Bootstrap tests for autocorrelation

The Durbin-Watson (D-W) test is one of the most widely used tests for autocorrelation in regression models. The D-W test has, however, an important limitation: the test is inconclusive when the test statistic falls into the so-called 'indeterminate range'. The indeterminate range exists because the true distribution of the D-W statistic is not tractable. Though there have been a number of approximation methods suggested to establish more accurate critical values for the D-W test, none has been found satisfactory. This paper proposes several bootstrap tests for autocorrelation. First, this paper applies bootstrap test procedures on the D-W statistic to eliminate the indeterminate range and improve the power of the test. A Monte Carlo study shows that the bootstrapped D-W test considerably outperforms the original D-W test and (a + bd_u) approximation. When bootstrap is utilized, however, a more powerful test than the bootstrapped D-W test can be designed. To this end, this paper directly bootstraps the estimated autocorrelation coefficient and shows that the suggested tests have even more accurate small sample properties than the bootstrapped D-W test.