Robustness to nonnormality of the Durbin-Watson test for autocorrelation

Abstract

Abstract This study investigates the robustness to nonnormality of the null distribution of the Durbin-Watson test for autocorrelation in regression errors. The first four moments of the null distribution are derived to the order O ( 1 n 3 ) when the regression errors are nonnormal, with n the sample size. It is found that nonnormality has an insignificant effect on the mean and the fourth central moment of the distribution. The variance tends to be deflated (inflated) if the error distribution is long-tailed (short-tailed). The third central moment is reduced if the error distribution is skewed (left or right). Both skewness and kurtosis of the distribution are affected by nonnormality, but these effects are negligible in large samples. It seems the test is relatively robust for moderate nonnormality and moderately large sample size. These effects are also found to have insignificant influence from the regressors.