A simple modification of the Busetti-Harvey stationarity tests with structural breaks at unknown time

In this paper a modification of the Busetti and Harvey (2001) test with structural break at unknown time is proposed. As the stationarity test with a super-consistent break date estimator is effective under large breaks and the infimum-test is effective under small breaks, although it has serious size distortions under large breaks, we propose a simple decision rule based on pre-testing for the presence of a break. The proposed modification shows good size properties. Also, an extension for the case of multiple structural breaks is proposed