r) Matrix Command. Version February 2004. Date of Run d/m/y 8/ 6/04. Time of Run h:m:s 14:49:44. => CALL LOADDATA$ => CALL LOAD(RTEST)$ => CALL AUTOBJ(CHEM :AUTOBUILD :PRINT)$ Time Series Parameter Estimation for Model 1 Data - Z = VAR= CHEM Observations 226 Differencing on Z - 1) 1 of order 1 Transformations Examined - None. Univariate Model Parameters. Parameter Beginning # Type Order Value 1 Autoregressive 1 1 0.8131 Output at each iteration has been suppressed. Residual output has been suppressed. Initial sum of Squares 4.013901639344329 Iteration stops - Relative parameter change < 4.000000000000000E-03 Correlation Matrix of the Parameters. 1/Cond = 1.000 1 1 1.0000 End of Estimation for Model 1 Summary of model 1 Data - Z = VAR= CHEM Observations 226 Differencing on Z - 1) 1 of order 1 Univariate Model Parameters. Parameter Estimated 95 Per Cent # Type Order Value Lower Limit t Upper Limit Std. Error 1 Autoregressive 1 1 0.8131 0.7363 21.17 0.8899 0.3841E-01 Other Information and results. Residual Sum of Squares 4.0139016 223 D.F. Residual Mean Square 1.799955892082633E-02 Number of residuals 224 Residual Standard error 0.1341624348348908 Backforecasting not used in Estimation B34S Matrix Command Ending. Last Command reached. Space available in allocator 2874961, peak space used 24884 Number variables used 32, peak number used 35 Number temp variables used 7, # user temp clean 0 B34S 8.10R (D:M:Y) 8/ 6/04 (H:M:S) 14:49:44 DATA STEP Box-Jenkins Series D PAGE 14 Variable Label # Cases Mean Std. Dev. Variance Maximum Minimum CHEMV 1 Chemical viscosity 310 9.13258 0.602640 0.363175 10.4000 7.40000 CONSTANT 2 310 1.00000 0.00000 0.00000 1.00000 1.00000 Number of observations in data file 310 Current missing variable code 1.000000000000000E+31 Time Series Parameter Estimation for Model 1 Data - Z = VAR=CHEMV Observations 310 Differencing on Z - None Transformations Examined - None. Univariate Model Parameters. Parameter Beginning # Type Order Value 1 Mean 0.5000 2 Autoregressive 1 1 0.1000 Output at each iteration has been suppressed. Residual output has been suppressed. Initial sum of Squares 18762.24709999999 Iteration stops - Relative parameter change < 4.000000189989805E-03 Correlation Matrix of the Parameters. 1/Cond = 0.5461E-01 1 2 1 1.0000 2 0.0432 1.0000 End of Estimation for Model 1 Summary of model 1 Data - Z = VAR=CHEMV Observations 310 Differencing on Z - None Univariate Model Parameters. Parameter Estimated 95 Per Cent # Type Order Value Lower Limit t Upper Limit Std. Error 1 Mean 9.158 8.912 74.24 9.405 0.1234 2 Autoregressive 1 1 0.8615 0.8048 30.41 0.9181 0.2833E-01 Other Information and results. Residual Sum of Squares 27.652484 307 D.F. Residual Mean Square 9.007323842049902E-02 Number of residuals 309 Residual Standard error 0.3001220392115498 Backforecasting not used in Estimation Autocorrelation Function Data - THE ESTIMATED RESIDUALS - MODEL 1 309 Observations Original Series Mean of the Series -2.258442114102827E-11 St. Dev. of Series 0.2991491937371221 Number of observations 309 S. E. of mean 1.704560728285917E-02 T value of mean (against zero) -1.324940834682895E-09 1- 12 0.01 -0.01 -0.02 -0.04 -0.03 0.03 0.00 0.00 -0.01 -0.05 0.00 0.05 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 0.1 0.1 0.2 0.6 0.9 1.1 1.1 1.1 1.1 1.8 1.8 2.7 13- 24 0.03 -0.06 -0.03 -0.08 -0.01 0.06 0.00 0.07 0.01 -0.02 0.04 0.07 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 3.0 4.1 4.3 6.2 6.3 7.3 7.3 8.8 8.8 9.0 9.6 11.2 Mean divided by St. Error (using N in S. D.) 1.327089969647183E-09 Q Statistic 10.507 DF 22 Prob. 0.18909E-01 Modified Q Statistic 11.160 DF 22 Prob. 0.27604E-01 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 1 309 Observations Original Series Mean of the Series -2.258442114102827E-11 St. Dev. of Series 0.2991491937371221 Number of observations 309 S. E. of mean 1.704560728285917E-02 T value of mean (against zero) -1.324940834682895E-09 1- 12 0.01 -0.01 -0.02 -0.04 -0.03 0.03 0.00 0.00 -0.01 -0.05 0.00 0.05 13- 24 0.02 -0.06 -0.02 -0.07 -0.01 0.05 -0.01 0.06 0.01 -0.01 0.05 0.06 Time Series Parameter Estimation for Model 1 Data - Z = VAR=CHEMV Observations 310 Differencing on Z - 1) 1 of order 1 Transformations Examined - None. Univariate Model Parameters. Parameter Beginning # Type Order Value 1 Moving average 1 1 0.1000 Output at each iteration has been suppressed. Residual output has been suppressed. Initial sum of Squares 29.76287459119371 Iteration stops - Relative parameter change < 4.000000189989805E-03 Correlation Matrix of the Parameters. 1/Cond = 1.000 1 1 1.0000 End of Estimation for Model 1 Summary of model 1 Data - Z = VAR=CHEMV Observations 310 Differencing on Z - 1) 1 of order 1 Univariate Model Parameters. Parameter Estimated 95 Per Cent # Type Order Value Lower Limit t Upper Limit Std. Error 1 Moving average 1 1 0.5921E-01 -0.5455E-01 1.041 0.1730 0.5688E-01 Other Information and results. Residual Sum of Squares 29.720604 308 D.F. Residual Mean Square 9.649546759498344E-02 Number of residuals 309 Residual Standard error 0.3106371960905253 Backforecasting not used in Estimation Autocorrelation Function Data - THE ESTIMATED RESIDUALS - MODEL 1 309 Observations Original Series Mean of the Series 3.783746641453905E-03 St. Dev. of Series 0.3101110571870764 Number of observations 309 S. E. of mean 1.767021742177349E-02 T value of mean (against zero) 0.2141313007723108 1- 12 0.00 -0.07 -0.08 -0.09 -0.07 0.00 -0.02 -0.02 -0.03 -0.07 -0.01 0.05 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 0.0 1.3 3.2 5.5 6.9 6.9 7.0 7.2 7.5 9.0 9.0 9.7 13- 24 0.02 -0.07 -0.04 -0.09 -0.03 0.05 -0.01 0.06 0.00 -0.04 0.03 0.06 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 9.8 11.5 12.2 14.9 15.2 15.8 15.9 16.9 16.9 17.3 17.7 18.7 Mean divided by St. Error (using N in S. D.) 0.2144786348217957 Q Statistic 17.918 DF 23 Prob. 0.23810 Modified Q Statistic 18.721 DF 23 Prob. 0.28268 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 1 309 Observations Original Series Mean of the Series 3.783746641453905E-03 St. Dev. of Series 0.3101110571870764 Number of observations 309 S. E. of mean 1.767021742177349E-02 T value of mean (against zero) 0.2141313007723108 1- 12 0.00 -0.07 -0.08 -0.09 -0.08 -0.02 -0.05 -0.05 -0.06 -0.09 -0.04 0.01 13- 24 -0.01 -0.10 -0.07 -0.12 -0.07 -0.02 -0.08 0.00 -0.06 -0.07 -0.01 0.00 B34S(r) Matrix Command. Version February 2004. Date of Run d/m/y 8/ 6/04. Time of Run h:m:s 14:49:44. => CALL LOADDATA$ => CALL LOAD(RTEST)$ => CALL AUTOBJ(CHEMV :AUTOBUILD :PRINT)$ Time Series Parameter Estimation for Model 1 Data - Z = VAR= CHEMV Observations 310 Differencing on Z - 1) 1 of order 1 Transformations Examined - None. Univariate Model Parameters. Parameter Beginning # Type Order Value 1 Autoregressive 1 1 0.8030 2 Moving average 1 1 0.9637 Output at each iteration has been suppressed. Residual output has been suppressed. Initial sum of Squares 27.84204177325907 Iteration stops - Relative parameter change < 4.000000000000000E-03 Correlation Matrix of the Parameters. 1/Cond = 0.6737E-01 1 2 1 1.0000 2 0.6404 1.0000 End of Estimation for Model 1 Summary of model 1 Data - Z = VAR= CHEMV Observations 310 Differencing on Z - 1) 1 of order 1 Univariate Model Parameters. Parameter Estimated 95 Per Cent # Type Order Value Lower Limit t Upper Limit Std. Error 1 Autoregressive 1 1 0.8030 0.7149 18.24 0.8910 0.4401E-01 2 Moving average 1 1 0.9637 0.9298 56.86 0.9976 0.1695E-01 Other Information and results. Residual Sum of Squares 27.842042 306 D.F. Residual Mean Square 9.098706461849314E-02 Number of residuals 308 Residual Standard error 0.3016406216319233 Backforecasting not used in Estimation B34S Matrix Command Ending. Last Command reached. Space available in allocator 2874961, peak space used 30848 Number variables used 35, peak number used 35 Number temp variables used 7, # user temp clean 0 B34S 8.10R (D:M:Y) 8/ 6/04 (H:M:S) 14:49:44 DATA STEP Wolfer Sunspot 1770-1896 PAGE 15 Variable Label # Cases Mean Std. Dev. Variance Maximum Minimum WOLFER 1 Wolfer sunspot series 100 46.9300 37.3650 1396.15 154.000 0.00000 CONSTANT 2 100 1.00000 0.00000 0.00000 1.00000 1.00000 Number of observations in data file 100 Current missing variable code 1.000000000000000E+31 Time Series Parameter Estimation for Model 1 Data - Z = VAR=WOLFER Observations 100 Differencing on Z - None Transformations Examined - None. Univariate Model Parameters. Parameter Beginning # Type Order Value 1 Mean 0.5000 2 Autoregressive 1 1 0.1000 3 Autoregressive 1 2 0.1000 Output at each iteration has been suppressed. Residual output has been suppressed. Initial sum of Squares 234592.3199999999 Iteration stops - Relative parameter change < 4.000000189989805E-03 Correlation Matrix of the Parameters. 1/Cond = 0.3696E-04 1 2 3 1 1.0000 2 0.0362 1.0000 3 -0.0207 -0.8217 1.0000 End of Estimation for Model 1 Summary of model 1 Data - Z = VAR=WOLFER Observations 100 Differencing on Z - None Univariate Model Parameters. Parameter Estimated 95 Per Cent # Type Order Value Lower Limit t Upper Limit Std. Error 1 Mean 47.35 37.25 9.377 57.45 5.049 2 Autoregressive 1 1 1.405 1.258 19.17 1.551 0.7329E-01 3 Autoregressive 1 2 -0.7115 -0.8565 -9.811 -0.5664 0.7252E-01 Other Information and results. Residual Sum of Squares 22295.468 95 D.F. Residual Mean Square 234.6891416738741 Number of residuals 98 Residual Standard error 15.31956728089518 Backforecasting not used in Estimation Autocorrelation Function Data - THE ESTIMATED RESIDUALS - MODEL 1 98 Observations Original Series Mean of the Series -4.751373444349258E-10 St. Dev. of Series 15.08326159005610 Number of observations 98 S. E. of mean 1.531473181317068 T value of mean (against zero) -3.102485569001655E-10 1- 12 0.15 -0.16 0.05 0.14 0.12 0.12 -0.04 0.00 0.22 0.05 0.15 0.15 St.E. 0.10 0.10 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.12 0.12 0.12 Mod. Q 2.2 4.9 5.2 7.2 8.7 10.3 10.5 10.5 15.6 15.9 18.6 21.1 13- 24 -0.03 -0.04 0.07 0.00 -0.01 -0.02 -0.12 -0.07 -0.04 -0.02 0.01 0.02 St.E. 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 Mod. Q 21.2 21.4 22.0 22.0 22.0 22.1 23.8 24.4 24.6 24.6 24.6 24.6 Mean divided by St. Error (using N in S. D.) 3.118436756761948E-10 Q Statistic 22.059 DF 21 Prob. 0.60391 Modified Q Statistic 24.633 DF 21 Prob. 0.73658 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 98 Observations Original Series Mean of the Series -4.751373444349258E-10 St. Dev. of Series 15.08326159005610 Number of observations 98 S. E. of mean 1.531473181317068 T value of mean (against zero) -3.102485569001655E-10 1- 12 0.15 -0.19 0.11 0.08 0.11 0.13 -0.06 0.04 0.17 -0.04 0.24 0.06 13- 24 -0.03 -0.04 -0.04 -0.06 -0.04 -0.09 -0.11 -0.15 -0.13 -0.04 -0.01 0.06 Time Series Parameter Estimation for Model 1 Data - Z = VAR=WOLFER Observations 100 Differencing on Z - None Transformations Examined - None. Univariate Model Parameters. Parameter Beginning # Type Order Value 1 Mean 0.5000 2 Autoregressive 1 1 0.1000 3 Autoregressive 1 2 0.1000 4 Autoregressive 1 3 0.1000 Output at each iteration has been suppressed. Residual output has been suppressed. Initial sum of Squares 204536.4825000000 Iteration stops - Relative parameter change < 4.000000189989805E-03 Correlation Matrix of the Parameters. 1/Cond = 0.1668E-04 1 2 3 4 1 1.0000 2 -0.0042 1.0000 3 0.0229 -0.8900 1.0000 4 -0.0326 0.7018 -0.8923 1.0000 End of Estimation for Model 1 Summary of model 1 Data - Z = VAR=WOLFER Observations 100 Differencing on Z - None Univariate Model Parameters. Parameter Estimated 95 Per Cent # Type Order Value Lower Limit t Upper Limit Std. Error 1 Mean 46.75 34.32 7.522 59.18 6.215 2 Autoregressive 1 1 1.552 1.349 15.27 1.755 0.1017 3 Autoregressive 1 2 -1.007 -1.326 -6.306 -0.6876 0.1597 4 Autoregressive 1 3 0.2076 0.4226E-02 2.042 0.4110 0.1017 Other Information and results. Residual Sum of Squares 21273.444 93 D.F. Residual Mean Square 228.7467066400151 Number of residuals 97 Residual Standard error 15.12437458673962 Backforecasting not used in Estimation Autocorrelation Function Data - THE ESTIMATED RESIDUALS - MODEL 1 97 Observations Original Series Mean of the Series 4.361256767948518E-07 St. Dev. of Series 14.80924889243045 Number of observations 97 S. E. of mean 1.511462635847147 T value of mean (against zero) 2.885454568649733E-07 1- 12 0.04 -0.12 0.09 0.05 -0.02 0.05 -0.07 -0.04 0.23 0.02 0.16 0.16 St.E. 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.11 0.11 0.11 0.11 0.11 Mod. Q 0.1 1.7 2.5 2.8 2.9 3.2 3.7 3.9 9.6 9.6 12.5 15.4 13- 24 -0.03 -0.06 0.06 -0.05 -0.05 -0.03 -0.12 -0.04 -0.01 0.00 0.02 0.05 St.E. 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 Mod. Q 15.5 15.9 16.3 16.6 16.9 17.0 18.7 18.9 19.0 19.0 19.0 19.4 Mean divided by St. Error (using N in S. D.) 2.900444043897519E-07 Q Statistic 16.915 DF 20 Prob. 0.34150 Modified Q Statistic 19.371 DF 20 Prob. 0.50214 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 97 Observations Original Series Mean of the Series 4.361256767948518E-07 St. Dev. of Series 14.80924889243045 Number of observations 97 S. E. of mean 1.511462635847147 T value of mean (against zero) 2.885454568649733E-07 1- 12 0.04 -0.13 0.10 0.03 0.00 0.06 -0.09 -0.01 0.21 -0.01 0.24 0.11 13- 24 -0.01 -0.04 -0.02 -0.04 -0.03 -0.08 -0.11 -0.14 -0.14 -0.04 -0.01 0.04 B34S(r) Matrix Command. Version February 2004. Date of Run d/m/y 8/ 6/04. Time of Run h:m:s 14:49:44. => CALL LOADDATA$ => CALL LOAD(RTEST)$ => CALL AUTOBJ(WOLFER :AUTOBUILD :PRINT)$ Time Series Parameter Estimation for Model 1 Data - Z = VAR= WOLFER Observations 100 Differencing on Z - 1) 1 of order 1 Transformations Examined - None. Univariate Model Parameters. Parameter Beginning # Type Order Value 1 Moving average 1 1 -0.7138 2 Moving average 1 3 0.5102 3 Moving average 1 4 0.4558 4 Moving average 1 5 0.3309 Output at each iteration has been suppressed. Residual output has been suppressed. Initial sum of Squares 23175.30542362361 Iteration stops - Relative parameter change < 4.000000000000000E-03 Correlation Matrix of the Parameters. 1/Cond = 0.1323 1 2 3 4 1 1.0000 2 -0.4123 1.0000 3 -0.3165 0.5712 1.0000 4 -0.0008 0.0847 0.4767 1.0000 End of Estimation for Model 1 Summary of model 1 Data - Z = VAR= WOLFER Observations 100 Differencing on Z - 1) 1 of order 1 Univariate Model Parameters. Parameter Estimated 95 Per Cent # Type Order Value Lower Limit t Upper Limit Std. Error 1 Moving average 1 1 -0.7136 -0.8720 -9.010 -0.5552 0.7920E-01 2 Moving average 1 3 0.5102 0.3204 5.377 0.7000 0.9489E-01 3 Moving average 1 4 0.4554 0.2428 4.283 0.6680 0.1063 4 Moving average 1 5 0.3303 0.1537 3.741 0.5070 0.8831E-01 Other Information and results. Residual Sum of Squares 23175.295 95 D.F. Residual Mean Square 243.9504740527639 Number of residuals 99 Residual Standard error 15.61891398442171 Backforecasting not used in Estimation B34S Matrix Command Ending. Last Command reached. Space available in allocator 2874961, peak space used 17615 Number variables used 53, peak number used 53 Number temp variables used 7, # user temp clean 0 B34S 8.10R (D:M:Y) 8/ 6/04 (H:M:S) 14:49:44 DATA STEP SCA / Workbench Data PAGE 16 Variable # Cases Mean Std Deviation Variance Maximum Minimum OBSNUM 1 312 156.5000000 90.21086409 8138.000000 312.0000000 1.000000000 APPL_TV 2 312 1787.448718 1222.457886 1494403.284 7540.000000 389.0000000 APPLANCE 3 312 540.0865385 200.6497698 40260.33011 1096.000000 194.0000000 FURNITUR 4 312 2811.080128 1393.206112 1941023.270 6676.000000 743.0000000 VARIETY 5 312 644.9294872 197.7280965 39096.40016 1497.000000 348.0000000 HSOLD 6 312 52.24358974 11.73905554 137.8054250 89.00000000 24.00000000 HSTART 7 312 128.5352564 39.60433460 1568.503319 234.0000000 47.20000000 INVENTRY 8 312 2152.426282 642.5376697 412854.6569 3304.000000 1056.000000 PPIHHOLD 9 312 93.80897436 25.39529635 644.9210768 129.3000000 51.40000000 CONSTANT 10 312 1.000000000 0.000000000 0.000000000 1.000000000 1.000000000 Number of observations in data file 312 Current missing variable code 1.000000000000000E+31 B34S(r) Matrix Command. Version February 2004. Date of Run d/m/y 8/ 6/04. Time of Run h:m:s 14:49:44. => CALL LOADDATA$ => CALL LOAD(MOVEBJ)$ => CALL PRINT(MOVEBJ)$ MOVEBJ = Subroutine SUBROUTINE MOVEBJ(SERIES,ISEAS,IBEGIN,ACTUAL,FORE,OBS,NOUT,IPRINT)$ IEND=NOROWS(SERIES)-NOUT$ IF(IBEGIN.GT.IEND)THEN$ CALL EPPRINT('ERROR: Call to movebj has ibegin > series length')$ GO TO ENDIT$ ENDIF$ ACTUAL=ARRAY(IEND-IBEGIN+2-NOUT:)$ FORE=ACTUAL$ OBS =ACTUAL$ IDONE=0$ DO I=IBEGIN,IEND$ J=INTEGERS(1,I)$ SERIES2=SERIES(J)$ IF(IPRINT.NE.0)THEN$ CALL AUTOBJ(SERIES2 :AUTOBUILD :PRINT :SEASONAL ISEAS :FORECAST INDEX(NOUT,NOROWS(SERIES2)))$ ENDIF$ IF(IPRINT.EQ.0)THEN$ CALL AUTOBJ(SERIES2 :AUTOBUILD :SEASONAL ISEAS :FORECAST INDEX(NOUT,NOROWS(SERIES2)))$ ENDIF$ IDONE=IDONE+1$ FORE(IDONE) =%FCAST(NOUT)$ OBS(IDONE) =%FOREOBS(NOUT)$ ACTUAL(IDONE) =SERIES(I+NOUT)$ ENDDO$ ENDIT CONTINUE$ RETURN$ END$ => CALL ECHOOFF$ Obs OBS ACTUAL FORE 1 201.0 751.0 783.3 2 202.0 789.0 828.1 3 203.0 798.0 836.8 4 204.0 1096. 1051. 5 205.0 680.0 758.9 6 206.0 606.0 635.1 7 207.0 655.0 689.7 8 208.0 651.0 670.9 9 209.0 676.0 737.9 10 210.0 713.0 728.2 11 211.0 776.0 802.0 12 212.0 745.0 745.7 13 213.0 689.0 704.8 14 214.0 686.0 737.8 15 215.0 768.0 739.8 16 216.0 997.0 1029. 17 217.0 590.0 634.0 18 218.0 561.0 521.1 19 219.0 629.0 610.4 20 220.0 655.0 617.7 21 221.0 679.0 679.3 22 222.0 787.0 709.1 23 223.0 786.0 825.1 24 224.0 774.0 771.6 25 225.0 685.0 716.9 26 226.0 699.0 715.5 27 227.0 810.0 782.2 28 228.0 1054. 1030. 29 229.0 677.0 642.5 30 230.0 605.0 619.4 31 231.0 708.0 676.8 32 232.0 697.0 691.4 33 233.0 776.0 741.9 34 234.0 819.0 836.0 35 235.0 798.0 861.2 36 236.0 783.0 818.6 37 237.0 734.0 707.3 38 238.0 750.0 739.8 39 239.0 861.0 842.2 40 240.0 1055. 1093. 41 241.0 678.0 681.1 42 242.0 611.0 616.6 43 243.0 697.0 701.3 44 244.0 681.0 694.4 45 245.0 762.0 764.5 46 246.0 778.0 815.5 47 247.0 775.0 784.4 48 248.0 726.0 775.3 49 249.0 666.0 685.5 50 250.0 722.0 695.2 51 251.0 760.0 812.9 52 252.0 911.0 993.6 53 253.0 596.0 574.2 54 254.0 561.0 520.4 55 255.0 643.0 628.2 56 256.0 678.0 631.9 57 257.0 739.0 736.3 58 258.0 712.0 774.4 59 259.0 777.0 740.2 60 260.0 717.0 713.1 61 261.0 612.0 677.1 62 262.0 674.0 698.3 63 263.0 713.0 725.9 64 264.0 840.0 890.3 65 265.0 621.0 540.3 66 266.0 590.0 524.7 67 267.0 641.0 639.1 68 268.0 649.0 676.4 69 269.0 664.0 707.6 70 270.0 744.0 671.6 71 271.0 759.0 780.1 72 272.0 719.0 695.4 73 273.0 671.0 613.5 74 274.0 718.0 728.4 75 275.0 736.0 744.0 76 276.0 895.0 876.1 77 277.0 628.0 648.9 78 278.0 582.0 583.7 79 279.0 655.0 644.0 80 280.0 688.0 656.9 81 281.0 714.0 710.5 82 282.0 790.0 767.1 83 283.0 905.0 790.5 84 284.0 806.0 787.6 85 285.0 731.0 733.3 86 286.0 763.0 791.5 87 287.0 794.0 801.3 88 288.0 935.0 961.4 89 289.0 633.0 675.4 90 290.0 586.0 616.8 91 291.0 683.0 663.4 92 292.0 665.0 695.4 93 293.0 691.0 707.9 94 294.0 813.0 766.2 95 295.0 768.0 875.5 96 296.0 746.0 729.9 97 297.0 686.0 672.2 98 298.0 711.0 724.7 99 299.0 838.0 748.7 100 300.0 948.0 943.2 101 301.0 685.0 645.6 102 302.0 606.0 612.0 103 303.0 715.0 699.5 104 304.0 645.0 694.8 105 305.0 728.0 722.8 106 306.0 782.0 816.3 107 307.0 813.0 805.3 108 308.0 785.0 775.4 109 309.0 695.0 698.0 110 310.0 691.0 733.1 111 311.0 768.0 801.5 112 312.0 877.0 914.2 Obs OBS ACTUAL FORE 1 203.0 798.0 871.8 2 204.0 1096. 1076. 3 205.0 680.0 756.2 4 206.0 606.0 652.6 5 207.0 655.0 738.7 6 208.0 651.0 701.8 7 209.0 676.0 764.8 8 210.0 713.0 770.7 9 211.0 776.0 842.2 10 212.0 745.0 767.2 11 213.0 689.0 718.5 12 214.0 686.0 746.5 13 215.0 768.0 771.7 14 216.0 997.0 1052. 15 217.0 590.0 622.3 16 218.0 561.0 556.1 17 219.0 629.0 620.6 18 220.0 655.0 576.7 19 221.0 679.0 649.7 20 222.0 787.0 689.6 21 223.0 786.0 784.3 22 224.0 774.0 751.7 23 225.0 685.0 737.0 24 226.0 699.0 731.1 25 227.0 810.0 808.2 26 228.0 1054. 1024. 27 229.0 677.0 614.7 28 230.0 605.0 578.7 29 231.0 708.0 661.5 30 232.0 697.0 684.8 31 233.0 776.0 722.7 32 234.0 819.0 815.2 33 235.0 798.0 851.0 34 236.0 783.0 850.4 35 237.0 734.0 757.3 36 238.0 750.0 744.3 37 239.0 861.0 823.2 38 240.0 1055. 1078. 39 241.0 678.0 690.8 40 242.0 611.0 637.3 41 243.0 697.0 705.7 42 244.0 681.0 699.4 43 245.0 762.0 773.5 44 246.0 778.0 823.6 45 247.0 775.0 804.7 46 248.0 726.0 799.1 47 249.0 666.0 716.6 48 250.0 722.0 731.2 49 251.0 760.0 809.3 50 252.0 911.0 1006. 51 253.0 596.0 646.2 52 254.0 561.0 553.3 53 255.0 643.0 594.7 54 256.0 678.0 602.7 55 257.0 739.0 703.6 56 258.0 712.0 747.3 57 259.0 777.0 771.9 58 260.0 717.0 727.3 59 261.0 612.0 654.9 60 262.0 674.0 731.9 61 263.0 713.0 771.6 62 264.0 840.0 909.1 63 265.0 621.0 574.5 64 266.0 590.0 507.2 65 267.0 641.0 563.3 66 268.0 649.0 641.5 67 269.0 664.0 720.6 68 270.0 744.0 707.5 69 271.0 759.0 767.2 70 272.0 719.0 673.8 71 273.0 671.0 611.5 72 274.0 718.0 671.5 73 275.0 736.0 713.5 74 276.0 895.0 885.5 75 277.0 628.0 644.1 76 278.0 582.0 586.1 77 279.0 655.0 654.5 78 280.0 688.0 652.2 79 281.0 714.0 689.5 80 282.0 790.0 750.0 81 283.0 905.0 777.6 82 284.0 806.0 743.5 83 285.0 731.0 692.5 84 286.0 763.0 782.9 85 287.0 794.0 819.3 86 288.0 935.0 977.4 87 289.0 633.0 692.0 88 290.0 586.0 650.7 89 291.0 683.0 700.0 90 292.0 665.0 700.9 91 293.0 691.0 713.2 92 294.0 813.0 798.2 93 295.0 768.0 868.5 94 296.0 746.0 772.5 95 297.0 686.0 724.6 96 298.0 711.0 697.7 97 299.0 838.0 748.7 98 300.0 948.0 905.9 99 301.0 685.0 599.2 100 302.0 606.0 589.4 101 303.0 715.0 682.5 102 304.0 645.0 690.1 103 305.0 728.0 738.5 104 306.0 782.0 837.4 105 307.0 813.0 818.9 106 308.0 785.0 788.4 107 309.0 695.0 689.5 108 310.0 691.0 729.9 109 311.0 768.0 823.0 110 312.0 877.0 951.1 B34S Matrix Command Ending. Last Command reached. Space available in allocator 2874817, peak space used 2203358 Number variables used 99, peak number used 687 Number temp variables used 4696, # user temp clean 0 B34S 8.10R (D:M:Y) 8/ 6/04 (H:M:S) 14:49:52 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+31 B34S(r) Matrix Command. Version February 2004. Date of Run d/m/y 8/ 6/04. Time of Run h:m:s 14:49:52. => CALL ECHOOFF$ Obs AA AATEST 1 9.920 0.9708 2 9.157 0.8960 3 8.099 0.7925 4 6.949 0.6800 5 5.871 0.5745 6 4.961 0.4854 7 4.252 0.4161 8 3.736 0.3656 9 3.376 0.3304 10 3.132 0.3065 11 2.943 0.2880 12 2.752 0.2693 13 2.527 0.2473 14 2.263 0.2215 15 1.972 0.1930 16 1.685 0.1649 17 1.428 0.1398 18 1.237 0.1210 19 1.128 0.1103 20 1.102 0.1078 21 1.136 0.1112 22 1.197 0.1171 23 1.254 0.1228 24 1.286 0.1259 25 1.286 0.1259 26 1.251 0.1224 27 1.181 0.1156 28 1.087 0.1064 29 0.9901 0.9688E-01 30 0.9280 0.9081E-01 31 0.9217 0.9019E-01 32 0.9692 0.9484E-01 33 1.041 0.1019 34 1.077 0.1054 35 1.048 0.1026 36 0.9447 0.9244E-01 37 0.7797 0.7630E-01 38 0.5883 0.5757E-01 39 0.3986 0.3900E-01 40 0.2284 0.2235E-01 41 0.8991E-01 0.8799E-02 42 -0.2390E-01 -0.2339E-02 43 -0.1274 -0.1247E-01 44 -0.2411 -0.2359E-01 45 -0.3844 -0.3762E-01 46 -0.5701 -0.5579E-01 47 -0.8053 -0.7881E-01 48 -1.086 -0.1062 49 -1.387 -0.1357 50 -1.685 -0.1649 51 -1.952 -0.1910 52 -2.153 -0.2107 53 -2.270 -0.2222 54 -2.298 -0.2249 55 -2.240 -0.2192 56 -2.119 -0.2073 57 -1.967 -0.1925 58 -1.814 -0.1775 59 -1.666 -0.1630 60 -1.517 -0.1485 61 -1.360 -0.1331 62 -1.195 -0.1169 63 -1.022 -0.1000 64 -0.8765 -0.8578E-01 65 -0.7793 -0.7626E-01 66 -0.7386 -0.7228E-01 67 -0.7523 -0.7361E-01