Test procedures for unit roots in time series with level shifts at unknown time

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 the known break date assumption. Different estimators of the break date are compared in a Monte Carlo experiment and a recommendation for choosing the break date in small samples is given. It is also shown that ignoring the fact that a break has occurred and applying a standard unit root test may lead to substantial size distortion and total loss of power. Example series from the Nelson-Plosser data set are used to illustrate the performance of our tests.