|_* |_* Efficient (FGLS) estimation with AR(1) errors |_* |_READ (DATA3-6) YEAR C Y 3 VARIABLES AND 36 OBSERVATIONS STARTING AT OBS 1 |_* |_* Estimate regression of C on Y. |_OLS C Y / EXACTDW REQUIRED MEMORY IS PAR= 14 CURRENT PAR= 500 OLS ESTIMATION 36 OBSERVATIONS DEPENDENT VARIABLE= C ...NOTE..SAMPLE RANGE SET TO: 1, 36 DURBIN-WATSON STATISTIC = 0.51370 DURBIN-WATSON P-VALUE = 0.000000 R-SQUARE = 0.9955 R-SQUARE ADJUSTED = 0.9954 VARIANCE OF THE ESTIMATE-SIGMA**2 = 39610. STANDARD ERROR OF THE ESTIMATE-SIGMA = 199.02 SUM OF SQUARED ERRORS-SSE= 0.13468E+07 MEAN OF DEPENDENT VARIABLE = 12491. LOG OF THE LIKELIHOOD FUNCTION = -240.616 VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 34 DF P-VALUE CORR. COEFFICIENT AT MEANS Y 0.93274 0.1070E-01 87.20 0.000 0.998 0.9978 1.0308 CONSTANT -384.11 151.3 -2.538 0.016-0.399 0.0000 -0.0308 |_* |_* The DW statistic flags serial correlation. |_* Reestimate the model using the Cochrane-Orcutt method. |_AUTO C Y / RSTAT REQUIRED MEMORY IS PAR= 5 CURRENT PAR= 500 DEPENDENT VARIABLE = C ..NOTE..R-SQUARE,ANOVA,RESIDUALS DONE ON ORIGINAL VARS LEAST SQUARES ESTIMATION 36 OBSERVATIONS BY COCHRANE-ORCUTT TYPE PROCEDURE WITH CONVERGENCE = 0.00100 ITERATION RHO LOG L.F. SSE 1 0.00000 -240.616 0.13468E+07 2 0.76830 -227.693 0.64078E+06 3 0.78666 -227.699 0.63974E+06 4 0.79078 -227.704 0.63960E+06 5 0.79183 -227.706 0.63958E+06 6 0.79211 -227.706 0.63957E+06 LOG L.F. = -227.706 AT RHO = 0.79211 ASYMPTOTIC ASYMPTOTIC ASYMPTOTIC ESTIMATE VARIANCE ST.ERROR T-RATIO RHO 0.79211 0.01035 0.10173 7.78636 R-SQUARE = 0.9979 R-SQUARE ADJUSTED = 0.9978 VARIANCE OF THE ESTIMATE-SIGMA**2 = 18811. STANDARD ERROR OF THE ESTIMATE-SIGMA = 137.15 SUM OF SQUARED ERRORS-SSE= 0.63957E+06 MEAN OF DEPENDENT VARIABLE = 12491. LOG OF THE LIKELIHOOD FUNCTION = -227.706 VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 34 DF P-VALUE CORR. COEFFICIENT AT MEANS Y 0.92942 0.2668E-01 34.83 0.000 0.986 0.9942 1.0271 CONSTANT -281.90 380.2 -0.7415 0.463-0.126 0.0000 -0.0226 DURBIN-WATSON = 1.9745 VON NEUMANN RATIO = 2.0309 RHO = -0.02438 RESIDUAL SUM = -100.39 RESIDUAL VARIANCE = 19107. SUM OF ABSOLUTE ERRORS= 3793.8 R-SQUARE BETWEEN OBSERVED AND PREDICTED = 0.9979 RUNS TEST: 17 RUNS, 19 POS, 0 ZERO, 17 NEG NORMAL STATISTIC = -0.6597 DURBIN H STATISTIC (ASYMPTOTIC NORMAL) = -0.18467 MODIFIED FOR AUTO ORDER=1 |_* Confirm using the Hildreth-Lu Grid Search (GS) procedure. |_AUTO C Y / GS RSTAT REQUIRED MEMORY IS PAR= 5 CURRENT PAR= 500 DEPENDENT VARIABLE = C ..NOTE..R-SQUARE,ANOVA,RESIDUALS DONE ON ORIGINAL VARS LEAST SQUARES ESTIMATION 36 OBSERVATIONS BY GRID SEARCH TO ACCURACY OF .01 ITERATION RHO LOG L.F. SSE 1 -0.90000 -260.191 0.38154E+07 2 -0.80000 -258.079 0.34538E+07 3 -0.70000 -256.041 0.31141E+07 4 -0.60000 -253.989 0.27961E+07 5 -0.50000 -251.895 0.25000E+07 6 -0.40000 -249.746 0.22257E+07 7 -0.30000 -247.539 0.19732E+07 8 -0.20000 -245.274 0.17425E+07 9 -0.10000 -242.961 0.15337E+07 10 0.00000 -240.616 0.13468E+07 11 0.10000 -238.267 0.11816E+07 12 0.20000 -235.956 0.10384E+07 13 0.30000 -233.745 0.91700E+06 14 0.40000 -231.719 0.81754E+06 15 0.50000 -229.983 0.74004E+06 16 0.60000 -228.658 0.68453E+06 17 0.70000 -227.869 0.65105E+06 18 0.80000 -227.719 0.63943E+06 19 0.90000 -228.286 0.64826E+06 ITERATION RHO LOG L.F. SSE 20 0.71000 -227.824 0.64891E+06 21 0.72000 -227.785 0.64699E+06 22 0.73000 -227.753 0.64529E+06 23 0.74000 -227.728 0.64380E+06 24 0.75000 -227.709 0.64254E+06 25 0.76000 -227.697 0.64149E+06 26 0.77000 -227.692 0.64065E+06 27 0.78000 -227.694 0.64003E+06 28 0.79000 -227.703 0.63963E+06 29 0.80000 -227.719 0.63943E+06 30 0.81000 -227.743 0.63945E+06 31 0.82000 -227.773 0.63966E+06 32 0.83000 -227.811 0.64009E+06 33 0.84000 -227.856 0.64071E+06 34 0.85000 -227.908 0.64152E+06 35 0.86000 -227.968 0.64253E+06 36 0.87000 -228.036 0.64371E+06 37 0.88000 -228.111 0.64507E+06 38 0.89000 -228.194 0.64659E+06 39 0.80000 -227.719 0.63943E+06 LOG L.F. = -227.719 AT RHO = 0.80000 ASYMPTOTIC ASYMPTOTIC ASYMPTOTIC ESTIMATE VARIANCE ST.ERROR T-RATIO RHO 0.80000 0.01000 0.10000 8.00000 R-SQUARE = 0.9979 R-SQUARE ADJUSTED = 0.9978 VARIANCE OF THE ESTIMATE-SIGMA**2 = 18807. STANDARD ERROR OF THE ESTIMATE-SIGMA = 137.14 SUM OF SQUARED ERRORS-SSE= 0.63943E+06 MEAN OF DEPENDENT VARIABLE = 12491. LOG OF THE LIKELIHOOD FUNCTION = -227.719 VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 34 DF P-VALUE CORR. COEFFICIENT AT MEANS Y 0.92897 0.2736E-01 33.95 0.000 0.986 0.9937 1.0266 CONSTANT -273.35 390.0 -0.7009 0.488-0.119 0.0000 -0.0219 DURBIN-WATSON = 1.9901 VON NEUMANN RATIO = 2.0469 RHO = -0.03098 RESIDUAL SUM = -97.694 RESIDUAL VARIANCE = 19088. SUM OF ABSOLUTE ERRORS= 3785.0 R-SQUARE BETWEEN OBSERVED AND PREDICTED = 0.9979 RUNS TEST: 17 RUNS, 19 POS, 0 ZERO, 17 NEG NORMAL STATISTIC = -0.6597 DURBIN H STATISTIC (ASYMPTOTIC NORMAL) = -0.23232 MODIFIED FOR AUTO ORDER=1 |_* |_* Try the Durbin two-step method (Kennedy, p. 125) |_* |_* Step 1: Regress with Clag and Ylag, keeping coefficients in BETA |_GENR CLAG = LAG(C) ..NOTE.LAG VALUE IN UNDEFINED OBSERVATIONS SET TO -99999. |_GENR YLAG = LAG(Y) ..NOTE.LAG VALUE IN UNDEFINED OBSERVATIONS SET TO -99999. |_SAMPLE 2 36 |_OLS C CLAG Y YLAG / COEF=BETA REQUIRED MEMORY IS PAR= 4 CURRENT PAR= 500 OLS ESTIMATION 35 OBSERVATIONS DEPENDENT VARIABLE= C ...NOTE..SAMPLE RANGE SET TO: 2, 36 R-SQUARE = 0.9981 R-SQUARE ADJUSTED = 0.9979 VARIANCE OF THE ESTIMATE-SIGMA**2 = 17644. STANDARD ERROR OF THE ESTIMATE-SIGMA = 132.83 SUM OF SQUARED ERRORS-SSE= 0.54697E+06 MEAN OF DEPENDENT VARIABLE = 12623. LOG OF THE LIKELIHOOD FUNCTION = -218.657 VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 31 DF P-VALUE CORR. COEFFICIENT AT MEANS CLAG 0.79953 0.1254 6.378 0.000 0.753 0.7989 0.7827 Y 0.76386 0.9504E-01 8.038 0.000 0.822 0.8141 0.8442 YLAG -0.56981 0.1452 -3.925 0.000-0.576 -0.6134 -0.6173 CONSTANT -122.31 119.2 -1.026 0.313-0.181 0.0000 -0.0097 |_* Step 2: Save the coefficient of CLAG in R |_GEN1 R = BETA(1) |_PRINT R R 0.7995333 |_* Step 3: Use this estimate of rho to calculate FGLS estimates |_SAMPLE 1 36 |_AUTO C Y / RHO=R RSTAT REQUIRED MEMORY IS PAR= 5 CURRENT PAR= 500 DEPENDENT VARIABLE = C ..NOTE..R-SQUARE,ANOVA,RESIDUALS DONE ON ORIGINAL VARS LEAST SQUARES ESTIMATION 36 OBSERVATIONS BY COCHRANE-ORCUTT TYPE PROCEDURE WITH CONVERGENCE = 0.00100 ITERATION RHO LOG L.F. SSE 1 0.79953 -227.718 0.63944E+06 LOG L.F. = -227.718 AT RHO = 0.79953 ASYMPTOTIC ASYMPTOTIC ASYMPTOTIC ESTIMATE VARIANCE ST.ERROR T-RATIO RHO 0.79953 0.01002 0.10010 7.98706 R-SQUARE = 0.9979 R-SQUARE ADJUSTED = 0.9978 VARIANCE OF THE ESTIMATE-SIGMA**2 = 18807. STANDARD ERROR OF THE ESTIMATE-SIGMA = 137.14 SUM OF SQUARED ERRORS-SSE= 0.63944E+06 MEAN OF DEPENDENT VARIABLE = 12491. LOG OF THE LIKELIHOOD FUNCTION = -227.718 VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 34 DF P-VALUE CORR. COEFFICIENT AT MEANS Y 0.92900 0.2732E-01 34.00 0.000 0.986 0.9938 1.0266 CONSTANT -273.87 389.4 -0.7033 0.487-0.120 0.0000 -0.0219 DURBIN-WATSON = 1.9892 VON NEUMANN RATIO = 2.0460 RHO = -0.03059 RESIDUAL SUM = -97.864 RESIDUAL VARIANCE = 19089. SUM OF ABSOLUTE ERRORS= 3785.6 R-SQUARE BETWEEN OBSERVED AND PREDICTED = 0.9979 RUNS TEST: 17 RUNS, 19 POS, 0 ZERO, 17 NEG NORMAL STATISTIC = -0.6597 DURBIN H STATISTIC (ASYMPTOTIC NORMAL) = -0.22957 MODIFIED FOR AUTO ORDER=1 ..INPUT FILE COMPLETED..TYPE A NEW COMMAND OR TYPE: STOP TYPE COMMAND