“Generalization of the durbin-watson statistic for higher order autoregressive processes

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Abstract
The Durbin-Watson statistic is used for testing the first order serial correlation among residuals in a linear model. It is based on the residuals from a corresponding regression analysis. In this paper a generalization of the statistic which tests for higher order dependence among residuals is proposed. The paper gives a brief review of the Durbin-Watson theory and the construction of the corresponding significance tables based on Jacobi orthogonal polynomials and the beta density. The distribution of the Durbin-Watson statistic based on Tmhof's distribution of Quadratic forms is indicated as an alternative method of directly computing the distribution function of the Durbin-Watson statistic, as well as its generalization, Significance values for 5 percent level of significance for lags 2 to 4 are given in Table II.