The Durbin-Watson Ratio under Infinite Variance Errors

Abstract

This paper studies the properties of the von Neumann ratio for time series with infinite variance. The asymptotic theory is developed using recent results on the weak convergence of partial sums of time series with infinite variance to stable processes and of sample serial correlations to functions of stable variables. Our asymptotics cover the null of iid variates and general moving average (MA) alternatives. Regression residuals are also considered. In the static regression model the Durbin-Watson statistic has the same limit distribution as the von Neumann ratio under general conditions. However, the dynamic models, the results are more complex and more interesting. When the regressors have thicker tail probabilities than the errors we find that the Durbin-Watson and von Neumann ration asymptotics are the same