On stationary tests in the presence of structural breaks

We examine the effect of a structural break on stationarity tests. It has been shown that stationarity tests suffer from size distortion problems if a structural break exists but is ignored. This problem parallels the power loss problem of unit root tests ignoring an existing break. Nonetheless, the distributions of stationarity tests are asymptotically invariant to the exclusion of the existing break under the alternative hypothesis of a unit root. Our results thus clarify the nature of the effects of a structural break on inference regarding integrated time series.