COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 898R

"The Durbin-Watson Ratio under Infinite Variance Errors"

Peter C.B. Phillips and Mico Loretan

January 1989
Revised August 1989

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.

JE Classification: 211, 212

Keywords: Durbin-Watson ratio, von Neumann ratio, serial correlation, dynamic models, time series, asymptotic theory