Trend and Initial Condition in Stationarity Tests : The Asymptotic Analysis

In this paper we 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 for different magnitudes of local trend and initial value different tests are efficient, we propose following Harvey et al. (2008) the decision rule based on the rejection of null hypothesis for multiple tests. Also we propose the modification of this decision rule using additional information obtained through pre-testing about magnitudes of local trend and/or initial value. The resulting modification has good size properties under both types of uncertainty