Power Comparison of Autocorrelation Tests in Dynamic Models

The four most readily available tests of autocorrelation in dynamic models namely Durbin's M test, Durbin's H test, Breusch-Godfrey (BGF) test and Ljung and Box (Q) test are compared in terms of their power for varying sample sizes, levels of autocorrelation and significance using Monte Carlo simulations in STATA. Power comparison reveals that the Durbin M test is the best option for testing the hypothesis of no autocorrelation in dynamic models for all sample sizes. Breusch-Godfrey's test has comparable and at times minutely better performance than Durbin's M test however in small sample sizes, Durbin's M test outperforms the Breusch-Godfrey test in terms of power. The Durbin H and the Ljung and Box Q tests consistently occupy the second last and last positions respectively in terms of power performance with maximum power gap of 63 and 60% respectively from the best test (M test).