The use of asymptotic critical values in stationarity tests against the alternative of a unit root process is known to lead to over-rejections in finite samples when the considered process is stationary but highly persistent. We claim that, in recent parametric tests, this is caused by...

Two types of unit root tests which accommodate a structural level shift at a known point in time are extended to the situation where the break date is unknown. It is shown that for any estimator for the break date the tests have the same asymptotic distribution as the corresponding tests under...