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Testing Residuals from Least Squares Regression for Being Generated by the Gaussian Random Walk

J. D. Sargan and Alok Bhargava
Econometrica
Vol. 51, No. 1 (Jan., 1983), pp. 153-174
Published by: The Econometric Society
DOI: 10.2307/1912252
Stable URL: http://www.jstor.org/stable/1912252
Page Count: 22
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Testing Residuals from Least Squares Regression for Being Generated by the Gaussian Random Walk
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Abstract

This paper considers the null hypothesis that the errors on a regression equation form a random walk. By using the standard Durbin-Watson assumptions, we derive three test statistics that are uniformly most powerful against the alternative hypothesis that the errors are being generated by the stationary first order Markoff process. Unfortunately, the tabulated lower and upper bounds are too wide apart and so we compare the powers of the three tests using simulated as well as economic data. It is then recommended that the Imhof routine should be attached to standard regression programs to calculate the exact limit of the Berenblut-Webb statistic.

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