We show that any consistent tests for serial correlation have unit local power against the nearly integrated, nearly white noise process. The expected higher power is confirmed in finite sample Monte Carlo simulations.

This paper studies issues related to the estimation of a structural change in the persistence of a univariate time series. The break is such that the process has a unit root [i.e., is I(1)] in the pre-break regime but reverts to a stationary [i.e., I(0)] process in the post-break regime or vice...