A Small-Sample Correction for Testing for Joint Serial Correlation with Artificial Regressions

Prior research (Belsley, 1997) has established that the common tests for single orders of serial correlation (e.g., Durbin-Watson, artificial regression) are badly distorted and result in grossly misleading tests in small samples. A corrected t-statistic has been derived that removes these difficulties, but it cannot be applied to joint tests. This research provides the needed generalizations. First it shows, to no surprise, that the same distortions plague the F-statistic typically used for testing joint orders of serial correlation with artificial regressions. And second it derives a corrected F-statistic that provides acceptable tests for arbitrarily stipulated joint orders of serial correlation. The test procedure is detailed and exemplar code provided.