REPLICATION OF TIME-SERIES ANALYSIS OF BLAISDELL DATA (NKNW pp. 504-516)
USING COCHRANE-ORCUTT, HILDRETH-LU, & FIRST DIFFERENCES PROCEDURES MON 3/22/99 9:10:04 AM SYSTAT VERSION 7.0.1 COPYRIGHT (C) 1997, SPSS INC. Welcome to SYSTAT! >USE 'C:\SYSTAT7\S209\BLAIS.SYD' SYSTAT Rectangular file C:\SYSTAT7\S209\BLAIS.SYD, created Fri Mar 19, 1999 at 16:06:42, contains variables: Y X >mglh >model y=constant+x >save blaisres/resid data >estimate Dep Var: Y N: 20 Multiple R: 0.999396 Squared multiple R: 0.998792 Adjusted squared multiple R: 0.998725 Standard error of estimate: 0.086056 Effect Coefficient Std Error Std Coef Tolerance t P(2 Tail) CONSTANT -1.454750 0.214146 0.0 . -6.79326 0.00000 X 0.176283 0.001445 0.999396 1.000000 1.22E02 0.00000 Analysis of Variance Source Sum-of-Squares df Mean-Square F-ratio P Regression 110.256878 1 110.256878 1.48881E+04 0.000000 Residual 0.133302 18 0.007406 Durbin-Watson D Statistic 0.735 First Order Autocorrelation 0.626 Residuals have been saved. ----------------------------------------------------------------------------------------------------------------------------------
Estimated rho (0.626) differs slightly from the one in NKNW (0.631166; Table 12.3 p. 510);
Estimated D-W statistic (0.735) is the same.
Next switch to file of residuals to do an index plot, then back to original
file >USE 'C:\SYSTAT7\S209\BLAISRES.SYD' SYSTAT Rectangular file C:\SYSTAT7\S209\BLAISRES.SYD, created Mon Mar 22, 1999 at 09:11:12, contains variables: ESTIMATE RESIDUAL LEVERAGE COOK STUDENT SEPRED Y X >plot residual/stick ylimit=0 line dash=11
>USE 'C:\SYSTAT7\S209\BLAIS.SYD' SYSTAT Rectangular file C:\SYSTAT7\S209\BLAIS.SYD, created Fri Mar 19, 1999 at 16:06:42, contains variables: Y X
>rem Cochrane-Orcutt procedure
>basic File in use is C:\SYSTAT7\S209\BLAIS.SYD. Variables in the SYSTAT Rectangular file are: Y X BASIC statements cleared. >let y1 = lag(y) >let x1 = lag(x) >let yp = y - 0.626*y1 >let xp = x - 0.626*x1 >run SYSTAT file created. 20 cases and 6 variables processed. BASIC statements cleared.
>page wide
>list x x1 xp y y1 yp Case number X X1 XP Y Y1 YP 1 127.300000 . . 20.960000 . . 2 130.000000 127.300000 50.310200 21.400000 20.960000 8.279040 3 132.700000 130.000000 51.320000 21.960000 21.400000 8.563600 4 129.400000 132.700000 46.329800 21.520000 21.960000 7.773040 5 135.000000 129.400000 53.995600 22.390000 21.520000 8.918480 6 137.100000 135.000000 52.590000 22.760000 22.390000 8.743860 7 141.200000 137.100000 55.375400 23.480000 22.760000 9.232240 8 142.800000 141.200000 54.408800 23.660000 23.480000 8.961520 9 145.500000 142.800000 56.107200 24.100000 23.660000 9.288840 10 145.300000 145.500000 54.217000 24.010000 24.100000 8.923400 11 148.300000 145.300000 57.342200 24.540000 24.010000 9.509740 12 146.400000 148.300000 53.564200 24.300000 24.540000 8.937960 13 150.200000 146.400000 58.553600 25.000000 24.300000 9.788200 14 153.100000 150.200000 59.074800 25.640000 25.000000 9.990000 15 157.300000 153.100000 61.459400 26.360000 25.640000 10.309360 16 160.700000 157.300000 62.230200 26.980000 26.360000 10.478640 17 164.200000 160.700000 63.601800 27.520000 26.980000 10.630520 18 165.600000 164.200000 62.810800 27.780000 27.520000 10.552480 19 168.700000 165.600000 65.034400 28.240000 27.780000 10.849720 20 171.700000 168.700000 66.093800 28.780000 28.240000 11.101760 >mglh >model yp = constant + xp >estimate 1 case(s) deleted due to missing data. Dep Var: YP N: 19 Multiple R: 0.997601 Squared multiple R: 0.995208 Adjusted squared multiple R: 0.994926 Standard error of estimate: 0.067195 Effect Coefficient Std Error Std Coef Tolerance t P(2 Tail) CONSTANT -0.403282 0.167675 0.0 . -2.40514 0.02784 XP 0.173821 0.002925 0.997601 1.000000 59.41838 0.00000 Analysis of Variance Source Sum-of-Squares df Mean-Square F-ratio P Regression 15.941142 1 15.941142 3530.543519 0.000000 Residual 0.076759 17 0.004515 ---------------------------------------------------------------------------------------------------------------------------------- Durbin-Watson D Statistic 1.644 First Order Autocorrelation 0.150 Now redo the D-W test; if D-W still significant one can iterate
the Cochrane-Orcutt procedure (see NKNW p. 510)
>rem Hildreth-Lu procedure using nonlin >nonlin >model y = rho*y1 + b0 + b1*(x-rho*x1) >estimate Iteration No. Loss RHO B0 B1 0 .631740D+02 .101000D+01-.102000D+01 .103000D+01 1 .133054D+00 .101044D+01 .848852D-01 .158714D+00 2 .722882D-01 .967085D+00 .768116D-01 .159566D+00 3 .716819D-01 .961296D+00 .718397D-01 .160309D+00 4 .716707D-01 .959414D+00 .716441D-01 .160463D+00 5 .716704D-01 .958978D+00 .716043D-01 .160508D+00 6 .716704D-01 .958861D+00 .716071D-01 .160519D+00 7 .716704D-01 .958831D+00 .716075D-01 .160522D+00 Dependent variable is Y Zero weights, missing data or estimates reduced degrees of freedom Source Sum-of-Squares df Mean-Square Regression 1.17437E+04 3 3914.570710 Residual 0.071670 16 0.004479 Total 1.17438E+04 19 Mean corrected 96.679779 18 Raw R-square (1-Residual/Total) = 0.999994 Mean corrected R-square (1-Residual/Corrected) = 0.999259 R(observed vs predicted) square = 0.999263 Wald Confidence Interval Parameter Estimate A.S.E. Param/ASE Lower < 95%> Upper RHO 0.958831 0.080054 11.977261 0.789123 1.128538 B0 0.071607 0.071555 1.000733 -0.080082 0.223297 B1 0.160522 0.007931 20.240415 0.143710 0.177335 >rem compare with NKNW Table 12.5 p. 513
>rem first differences procedure >mglh >let dy = y - y1 >let dx = x - x1 >list x x1 dx y y1 dy Case number X X1 DX Y Y1 DY 1 127.300000 . . 20.960000 . . 2 130.000000 127.300000 2.700000 21.400000 20.960000 0.440000 3 132.700000 130.000000 2.700000 21.960000 21.400000 0.560000 4 129.400000 132.700000 -3.300000 21.520000 21.960000 -0.440000 5 135.000000 129.400000 5.600000 22.390000 21.520000 0.870000 6 137.100000 135.000000 2.100000 22.760000 22.390000 0.370000 7 141.200000 137.100000 4.100000 23.480000 22.760000 0.720000 8 142.800000 141.200000 1.600000 23.660000 23.480000 0.180000 9 145.500000 142.800000 2.700000 24.100000 23.660000 0.440000 10 145.300000 145.500000 -0.200000 24.010000 24.100000 -0.090000 11 148.300000 145.300000 3.000000 24.540000 24.010000 0.530000 12 146.400000 148.300000 -1.900000 24.300000 24.540000 -0.240000 13 150.200000 146.400000 3.800000 25.000000 24.300000 0.700000 14 153.100000 150.200000 2.900000 25.640000 25.000000 0.640000 15 157.300000 153.100000 4.200000 26.360000 25.640000 0.720000 16 160.700000 157.300000 3.400000 26.980000 26.360000 0.620000 17 164.200000 160.700000 3.500000 27.520000 26.980000 0.540000 18 165.600000 164.200000 1.400000 27.780000 27.520000 0.260000 19 168.700000 165.600000 3.100000 28.240000 27.780000 0.460000 20 171.700000 168.700000 3.000000 28.780000 28.240000 0.540000
The first differences model is run without a constant term
>model dy = dx >estimate 1 case(s) deleted due to missing data. Model contains no constant Dep Var: DY N: 19 Multiple R: 0.991867 Squared multiple R: 0.983800 Adjusted squared multiple R: 0.983800 Standard error of estimate: 0.069392 Effect Coefficient Std Error Std Coef Tolerance t P(2 Tail) DX 0.168488 0.005096 0.991867 1.000000 33.06272 0.00000 Analysis of Variance Source Sum-of-Squares df Mean-Square F-ratio P Regression 5.263726 1 5.263726 1093.143324 0.000000 Residual 0.086674 18 0.004815 ---------------------------------------------------------------------------------------------------------------------------------- Durbin-Watson D Statistic 1.739 First Order Autocorrelation 0.122
But to calculate the D-W statistic one must run the same model WITH a
constant
>model dy = constant + dx >estimate 1 case(s) deleted due to missing data. Dep Var: DY N: 19 Multiple R: 0.982747 Squared multiple R: 0.965791 Adjusted squared multiple R: 0.963778 Standard error of estimate: 0.065498 Effect Coefficient Std Error Std Coef Tolerance t P(2 Tail) CONSTANT 0.040528 0.022642 0.0 . 1.78996 0.09129 DX 0.158783 0.007248 0.982747 1.000000 21.90756 0.00000 Analysis of Variance Source Sum-of-Squares df Mean-Square F-ratio P Regression 2.058923 1 2.058923 479.941009 0.000000 Residual 0.072929 17 0.004290 ---------------------------------------------------------------------------------------------------------------------------------- *** WARNING *** Case 4 has large leverage (Leverage = 0.441713) Durbin-Watson D Statistic 1.749 First Order Autocorrelation 0.116
Last modified 22 April 1999