In this paper, we propose a likelihood ratio test for a change in persistence of a time series. We consider the null hypothesis of a constant persistence I(1) and an alternative in which the series changes from a stationary regime to a unit root regime or vice versa. Both known and unknown break dates are analyzed. Moreover, we consider a modification of a lag length selection procedure which provides better size control over various data generation processes. The bootstrap with recoloring also improves size. In general, our likelihood ratio-based tests show the best finite sample properties from all persistence change tests that use the null hypothesis of a unit root throughout.