INTRODUCTION TO ECONOMETRICS II ECO 306 NOUN 123 If ( ) , we reject the null hypothesis of no autocorrelation. If ( ) we do not reject the null hypothesis. If ( ) ( the testis inconclusive. The upper bound of the DW statistic is a good approximation to its distribution when the regressors are slowly changing. DW argue that economic time series are slowly changing, and hence one can use ( as the correct significance point. The significance points in the DW tables are tabulated for testing = 0 against > 0. If d > 2 and we wish to test the hypothesis = 0 against <0, we consider 4…d and refer to the DW tables as if we are testing for positive autocorrelation. Although we have said that
→ ( ) this approximation is valid only in large samples. The mean of when has been shown to be given approximately by ( ) ( )
…[4.19] wherek is the number of regression parameters estimated (including the constant term, and n is the sample size. Thus, even for zero serial correlation, the statistic is biased upward from 2. If k = 5 and n= 15, the bias is as large as 0.8.
