TIME=19:07:03 DATE= 5/19/97 THE MAXIMUM NUMBER OF OBSERVATIONS ALLOWED IN A SERIES IS: 600 THE MAXIMUM NUMBER OF SERIES ALLOWED IN A MODEL IS: 30 THE SERIAL NUMBER IS: 556 THE PRODUCT NUMBER IS: 6 NOTE -> THE PROGRAM IS USING THE STANDARD PROCEDURE FOR COMPUTING THE AUTOCORRELATION AND PARTIAL AUTOCORRELATION FUNCTIONS. Analysis for Variable Y = PRICE SERIES STATISTICS ARE IN TERMS OF THE DIFFERENCED AND TRANSFORMED DATA Differencing Orders Applied to Y NONE Power Transformation (Lambda) on Y 1.00 Number of Effective Observations n 20 Mean of the Series Y 63.00000 Variance of the Series Y 533.4000 Standard Deviation of the Series Y 23.09545 Standard Error of the Mean / n 5.164301 Mean divided by its Standard Error /[ / n] 12.19914 THE STARTING MODEL FOR THIS VARIABLE MODEL COMPONENT LAG COEFFICIENT STANDARD T-RATIO # (BOP) ERROR 1 PURE RIGHT-HAND SIDE CONS 63.00000 2 Autoregressive-Factor # 1 1 1.245311 3 2 -0.3800780 4 Moving Average-Factor # 2 1 0.2635536 Y(T) = 467.47 + [(1- 1.2453B** 1+ 0.380B** 2)]**-1 [ (1- 0.264B** 1)] [A(T)] THE STARTING MODEL FOR THIS VARIABLE MODEL COMPONENT LAG COEFFICIENT STANDARD T-RATIO # (BOP) ERROR 1 PURE RIGHT-HAND SIDE CONS 63.00000 2 Autoregressive-Factor # 1 1 1.245311 3 2 -0.3800780 4 Moving Average-Factor # 2 1 0.2635536 Y(T) = 467.47 + [(1- 1.2453B** 1+ 0.380B** 2)]**-1 [ (1- 0.264B** 1)] [A(T)] ADVISORY THE TEST FOR CONSTANCY OF PARAMETERS WILL NOT BE EXECUTED. NOTE -> THE PROGRAM IS USING THE STANDARD PROCEDURE FOR COMPUTING THE AUTOCORRELATION AND PARTIAL AUTOCORRELATION FUNCTIONS. Analysis for Variable Y = DEMAND SERIES STATISTICS ARE IN TERMS OF THE DIFFERENCED AND TRANSFORMED DATA Differencing Orders Applied to Y NONE Power Transformation (Lambda) on Y 1.00 Number of Effective Observations n 20 Mean of the Series Y 69.00000 Variance of the Series Y 1041.900 Standard Deviation of the Series Y 32.27848 Standard Error of the Mean / n 7.217687 Mean divided by its Standard Error /[ / n] 9.559850 THE STARTING MODEL FOR THIS VARIABLE MODEL COMPONENT LAG COEFFICIENT STANDARD T-RATIO # (BOP) ERROR 1 PURE RIGHT-HAND SIDE CONS 69.00000 2 Autoregressive-Factor # 1 1 0.6176537 3 Moving Average-Factor # 2 1 0.6576986E-01 4 2 -0.4898755 Y(T) = 180.46 + [(1- 0.618B** 1)]**-1 [(1- 0.066B** 1 + 0.490B** 2)] [A(T)] THE STARTING MODEL FOR THIS VARIABLE MODEL COMPONENT LAG COEFFICIENT STANDARD T-RATIO # (BOP) ERROR 1 PURE RIGHT-HAND SIDE CONS 69.00000 2 Autoregressive-Factor # 1 1 0.6176537 3 Moving Average-Factor # 2 1 0.6576986E-01 4 2 -0.4898755 Y(T) = 180.46 + [(1- 0.618B** 1)]**-1 [(1- 0.066B** 1 + 0.490B** 2)] [A(T)] ADVISORY THE TEST FOR CONSTANCY OF PARAMETERS WILL NOT BE EXECUTED. NOTE -> THE PROGRAM IS USING THE STANDARD PROCEDURE FOR COMPUTING THE AUTOCORRELATION AND PARTIAL AUTOCORRELATION FUNCTIONS. PLOT OF THE OBSERVED (ACTUAL) SERIES GRAPH KEY A = PRICE B = DEMAND 30.000 136.00 DATE ³++++++++++++++++++++++++++++++++++++++++++++++++++++++++³ 1960 ³A B ³ 30.000 134.00 1961 ³ A B ³ 31.000 112.00 1962 ³ A B³ 37.000 136.00 1963 ³ A B ³ 42.000 109.00 1964 ³ A B ³ 43.000 105.00 1965 ³ A B ³ 45.000 87.000 1966 ³ A B ³ 50.000 56.000 1967 ³ B A ³ 54.000 43.000 1968 ³ A B ³ 54.000 77.000 1969 Ã B A ´ 57.000 35.000 1970 ³ A B ³ 58.000 65.000 1971 ³ B A ³ 58.000 56.000 1972 ³ BA ³ 60.000 58.000 1973 ³ B A ³ 73.000 55.000 1974 ³ B A ³ 88.000 49.000 1975 ³ B A ³ 89.000 39.000 1976 ³ B A ³ 92.000 36.000 1977 ³ B A ³ 97.000 46.000 1978 ³ B A ³ 100.00 40.000 1979 Ã B A ´ 102.00 42.000 Ã++++++++++++++++++++++++++++++++++++++++++++++++++++++++´ Analysis for Variable Y = DEMAND as a f(input var(s)) X1 = PRICE SERIES NAME IS : PRICE THE FILTER APPLIED TO THE INPUT SERIES MODEL COMPONENT LAG COEFFICIENT STANDARD T-RATIO # (BOP) ERROR Differencing 1 1 PURE RIGHT-HAND SIDE CONS 3.789473 [(1-B**1)]Y(T) = 3.7895 + [A(T)] THE FILTER APPLIED TO THE OUTPUT SERIES MODEL COMPONENT LAG COEFFICIENT STANDARD T-RATIO # (BOP) ERROR 1 PURE RIGHT-HAND SIDE CONS 13.91611 Y(T) = 13.916 + [A(T)] CROSS CORRELATIONS BETWEEN: FILTERED INPUT AND FILTERED OUTPUT SERIES Mean of X1 0.36132E-06 Mean of Y 51.663 Variance of X1 15.324 Variance of Y 862.66 St. Deviation of X1 3.9146 St. Deviation of Y 29.371 LAG CROSS- STANDARD T-RATIO LAG CROSS- STANDARD T-RATIO CORRELATION ERROR CORRELATION ERROR 0 -0.092 0.229 -0.40 0 -0.092 0.229 -0.40 LAG IMPULSE STANDARD T-RATIO RESPONSE WEIGHT ERROR 0 -0.68926 1.721 -.400 LAG CCF T FB CCF T VALUE RATIO -1 0 +1 VALUE RATIO -1 0 +1 0 -0.092 -0.40 { ** } -0.092 -0.40 { ** } THE STARTING MODEL FOR THIS VARIABLE MODEL COMPONENT LAG COEFFICIENT STANDARD T-RATIO # (BOP) ERROR 1 PURE RIGHT-HAND SIDE CONS 0.1000000 2 Autoregressive-Factor # 1 1 0.1000000 INPUT SERIES X1 PRICE Lambda Value 3 Omega (input) -Factor # 2 0 0.1000000 Y(T) = 0.11111 +[X1(T)][(+ 0.100)] + [(1- 0.100B** 1)]**-1 [A(T)] Estimation/Diagnostic Checking for Variable Y = DEMAND as a f(input var(s)) X1 = PRICE MODEL STATISTICS IN TERMS OF THE ORIGINAL DATA Number of Residuals (R) =n 19 Number of Degrees of Freedom =n-m 16 Residual Mean = R/n 0.114184E-03 Sum of Squares = R 4930.71 Variance var= R /(n) 259.511 Adjusted Variance = R /(n-m) 308.169 Standard Deviation = 17.5548 Standard Error of the Mean = / (n-m) 4.38869 Mean / its Standard Error = /[ / (n-m)] 0.260179E-04 Mean Absolute Deviation = R /n 11.5232 AIC Value ( Uses var ) =nln +2m 111.617 SBC Value ( Uses var ) =nln +m*lnn 114.451 BIC Value ( Uses var ) =see Wei p153 71.7175 R Square =1-[ R / (A- A) ] 0.699175 THE ESTIMATED MODEL PARAMETERS MODEL COMPONENT LAG COEFFICIENT STANDARD T-RATIO # (BOP) ERROR 1 PURE RIGHT-HAND SIDE CONS 56.51168 28.4044 1.990 2 Autoregressive-Factor # 1 1 0.5122459 0.183934 2.785 INPUT SERIES X1 PRICE Lambda Value 3 Omega (input) -Factor # 2 0 -0.8057372 0.342424 -2.353 Y(T) = 115.86 +[X1(T)][(- 0.806)] + [(1- 0.512B** 1)]**-1 [A(T)] CORRELATION MATRIX OF THE PARAMETER ESTIMATES # 1 2 3 4 5 6 7 8 9 10 1 1.000 -.677 -.917 2 -.677 1.000 0.353 3 -.917 0.353 1.000 DIAGNOSTIC CHECK #1: THE NECESSITY TEST PARAMETER # T-VALUE TEST RESULT 1 56.51 Significant 2 2.785 Significant * 3 -2.353 Significant * THE ASTERISK INDICATES THE PARAMETER THAT IS BEING CONSIDERED FOR DELETION, UNLESS DIFFERENCING IS INVOKED. ACF & PACF OF RESIDUALS FROM THE ESTIMATED MODEL LAG ACF STND. T- CHI-SQUARE & PACF STND. T- VALUE ERROR RATIO PROBABILITY VALUE ERROR RATIO 1 -0.248 0.229 -1.08 1.36 NA -0.248 0.229 -1.08 2 0.213 0.243 0.88 2.42 NA 0.161 0.229 0.70 3 0.002 0.253 0.01 2.42 NA 0.095 0.229 0.41 4 -0.139 0.253 -0.55 2.94 0.0867 -0.169 0.229 -0.74 5 -0.211 0.257 -0.82 4.21 0.1220 -0.335 0.229 -1.46 6 0.233 0.266 0.88 5.87 0.1180 0.226 0.229 0.99 7 -0.326 0.276 -1.18 9.40 0.0518 -0.126 0.229 -0.55 8 -0.003 0.296 -0.01 9.40 0.0940 -0.291 0.229 -1.27 LAG ACF T PACF T VALUE RATIO -1 0 +1 VALUE RATIO -1 0 +1 1 -0.248 -1.08 { *** } -0.248 -1.08 { *** } 2 0.213 0.88 { *** } 0.161 0.66 { *** } 3 0.002 0.01 { * } 0.095 0.37 { ** } 4 -0.139 -0.55 { ** } -0.169 -0.67 { *** } 5 -0.211 -0.82 { *** } -0.335 -1.30 {**** } 6 0.233 0.88 { *** } 0.226 0.85 { *** } 7 -0.326 -1.18 { **** } -0.126 -0.45 { ** } 8 -0.003 -0.01 { * } -0.291 -0.98 {**** } SERIES NAME IS : PRICE THE CROSS CORRELATIONS BETWEEN THE FILTERED INPUT AND THE RESIDUALS (R) Mean of X1 0.36132E-06 Mean of R 0.11418E-03 Variance of X1 15.324 Variance of R 259.51 St. Deviation of X1 3.9146 St. Deviation of R 16.109 LAG CROSS- STANDARD T-RATIO LAG CROSS- STANDARD T-RATIO CORRELATION ERROR CORRELATION ERROR 0 0.092 0.229 0.40 0 0.092 0.229 0.40 LAG CCF T FB CCF T VALUE RATIO -1 0 +1 VALUE RATIO -1 0 +1 0 0.092 0.40 { ** } 0.092 0.40 { ** } DIAGNOSTIC CHECK #2B: THE INVERTIBILITY TEST FACTOR # TEST RESULT 1 Invertible DIAGNOSTIC CHECK #3: THE SUFFICIENCY TEST The Critical Value used for this test : 1.96 For the NOISE model : Recommended Adjustment The model is sufficient CCF lags that are significant NONE Estimation/Diagnostic Checking for Variable Y = DEMAND as a f(input var(s)) X1 = PRICE MODEL STATISTICS IN TERMS OF THE ORIGINAL DATA Number of Residuals (R) =n 19 Number of Degrees of Freedom =n-m 16 Residual Mean = R/n 0.322376E-04 Sum of Squares = R 4930.71 Variance var= R /(n) 259.511 Adjusted Variance = R /(n-m) 308.169 Standard Deviation = 17.5548 Standard Error of the Mean = / (n-m) 4.38869 Mean / its Standard Error = /[ / (n-m)] 0.734560E-05 Mean Absolute Deviation = R /n 11.5233 AIC Value ( Uses var ) =nln +2m 111.617 SBC Value ( Uses var ) =nln +m*lnn 114.451 BIC Value ( Uses var ) =see Wei p153 71.7175 R Square =1-[ R / (A- A) ] 0.699175 THE ESTIMATED MODEL PARAMETERS MODEL COMPONENT LAG COEFFICIENT STANDARD T-RATIO # (BOP) ERROR 1 PURE RIGHT-HAND SIDE CONS 56.52104 28.4046 1.990 2 Autoregressive-Factor # 1 1 0.5121880 0.183935 2.785 INPUT SERIES X1 PRICE Lambda Value 3 Omega (input) -Factor # 2 0 -0.8058079 0.342382 -2.354 Y(T) = 115.87 +[X1(T)][(- 0.806)] + [(1- 0.512B** 1)]**-1 [A(T)] CORRELATION MATRIX OF THE PARAMETER ESTIMATES # 1 2 3 4 5 6 7 8 9 10 1 1.000 -.677 -.917 2 -.677 1.000 0.353 3 -.917 0.353 1.000 DIAGNOSTIC CHECK #1: THE NECESSITY TEST PARAMETER # T-VALUE TEST RESULT 1 56.52 Significant 2 2.785 Significant * 3 -2.354 Significant * THE ASTERISK INDICATES THE PARAMETER THAT IS BEING CONSIDERED FOR DELETION, UNLESS DIFFERENCING IS INVOKED. ACF & PACF OF RESIDUALS FROM THE ESTIMATED MODEL LAG ACF STND. T- CHI-SQUARE & PACF STND. T- VALUE ERROR RATIO PROBABILITY VALUE ERROR RATIO 1 -0.248 0.229 -1.08 1.36 NA -0.248 0.229 -1.08 2 0.213 0.243 0.88 2.42 NA 0.161 0.229 0.70 3 0.002 0.253 0.01 2.42 NA 0.094 0.229 0.41 4 -0.139 0.253 -0.55 2.93 0.0867 -0.169 0.229 -0.74 5 -0.211 0.257 -0.82 4.21 0.1220 -0.335 0.229 -1.46 6 0.233 0.266 0.88 5.87 0.1181 0.226 0.229 0.99 7 -0.326 0.276 -1.18 9.40 0.0518 -0.126 0.229 -0.55 8 -0.003 0.296 -0.01 9.40 0.0941 -0.291 0.229 -1.27 LAG ACF T PACF T VALUE RATIO -1 0 +1 VALUE RATIO -1 0 +1 1 -0.248 -1.08 { *** } -0.248 -1.08 { *** } 2 0.213 0.88 { *** } 0.161 0.66 { *** } 3 0.002 0.01 { * } 0.094 0.37 { ** } 4 -0.139 -0.55 { ** } -0.169 -0.67 { *** } 5 -0.211 -0.82 { *** } -0.335 -1.30 {**** } 6 0.233 0.88 { *** } 0.226 0.85 { *** } 7 -0.326 -1.18 { **** } -0.126 -0.45 { ** } 8 -0.003 -0.01 { * } -0.291 -0.98 {**** } SERIES NAME IS : PRICE THE CROSS CORRELATIONS BETWEEN THE FILTERED INPUT AND THE RESIDUALS (R) Mean of X1 0.36132E-06 Mean of R 0.32238E-04 Variance of X1 15.324 Variance of R 259.51 St. Deviation of X1 3.9146 St. Deviation of R 16.109 LAG CROSS- STANDARD T-RATIO LAG CROSS- STANDARD T-RATIO CORRELATION ERROR CORRELATION ERROR 0 0.092 0.229 0.40 0 0.092 0.229 0.40 LAG CCF T FB CCF T VALUE RATIO -1 0 +1 VALUE RATIO -1 0 +1 0 0.092 0.40 { ** } 0.092 0.40 { ** } DIAGNOSTIC CHECK #2B: THE INVERTIBILITY TEST FACTOR # TEST RESULT 1 Invertible DIAGNOSTIC CHECK #3: THE SUFFICIENCY TEST The Critical Value used for this test : 1.96 For the NOISE model : Recommended Adjustment The model is sufficient CCF lags that are significant NONE Estimation/Diagnostic Checking for Variable Y = DEMAND as a f(input var(s)) X1 = PRICE MODEL STATISTICS IN TERMS OF THE ORIGINAL DATA Number of Residuals (R) =n 19 Number of Degrees of Freedom =n-m 16 Residual Mean = R/n 0.879556E-05 Sum of Squares = R 4930.71 Variance var= R /(n) 259.511 Adjusted Variance = R /(n-m) 308.169 Standard Deviation = 17.5548 Standard Error of the Mean = / (n-m) 4.38869 Mean / its Standard Error = /[ / (n-m)] 0.200414E-05 Mean Absolute Deviation = R /n 11.5234 AIC Value ( Uses var ) =nln +2m 111.617 SBC Value ( Uses var ) =nln +m*lnn 114.451 BIC Value ( Uses var ) =see Wei p153 71.7175 R Square =1-[ R / (A- A) ] 0.699175 THE ESTIMATED MODEL PARAMETERS MODEL COMPONENT LAG COEFFICIENT STANDARD T-RATIO # (BOP) ERROR 1 PURE RIGHT-HAND SIDE CONS 56.52360 28.4046 1.990 2 Autoregressive-Factor # 1 1 0.5121725 0.183935 2.785 INPUT SERIES X1 PRICE Lambda Value 3 Omega (input) -Factor # 2 0 -0.8058284 0.342370 -2.354 Y(T) = 115.87 +[X1(T)][(- 0.806)] + [(1- 0.512B** 1)]**-1 [A(T)] CORRELATION MATRIX OF THE PARAMETER ESTIMATES # 1 2 3 4 5 6 7 8 9 10 1 1.000 -.677 -.917 2 -.677 1.000 0.353 3 -.917 0.353 1.000 DIAGNOSTIC CHECK #1: THE NECESSITY TEST PARAMETER # T-VALUE TEST RESULT 1 56.52 Significant 2 2.785 Significant * 3 -2.354 Significant * THE ASTERISK INDICATES THE PARAMETER THAT IS BEING CONSIDERED FOR DELETION, UNLESS DIFFERENCING IS INVOKED. ACF & PACF OF RESIDUALS FROM THE ESTIMATED MODEL LAG ACF STND. T- CHI-SQUARE & PACF STND. T- VALUE ERROR RATIO PROBABILITY VALUE ERROR RATIO 1 -0.248 0.229 -1.08 1.36 NA -0.248 0.229 -1.08 2 0.213 0.243 0.88 2.42 NA 0.161 0.229 0.70 3 0.002 0.253 0.01 2.42 NA 0.094 0.229 0.41 4 -0.139 0.253 -0.55 2.93 0.0867 -0.169 0.229 -0.74 5 -0.211 0.257 -0.82 4.21 0.1220 -0.335 0.229 -1.46 6 0.233 0.266 0.88 5.87 0.1181 0.226 0.229 0.99 7 -0.326 0.276 -1.18 9.40 0.0518 -0.126 0.229 -0.55 8 -0.003 0.296 -0.01 9.40 0.0941 -0.291 0.229 -1.27 LAG ACF T PACF T VALUE RATIO -1 0 +1 VALUE RATIO -1 0 +1 1 -0.248 -1.08 { *** } -0.248 -1.08 { *** } 2 0.213 0.88 { *** } 0.161 0.66 { *** } 3 0.002 0.01 { * } 0.094 0.37 { ** } 4 -0.139 -0.55 { ** } -0.169 -0.67 { *** } 5 -0.211 -0.82 { *** } -0.335 -1.30 {**** } 6 0.233 0.88 { *** } 0.226 0.85 { *** } 7 -0.326 -1.18 { **** } -0.126 -0.45 { ** } 8 -0.003 -0.01 { * } -0.291 -0.98 {**** } SERIES NAME IS : PRICE THE CROSS CORRELATIONS BETWEEN THE FILTERED INPUT AND THE RESIDUALS (R) Mean of X1 0.36132E-06 Mean of R 0.87956E-05 Variance of X1 15.324 Variance of R 259.51 St. Deviation of X1 3.9146 St. Deviation of R 16.109 LAG CROSS- STANDARD T-RATIO LAG CROSS- STANDARD T-RATIO CORRELATION ERROR CORRELATION ERROR 0 0.092 0.229 0.40 0 0.092 0.229 0.40 LAG CCF T FB CCF T VALUE RATIO -1 0 +1 VALUE RATIO -1 0 +1 0 0.092 0.40 { ** } 0.092 0.40 { ** } DIAGNOSTIC CHECK #2B: THE INVERTIBILITY TEST FACTOR # TEST RESULT 1 Invertible DIAGNOSTIC CHECK #3: THE SUFFICIENCY TEST The Critical Value used for this test : 1.96 For the NOISE model : Recommended Adjustment The model is sufficient CCF lags that are significant NONE KENDALL RANK CORRELATION ( TEST) FOR SUFFICIENCY SERIES NAME TAU( ) P VALUE PRICE 0.032 0.920 ADVISORY THE TEST FOR CONSTANCY OF PARAMETERS WILL NOT BE EXECUTED. Analysis for Variable Y = DEMAND as a f(input var(s)) X1 = PRICE DIAGNOSTIC CHECK #4: THE OUTLIER TEST The Critical Value used for this test : 0.10 TYPE OF THE PATTERN CYCLE TIME DATE REGRESSION P VALUE INTERVENTION (T) WEIGHT (OUTLIER) Additive Pulse NA 10 1969 -35.191 0.0512 Additive Pulse NA 3 1962 30.374 0.0387 Additive Pulse NA 8 1967 -23.524 0.0516 Additive Pulse NA 7 1966 -20.203 0.0387 Since the automatic model fixup option for the Outlier Test is enabled, the program will add variables to the model for the identified outliers, subject to the program maximum. The program will then start the the iterative process of transfer function model identification, estimation and diagnostic checking. The forecasts will include the 'known' future values of the intervention variables in the computation of the output series forecast values. Estimation/Diagnostic Checking for Variable Y = DEMAND as a f(input var(s)) X1 = PRICE : NEWLY IDENTIFIED VARIABLE X2 = I~AP0010 0010 PULSE : NEWLY IDENTIFIED VARIABLE X3 = I~AP0003 0003 PULSE : NEWLY IDENTIFIED VARIABLE X4 = I~AP0008 0008 PULSE : NEWLY IDENTIFIED VARIABLE X5 = I~AP0007 0007 PULSE MODEL STATISTICS IN TERMS OF THE ORIGINAL DATA Number of Residuals (R) =n 19 Number of Degrees of Freedom =n-m 12 Residual Mean = R/n -0.389655E-03 Sum of Squares = R 620.938 Variance var= R /(n) 32.6810 Adjusted Variance = R /(n-m) 51.7449 Standard Deviation = 7.19339 Standard Error of the Mean = / (n-m) 2.07655 Mean / its Standard Error = /[ / (n-m)] -0.187645E-03 Mean Absolute Deviation = R /n 4.91108 AIC Value ( Uses var ) =nln +2m 80.2491 SBC Value ( Uses var ) =nln +m*lnn 86.8601 BIC Value ( Uses var ) =see Wei p153 89.6710 R Square =1-[ R / (A- A) ] 0.962116 THE ESTIMATED MODEL PARAMETERS MODEL COMPONENT LAG COEFFICIENT STANDARD T-RATIO # (BOP) ERROR 1 PURE RIGHT-HAND SIDE CONS 1.991932 6.82904 0.2917 2 Autoregressive-Factor # 1 1 0.8887720 0.547338E-01 16.24 INPUT SERIES X1 PRICE Lambda Value 3 Omega (input) -Factor # 2 0 0.1354636 0.361948 0.3743 INPUT SERIES X2 I~AP0010 0010 PULSE Lambda Value 4 Omega (input) -Factor # 3 0 -35.82109 4.29370 -8.343 INPUT SERIES X3 I~AP0003 0003 PULSE Lambda Value 5 Omega (input) -Factor # 4 0 26.03969 4.28070 6.083 INPUT SERIES X4 I~AP0008 0008 PULSE Lambda Value 6 Omega (input) -Factor # 5 0 -36.95915 5.04126 -7.331 INPUT SERIES X5 I~AP0007 0007 PULSE Lambda Value 7 Omega (input) -Factor # 6 0 -27.13980 4.98094 -5.449 Y(T) = 17.909 +[X1(T)][(+ 0.135)] +[X2(T)][(- 35.8211)] +[X3(T)][(+ 26.0397)] +[X4(T)][(- 36.9591)] +[X5(T)][(- 27.1398)] + [(1- 0.889B** 1)]**-1 [A(T)] CORRELATION MATRIX OF THE PARAMETER ESTIMATES # 1 2 3 4 5 6 7 8 9 10 1 1.000 -.891 0.091 0.049 0.198 0.139 -.880 2 -.891 1.000 -.090 -.041 -.208 -.140 0.629 3 0.091 -.090 1.000 0.005 0.021 0.015 -.083 4 0.049 -.041 0.005 1.000 0.011 0.008 -.057 5 0.198 -.208 0.021 0.011 1.000 0.512 -.166 6 0.139 -.140 0.015 0.008 0.512 1.000 -.127 7 -.880 0.629 -.083 -.057 -.166 -.127 1.000 DIAGNOSTIC CHECK #1: THE NECESSITY TEST PARAMETER # T-VALUE TEST RESULT 1 1.992 Significant 2 16.24 Significant * 3 0.3743 Not Significant 4 -8.343 Significant 5 6.083 Significant 6 -7.331 Significant 7 -5.449 Significant Since the automatic model fixup option for the Necessity Test is enabled, the program will now delete the parameter with the lowest non-significant T-ratio and return to the estimation stage in order to complete this iterative step. * THE ASTERISK INDICATES THE PARAMETER THAT IS BEING CONSIDERED FOR DELETION, UNLESS DIFFERENCING IS INVOKED. NOTE -> Deleting model structure. NOTE -> The program is deleting the input series from the model since it does not have any significant parameters. Estimation/Diagnostic Checking for Variable Y = DEMAND as a f(input : NEWLY IDENTIFIED VARIABLE X1 = I~AP0010 0010 PULSE : NEWLY IDENTIFIED VARIABLE X2 = I~AP0003 0003 PULSE : NEWLY IDENTIFIED VARIABLE X3 = I~AP0008 0008 PULSE : NEWLY IDENTIFIED VARIABLE X4 = I~AP0007 0007 PULSE MODEL STATISTICS IN TERMS OF THE ORIGINAL DATA Number of Residuals (R) =n 19 Number of Degrees of Freedom =n-m 13 Residual Mean = R/n 0.837719E-04 Sum of Squares = R 624.601 Variance var= R /(n) 32.8737 Adjusted Variance = R /(n-m) 48.0462 Standard Deviation = 6.93154 Standard Error of the Mean = / (n-m) 1.92246 Mean / its Standard Error = /[ / (n-m)] 0.435753E-04 Mean Absolute Deviation = R /n 4.86044 AIC Value ( Uses var ) =nln +2m 78.3608 SBC Value ( Uses var ) =nln +m*lnn 84.0274 BIC Value ( Uses var ) =see Wei p153 87.8265 R Square =1-[ R / (A- A) ] 0.961893 THE ESTIMATED MODEL PARAMETERS MODEL COMPONENT LAG COEFFICIENT STANDARD T-RATIO # (BOP) ERROR 1 PURE RIGHT-HAND SIDE CONS 4.630757 3.71536 1.246 2 Autoregressive-Factor # 1 1 0.8724247 0.468602E-01 18.62 INPUT SERIES X1 I~AP0010 0010 PULSE Lambda Value 3 Omega (input) -Factor # 2 0 -35.67920 4.32434 -8.251 INPUT SERIES X2 I~AP0003 0003 PULSE Lambda Value 4 Omega (input) -Factor # 3 0 26.18501 4.32522 6.054 INPUT SERIES X3 I~AP0008 0008 PULSE Lambda Value 5 Omega (input) -Factor # 4 0 -36.50726 4.98266 -7.327 INPUT SERIES X4 I~AP0007 0007 PULSE Lambda Value 6 Omega (input) -Factor # 5 0 -26.81997 4.98379 -5.381 Y(T) = 36.298 +[X1(T)][(- 35.6792)] +[X2(T)][(+ 26.1850)] +[X3(T)][(- 36.5073)] +[X4(T)][(- 26.8200)] + [(1- 0.872B** 1)]**-1 [A(T)] CORRELATION MATRIX OF THE PARAMETER ESTIMATES # 1 2 3 4 5 6 7 8 9 10 1 1.000 0.026 0.031 0.030 0.035 -.935 2 0.026 1.000 0.002 0.003 0.003 -.036 3 0.031 0.002 1.000 0.003 0.003 -.041 4 0.030 0.003 0.003 1.000 0.497 -.047 5 0.035 0.003 0.003 0.497 1.000 -.051 6 -.935 -.036 -.041 -.047 -.051 1.000 DIAGNOSTIC CHECK #1: THE NECESSITY TEST PARAMETER # T-VALUE TEST RESULT 1 4.631 Significant 2 18.62 Significant 3 -8.251 Significant 4 6.054 Significant 5 -7.327 Significant * 6 -5.381 Significant * THE ASTERISK INDICATES THE PARAMETER THAT IS BEING CONSIDERED FOR DELETION, UNLESS DIFFERENCING IS INVOKED. ACF & PACF OF RESIDUALS FROM THE ESTIMATED MODEL LAG ACF STND. T- CHI-SQUARE & PACF STND. T- VALUE ERROR RATIO PROBABILITY VALUE ERROR RATIO 1 -0.113 0.229 -0.49 0.28 NA -0.113 0.229 -0.49 2 -0.293 0.232 -1.26 2.30 NA -0.310 0.229 -1.35 3 -0.258 0.251 -1.03 3.95 NA -0.377 0.229 -1.64 4 0.292 0.265 1.10 6.22 NA 0.097 0.229 0.42 5 0.152 0.281 0.54 6.88 NA 0.054 0.229 0.24 6 -0.053 0.285 -0.19 6.96 NA 0.033 0.229 0.15 7 -0.203 0.286 -0.71 8.33 0.0039 -0.027 0.229 -0.12 8 -0.120 0.293 -0.41 8.85 0.0120 -0.199 0.229 -0.87 LAG ACF T PACF T VALUE RATIO -1 0 +1 VALUE RATIO -1 0 +1 1 -0.113 -0.49 { ** } -0.113 -0.49 { ** } 2 -0.293 -1.26 { **** } -0.310 -1.33 {**** } 3 -0.258 -1.03 { **** } -0.377 -1.50 {**** } 4 0.292 1.10 { **** } 0.097 0.37 { ** } 5 0.152 0.54 { *** } 0.054 0.19 { ** } 6 -0.053 -0.19 { ** } 0.033 0.12 { * } 7 -0.203 -0.71 { *** } -0.027 -0.10 { * } 8 -0.120 -0.41 { ** } -0.199 -0.68 { *** } DIAGNOSTIC CHECK #2B: THE INVERTIBILITY TEST FACTOR # TEST RESULT 1 Invertible 2 Invertible 3 Invertible 4 Invertible DIAGNOSTIC CHECK #3: THE SUFFICIENCY TEST The Critical Value used for this test : 1.96 For the NOISE model : Recommended Adjustment The model is sufficient ADVISORY THE TEST FOR CONSTANCY OF PARAMETERS WILL NOT BE EXECUTED. Estimation/Diagnostic Checking for Variable Y = DEMAND as a f(input : NEWLY IDENTIFIED VARIABLE X1 = I~AP0010 0010 PULSE : NEWLY IDENTIFIED VARIABLE X2 = I~AP0003 0003 PULSE : NEWLY IDENTIFIED VARIABLE X3 = I~AP0008 0008 PULSE : NEWLY IDENTIFIED VARIABLE X4 = I~AP0007 0007 PULSE MODEL STATISTICS IN TERMS OF THE ORIGINAL DATA Number of Residuals (R) =n 19 Number of Degrees of Freedom =n-m 13 Residual Mean = R/n 0.837719E-04 Sum of Squares = R 624.601 Variance var= R /(n) 32.8737 Adjusted Variance = R /(n-m) 48.0462 Standard Deviation = 6.93154 Standard Error of the Mean = / (n-m) 1.92246 Mean / its Standard Error = /[ / (n-m)] 0.435753E-04 Mean Absolute Deviation = R /n 4.86044 AIC Value ( Uses var ) =nln +2m 78.3608 SBC Value ( Uses var ) =nln +m*lnn 84.0274 BIC Value ( Uses var ) =see Wei p153 87.8265 R Square =1-[ R / (A- A) ] 0.961893 THE ESTIMATED MODEL PARAMETERS MODEL COMPONENT LAG COEFFICIENT STANDARD T-RATIO # (BOP) ERROR 1 PURE RIGHT-HAND SIDE CONS 4.630757 3.71536 1.246 2 Autoregressive-Factor # 1 1 0.8724247 0.468602E-01 18.62 INPUT SERIES X1 I~AP0010 0010 PULSE Lambda Value 3 Omega (input) -Factor # 2 0 -35.67920 4.32434 -8.251 INPUT SERIES X2 I~AP0003 0003 PULSE Lambda Value 4 Omega (input) -Factor # 3 0 26.18501 4.32522 6.054 INPUT SERIES X3 I~AP0008 0008 PULSE Lambda Value 5 Omega (input) -Factor # 4 0 -36.50726 4.98266 -7.327 INPUT SERIES X4 I~AP0007 0007 PULSE Lambda Value 6 Omega (input) -Factor # 5 0 -26.81997 4.98379 -5.381 Y(T) = 36.298 +[X1(T)][(- 35.6792)] +[X2(T)][(+ 26.1850)] +[X3(T)][(- 36.5073)] +[X4(T)][(- 26.8200)] + [(1- 0.872B** 1)]**-1 [A(T)] CORRELATION MATRIX OF THE PARAMETER ESTIMATES # 1 2 3 4 5 6 7 8 9 10 1 1.000 0.026 0.031 0.030 0.035 -.935 2 0.026 1.000 0.002 0.003 0.003 -.036 3 0.031 0.002 1.000 0.003 0.003 -.041 4 0.030 0.003 0.003 1.000 0.497 -.047 5 0.035 0.003 0.003 0.497 1.000 -.051 6 -.935 -.036 -.041 -.047 -.051 1.000 ACF & PACF OF RESIDUALS FROM THE ESTIMATED MODEL LAG ACF STND. T- CHI-SQUARE & PACF STND. T- VALUE ERROR RATIO PROBABILITY VALUE ERROR RATIO 1 -0.113 0.229 -0.49 0.28 NA -0.113 0.229 -0.49 2 -0.293 0.232 -1.26 2.30 NA -0.310 0.229 -1.35 3 -0.258 0.251 -1.03 3.95 NA -0.377 0.229 -1.64 4 0.292 0.265 1.10 6.22 NA 0.097 0.229 0.42 5 0.152 0.281 0.54 6.88 NA 0.054 0.229 0.24 6 -0.053 0.285 -0.19 6.96 NA 0.033 0.229 0.15 7 -0.203 0.286 -0.71 8.33 0.0039 -0.027 0.229 -0.12 8 -0.120 0.293 -0.41 8.85 0.0120 -0.199 0.229 -0.87 LAG ACF T PACF T VALUE RATIO -1 0 +1 VALUE RATIO -1 0 +1 1 -0.113 -0.49 { ** } -0.113 -0.49 { ** } 2 -0.293 -1.26 { **** } -0.310 -1.33 {**** } 3 -0.258 -1.03 { **** } -0.377 -1.50 {**** } 4 0.292 1.10 { **** } 0.097 0.37 { ** } 5 0.152 0.54 { *** } 0.054 0.19 { ** } 6 -0.053 -0.19 { ** } 0.033 0.12 { * } 7 -0.203 -0.71 { *** } -0.027 -0.10 { * } 8 -0.120 -0.41 { ** } -0.199 -0.68 { *** } Analysis for Variable Y = DEMAND as : NEWLY IDENTIFIED VARIABLE X1 = I~AP0010 0010 PULSE : NEWLY IDENTIFIED VARIABLE X2 = I~AP0003 0003 PULSE : NEWLY IDENTIFIED VARIABLE X3 = I~AP0008 0008 PULSE : NEWLY IDENTIFIED VARIABLE X4 = I~AP0007 0007 PULSE DIAGNOSTIC CHECK #5: THE VARIANCE STABILITY TEST The Critical value used for this test : 0.00 The minimum group or interval size was: 0 There are 0 variance changes at this alpha level VALUES ARE IN THE ORIGINAL METRIC TIME DATE WEIGHTS TO ACTUAL 1PERIOD AHEAD RESIDUAL % (T) STABILIZE OBSERVATION FORECAST(FIT) ERROR 1 1960 1.00000 134.00 NA NA NA 2 1961 1.00000 112.00 121.54 -9.54 -8.51 3 1962 1.00000 136.00 128.53 7.47 5.49 4 1963 1.00000 109.00 100.44 8.56 7.86 5 1964 1.00000 105.00 99.725 5.27 5.02 6 1965 1.00000 87.000 96.235 -9.24 -10.62 7 1966 1.00000 56.000 53.712 2.29 4.09 8 1967 1.00000 43.000 40.378 2.62 6.10 9 1968 1.00000 77.000 73.995 3.01 3.90 10 1969 1.00000 35.000 36.128 -1.13 -3.22 11 1970 1.00000 65.000 66.293 -1.29 -1.99 12 1971 1.00000 56.000 61.338 -5.34 -9.53 13 1972 1.00000 58.000 53.487 4.51 7.78 14 1973 1.00000 55.000 55.231 -0.231 -0.42 15 1974 1.00000 49.000 52.614 -3.61 -7.38 16 1975 1.00000 39.000 47.380 -8.38 -21.49 17 1976 1.00000 36.000 38.655 -2.66 -7.38 18 1977 1.00000 46.000 36.038 9.96 21.66 19 1978 1.00000 40.000 44.762 -4.76 -11.91 20 1979 1.00000 42.000 39.528 2.47 5.89 MODEL STATISTICS IN TERMS OF THE ORIGINAL DATA Number of Residuals (R) =n 19 Number of Degrees of Freedom =n-m 13 Residual Mean = R/n 0.837719E-04 Sum of Squares = R 624.601 Variance var= R /(n) 32.8737 Adjusted Variance = R /(n-m) 48.0462 Standard Deviation = 6.93154 Standard Error of the Mean = / (n-m) 1.92246 Mean / its Standard Error = /[ / (n-m)] 0.435753E-04 Mean Absolute Deviation = R /n 4.86044 AIC Value ( Uses var ) =nln +2m 78.3608 SBC Value ( Uses var ) =nln +m*lnn 84.0274 BIC Value ( Uses var ) =see Wei p153 87.8265 R Square =1-[ R / (A- A) ] 0.961893 Model Forecasting for Time Series Variable Y = DEMAND as a f(inp: NEWLY IDENTIFIED VARIABLE X1 = I~AP0010 0010 PULSE : NEWLY IDENTIFIED VARIABLE X2 = I~AP0003 0003 PULSE : NEWLY IDENTIFIED VARIABLE X3 = I~AP0008 0008 PULSE : NEWLY IDENTIFIED VARIABLE X4 = I~AP0007 0007 PULSE THE FORECAST MODEL USED FOR THIS VARIABLE MODEL COMPONENT LAG COEFFICIENT STANDARD T-RATIO # (BOP) ERROR 1 PURE RIGHT-HAND SIDE CONS 4.630757 2 Autoregressive-Factor # 1 1 0.8724247 INPUT SERIES X1 I~AP0010 0010 PULSE Lambda Value 3 Omega (input) -Factor # 2 0 -35.67920 INPUT SERIES X2 I~AP0003 0003 PULSE Lambda Value 4 Omega (input) -Factor # 3 0 26.18501 INPUT SERIES X3 I~AP0008 0008 PULSE Lambda Value 5 Omega (input) -Factor # 4 0 -36.50726 INPUT SERIES X4 I~AP0007 0007 PULSE Lambda Value 6 Omega (input) -Factor # 5 0 -26.81997 Y(T) = 36.298 +[X1(T)][(- 35.6792)] +[X2(T)][(+ 26.1850)] +[X3(T)][(- 36.5073)] +[X4(T)][(- 26.8200)] + [(1- 0.872B** 1)]**-1 [A(T)] VALUES ARE IN TERMS OF THE ORIGINAL METRIC TIME DATE LOWER 80% UPPER 80% FORECAST (T) LIMIT LIMIT 21 1980 32.71 49.83 41.27 22 1981 29.28 52.00 40.64 23 1982 26.99 53.18 40.08 24 1983 25.33 53.88 39.60 25 1984 24.07 54.29 39.18 26 1985 23.09 54.53 38.81 27 1986 22.33 54.66 38.49 28 1987 21.71 54.71 38.21 29 1988 21.22 54.71 37.97 30 1989 20.82 54.69 37.75 31 1990 20.50 54.64 37.57 32 1991 20.23 54.59 37.41 THE AGGREGATE 453.5 480.5 467.0 PLOT OF THE OBSERVED (ACTUAL) & THE FORECAST SERIES GRAPH KEY A = DEMAND F = FORECASTS 20.227 136.00 DATE ³++++++++++++++++++++++++++++++++++++++++++++++++++++++++³ 1960 ³ A ³ 134.00 1961 ³ A ³ 112.00 1962 ³ A³ 136.00 1963 ³ A ³ 109.00 1964 ³ A ³ 105.00 1965 ³ A ³ 87.000 1966 ³ A ³ 56.000 1967 ³ A ³ 43.000 1968 ³ A ³ 77.000 1969 Ã A ´ 35.000 1970 ³ A ³ 65.000 1971 ³ A ³ 56.000 1972 ³ A ³ 58.000 1973 ³ A ³ 55.000 1974 ³ A ³ 49.000 1975 ³ A ³ 39.000 1976 ³ A ³ 36.000 1977 ³ A ³ 46.000 1978 ³ A ³ 40.000 1979 Ã A ´ 42.000 1980 ³ L F U ³ 41.273 1981 ³ L F U ³ 40.638 1982 ³ L F U ³ 40.084 1983 ³ L F U ³ 39.601 1984 ³ L F U ³ 39.180 1985 ³ L F U ³ 38.812 1986 ³ L F U ³ 38.492 1987 ³ L F U ³ 38.212 1988 ³L F U ³ 37.968 1989 ÃL F U ´ 37.755 1990 ³L F U ³ 37.569 1991 ³L F U ³ 37.407 ³++++++++++++++++++++++++++++++++++++++++++++++++++++++++³ THE WORK WAS STARTED AT: TIME=19:07:03 IT IS TIME TO STOP AND ADMIRE THE WORK ! TIME=19:07:11