TESTING FOR A UNIT ROOT IN THE PRESENCE OF A POSSIBLE BREAK IN TREND

Abstract

We consider the issue of testing a time series for a unit root in the possible presence of a break in a linear deterministic trend at an unknown point in the series. We propose a new break fraction estimator which, where a break in trend occurs, is consistent for the true break fraction at rate Op(T 1). Unlike other available estimators, however, when there is no trend break, our estimator converges to zero at rate Op(T 1/2). Used in conjunction with a quasi difference (QD) detrended unit root test that incorporates a trend break regressor, we show that these rates of convergence ensure that known break fraction null critical values are asymptotically valid. Unlike available procedures in th..