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Testing for Serial Correlation in Least Squares Regression. III

J. Durbin and G. S. Watson
Biometrika
Vol. 58, No. 1 (Apr., 1971), pp. 1-19
Published by: Oxford University Press on behalf of Biometrika Trust
DOI: 10.2307/2334313
Stable URL: http://www.jstor.org/stable/2334313
Page Count: 19
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Testing for Serial Correlation in Least Squares Regression. III
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Abstract

The paper considers a number of problems arising from the test of serial correlation based on the d statistic proposed earlier by the authors (Durbin & Watson, 1950, 1951). Methods of computing the exact distribution of d are investigated and the exact distribution is compared with six approximations to it for four sets of published data. It is found that approximations suggested by Theil and Nagar and by Hannan are too inaccurate for practical use but that the beta approximation proposed in the 1950 and 1951 papers and a new approximation, called by us the a + bdU approximation and based, like the beta approximation, on the exact first two moments of d, both perform well. The power of the d test is compared with that of certain exact tests proposed by Theil, Durbin, Koerts and Abrahamse from the standpoint of invariance theory. It is shown that the d test is locally most powerful invariant but that the other tests are not. There are three appendices. The first gives an account of the exact distribution of d. The second derives the mean and variance to a second order of approximation of a modified maximum likelihood statistic closely related to d. The third sets out details of the computations required for the a + bdU approximation.

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