The Runs Test for Autocorrelated Errors: Unacceptable Properties

Abstract

The runs test is frequently recommended as a method of testing for nonindependent errors in time-series regression models. A Monte Carlo investigation was carried out to evaluate the empirical properties of this test using (a) several intervention and nonintervention regression models, (b) sample sizes ranging from 12 to 100, (c) three levels of α, (d) directional and nondirectional tests, and (e) 19 levels of autocorrelation among the errors. The results indicate that the runs test yields markedly asymmetrical error rates in the two tails and that neither directional nor nondirectional tests are satisfactory with respect to Type I error, even when the ratio of degrees of freedom to sample size is as high as .98. It is recommended that the test generally not be employed in evaluating the independence of the errors in time-series regression models.