Local asymptotic distributions of stationarity tests

In this paper, we study the asymptotic behaviour of several test statistics of the null hypothesis of stationarity under a sequence of local alternatives. The sequence of local alternatives is modelled as a nearly stationary process, i.e. a non-stationary process in any finite sample which converges to a stationary process as the sample size goes to infinity. From the asymptotic distributions, we find that the stationarity tests have non-trivial power under the above sequence of local alternatives. Our results complement those of Wright [Econometric Theory (1999) Vol. 15, pp. 704–709] who found that the Kwiatkowski, Phillips, Schmidt and Shin (KPSS) and the modified range statistics (MRS) tests have power equal to their size under a sequence of fractional alternatives. Finally, a simulation study investigates the power properties of the stationarity tests in finite samples.