The paper analyzes the impact of the initial observation on the problem of testing for unit roots. To this end, we derive a family of optimal tests that maximize a weighted average power criterion with respect to the initial observation. We then investigate the relationship of this optimal...

Tests for stationarity are routinely applied to highly persistent time series. Following Kwiatkowski, Phillips, Schmidt and Shin (1992), standard stationarity employs a rescaling by an estimator of the long-run variance of the (potentially) stationary series. This paper analytically investigates...