Trend and initial condition in stationarity tests: the asymptotic analysis

In this paperwe investigate the behavior of stationarity tests proposed by Muller (2005) and Harris et al. (2007) with uncertainty over the trend and/or initial condition. As dierent tests are e cient for dierent magnitudes of local trend and initial condition, following Harvey et al. (2012) we propose decision rule based on the rejection of null hypothesis for multiple tests. Additionally, we propose a modi cation of this decision rule, relying on additional information about the magnitudes of the local trend and/or the initial condition that is obtained through pre-testing. The resulting modification has satisfactory size properties under both uncertainty types.