Unit root tests for time series with a structural break: When the break point is known

Abstract

Unit root tests for time series with level shifts are considered. The level shift is assumed to occur at a known time point. In contrast to some other proposals the level shift is modeled as part of the intercept term of the stationary component of the data generation process which is separated from the unit root component. In this framework simple shift functions result in a smooth transition from one state to another both under the null and under the alternative hypothesis. In order to test for a unit root in this context the nuisance parameters are estimated in a first step and a standard unit root test e.g. of the Dickey-Fuller type is then applied to the residuals. The resulting test is shown to have a known asymptotic distribution under the null hypothesis of a unit root and nearly optimal asymptotic power under local alternatives. An empirical comparison with previous proposals is performed.