A simple and powerful test for autocorrelated errors in OLS intervention models

The important assumption of independent errors should be evaluated routinely in the application of interrupted time-series regression models. The two most frequently recommended tests of this assumption [Mood's runs test and the Durbin-Watson (D-W) bounds test] have several weaknesses. The former has poor small sample Type I error performance and the latter has the bothersome property that results are often declared to be "inconclusive." The test proposed in this article is simple to compute (special software is not required), there is no inconclusive region, an exact p-value is provided, and it has good Type I error and power properties relative to competing procedures. It is shown that these desirable properties hold when design matrices of a specified form are used to model the response variable. A Monte Carlo evaluation of the method, including comparisons with other tests (viz., runs, D-W bounds, and D-W beta), and examples of application are provided.