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

Monte Carlo experiments establish that the usual ``t-statistic'' used fortesting for first-order serial correlation with artificial regressions is far from being distributed as a Student's t in small samples. Rather, it is badly biased in both mean and variance and results in grossly misleading tests of hypotheses when treated as a Student's t. Simply computed corrections for the mean and variance are derived, however, which are shown to lead to a transformed statistic producing acceptable tests. The test procedure is detailed and exemplar code provided.