where X1 represents a series of T observations (t = 1, . .. , T). This ratio is not appropriate for testing the independence of residuals from least squares regression; its purpose is to test for autocorrelation among observed variables. The Durbin-Watson development (1950, 1951) of the von Neumann ratio was concerned with testing residuals from regression for serial correlation. They test the null hypothesis H,, that there is no serial correlation between the residuals (Ut) against the alternative hypothesis H1 that the Ut are positively correlated. The Durbin-Watson test statistic is