## Using Durbin's h testWhen the regression includes lagged dependent variables the Durbin-Watson d-statistic is not valid as a test for autocorrelated residuals. The d-statistic tends to be biased towards 2. In this case, Durbin's h test can be considered. This example returns to the analysis of the data set on monthly sales and advertising expenditures of a dietary weight control product. An application with this data set that illustrated regression with a lagged dependent variable was given in a previous section. The next set of SHAZAM commands show the use of the
As an alternative to the above commands a special lag notation can
be used. On the
where var is an explanatory variable and first and last specify the range of periods to use for lags. SHAZAM automatically deletes the required number of initial undefined observations. The use of the special lag notation is shown in the next list of SHAZAM commands.
The SHAZAM output can be viewed. The estimation results report: DURBIN H STATISTIC (ASYMPTOTIC NORMAL) = -0.41847 The term By applying this decision rule it can be seen that there is no evidence for autocorrelation in the residuals. As a cautionary note users should consider that this test may not be accurate in "small samples".
[SHAZAM Guide home] ## SHAZAM output|_SAMPLE 1 36 |_READ (SALES.txt) SALES ADVERT UNIT 88 IS NOW ASSIGNED TO: SALES.txt 2 VARIABLES AND 36 OBSERVATIONS STARTING AT OBS 1 |_OLS SALES SALES(1.1) ADVERT / DLAG OLS ESTIMATION 35 OBSERVATIONS DEPENDENT VARIABLE = SALES ...NOTE..SAMPLE RANGE SET TO: 2, 36 R-SQUARE = 0.6720 R-SQUARE ADJUSTED = 0.6515 VARIANCE OF THE ESTIMATE-SIGMA**2 = 12.142 STANDARD ERROR OF THE ESTIMATE-SIGMA = 3.4845 SUM OF SQUARED ERRORS-SSE= 388.53 MEAN OF DEPENDENT VARIABLE = 24.606 LOG OF THE LIKELIHOOD FUNCTION = -91.7859 VARIABLE SUM OF LAG COEFS STD ERROR T-RATIO MEAN LAG SALES 0.52793 0.10212 5.1698 1.0000 VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 32 DF P-VALUE CORR. COEFFICIENT AT MEANS SALES 0.52793 0.1021 5.170 0.000 0.675 0.5478 0.5252 ADVERT 0.14647 0.3308E-01 4.428 0.000 0.616 0.4692 0.1721 CONSTANT 7.4469 2.470 3.015 0.005 0.470 0.0000 0.3027 DURBIN-WATSON = 2.0275 VON NEUMANN RATIO = 2.0871 RHO = -0.05637 RESIDUAL SUM = 0.18874E-12 RESIDUAL VARIANCE = 12.142 SUM OF ABSOLUTE ERRORS= 99.086 R-SQUARE BETWEEN OBSERVED AND PREDICTED = 0.6720 RUNS TEST: 20 RUNS, 19 POS, 0 ZERO, 16 NEG NORMAL STATISTIC = 0.5631 DURBIN H STATISTIC (ASYMPTOTIC NORMAL) = -0.41847 |_STOP [SHAZAM Guide home] |