On the Durbin-Watson statistic based on a Z-test in large samples

This paper formulates the Z-test of the Durbin-Watson (DW) statistic by the true sampling distribution of the DW statistic under the null hypothesis of no serial correlation. Two important results are determined. First, the variance of the DW statistic is convexly related to the degree of freedom, T - k - 1. Thus, the degree of freedom determines the Z-test formula of the DW test. Secondly, the law of large numbers induces the sampling distribution of the DW statistic to converge to a normal distribution.