Local asymptotic distributions of stationarity tests

In this paper we study the asymptotic behavior of several test statistics of the null hypothesis of stationarity under a sequence of local alternatives. The sequence of local alternatives is modeled as a nearly stationary process, i.e. a non stationary process in any finite sample which converges to a stationary process as $T \uparrow \infty$. 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 in \citet{wright1999} who found that the $KPSS$ and the $MRS$ tests have power equal to their size under a sequence of fractionaly alternatives. Finally, a simulation study investigates the power properties of the stationarity tests in finite samples