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

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.

[1]  Gilbert T. Walker,et al.  On Periodicity in Series of Related Terms , 1931 .

[2]  T. W. Anderson,et al.  Distribution of the Circular Serial Correlation Coefficient for Residuals from a Fitted Fourier Series , 1950 .

[3]  James Durbin,et al.  An Alternative to the Bounds Test for Testing for Serial Correlation in Least-Squares Regression , 1970 .

[4]  T. W. Anderson.  On the theory of testing serial correlation , 1948 .

[5]  E. J. Hannan,et al.  Testing for Serial Correlation after Least Squares Regression , 1968 .

[6]  Kenneth F. Wallis,et al.  Testing for Fourth Order Autocorrelation in Qtrly Regression Equations , 1972 .

[7]  G. Yule.  On a Method of Investigating Periodicities in Disturbed Series, with Special Reference to Wolfer's Sunspot Numbers , 1927 .

[8]  H. Theil,et al.  Testing the Independence of Regression Disturbances , 1961 .

[9]  J. Neumann.  Distribution of the Ratio of the Mean Square Successive Difference to the Variance , 1941 .

[10]  R. C. Henshaw.  Testing Single-Equation Least Squares Regression Models for Autocorrelated Disturbances , 1966 .

[11]  J. Durbin,et al.  Testing for serial correlation in least squares regression. II. , 1950, Biometrika.

[12]  J. Imhof.  Computing the distribution of quadratic forms in normal variables , 1961 .

[13]  James Durbin,et al.  Tests of serial independence based on the cumulated periodogram , 1967 .

[14]  John von Neumann,et al.  Tabulation of the Probabilities for the Ratio of the Mean Square Successive Difference to the Variance , 1942 .

[15]  James Durbin,et al.  Tests for serial correlation in regression analysis based on the periodogram of least-squares residuals , 1969 .

[16]  H. Theil.  The Analysis of Disturbances in Regression Analysis , 1965 .

[17]  J. Koerts.  Some Further Notes on Disturbance Estimates in Regression Analysis , 1967 .