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...

This paper proposes tests for a mean shift based on a new hybrid estimator of the long-run variance. It is shown that these tests can bypass the non-monotonic power problem of the LM tests while maintaining adequate size properties.