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. 4.2.5.0 SUMMARY The unit explained the concept of autocorrelation at first order, its possible causes and detection (with particular interest on the first-order autoregressive autocorrelation, denoted by AR (1)) using Durbin-Watson test. 4.2.4.0 CONCLUSION In this unit, autocorrelation is statistically explained as a random process that measures the linear correlation between values of the process at different times, as a function of time or of the time lag. The significances of autocorrelation for OLS are shown to be comparable to those of heteroscedasticity and have two forms of occurrences, which could either be positive or negative. Students are advised to use the further reading materials to look at more autocorrelation techniques and study more on the correlation between the error terms arising in time series data as indicated in the introduction section of this unit.
