Finite-sample power of the Durbin--Watson test against fractionally integrated disturbances

We consider the finite-sample power of various tests against serial correlation in the disturbances of a linear regression model when these disturbances follow certain stationary long-memory processes. It emerges that the power depends on the form of the regressor matrix and that, for the Durbin--Watson test and many other tests that can be written as ratios of quadratic forms in the disturbances, the power can drop to zero as the long-memory parameter approaches the boundary of the stationarity region. The problem does not arise when the regression includes an intercept. We also provide a means to detect this zero-power trap for given regressors. Our analytical results are illustrated using fractionally integrated white noise and ARFIMA(1, d, 0) disturbances with artificial regressors and with a real data set. Copyright 2005 Royal Economic Society