Reducing size distortions of parametric stationarity tests

The use of asymptotic critical values in stationarity tests against the alternative of a unit rot process is known to lead to overrejections in finite samples when the considered process is stationary but highly persistent. We claim that in recent parametric tests this is caused by estimation errors which result when the autoregressive parameters used to describe the short-run dynamics of the process are replaced by estimators. We suggest a modification that corrects for these errors and show by simulation that the modified test works reasonably well whenn the persistence is moderate and there is no time trend in the model. An empirical illustration withinflation rate data is provided.