COMPUTING P-VALUES FOR THE GENERALIZED DURBIN-WATSON AND OTHER INVARIANT TEST STATISTICS

Shively, Ansley, and Kohn (1990) give an O(n) algorithm for computing the p-values of the Durbin-Watson and other invariant test statistics in time series regression. They do so by evaluating the characteristic function of a quadratic form in standard normal random variables and then numerically inverting it. In this paper we obtain a new expression for the characteristic function which simplifies the handling of the independent regressors and so is easier to evaluate. We also obtain general, easily computable bounds on the integration and truncation errors which arise in the numerical inversion of the characteristic function. Empirical results are presented on the speed and accuracy of our algorithm.