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This paper studies the properties of the von Neumann ratio for time series with infinite variance. 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. In dynamic models the results are more complex. In finite-variance models our results specialize to those of the Durbin h-statistic and equivalent LM test asymptotics. Some Monte Carlo results are reported, illustrating the effects of infinite-variance errors and regressors in finite samples.