This paper introduces a simple and easy to implement procedure to test for changes in persistence. The time-varying parameter that characterizes persistence changes under the alternative hypothesis is approximated by a parsimonious cosine function. The new test procedure is the minimum of a t-statistic, computed from a test regression that considers a set of reasonable values for a frequency term that is used to evaluate the time varying properties of persistence. The asymptotic distributions of the new tests are derived and critical values are provided. An indepth Monte Carlo analysis shows that the new procedure has important power gains when compared to the local GLS de-trended Dickey-Fuller (DFGLS) type tests introduced by Elliott et al. (1996) under various data generating processes with persistence changes. Moreover, an empirical application to OECD countries’ inflation series shows that for most countries analysed persistence was high in the first half of the sample and subsequently decreased. These results are compatible with modern macroeconomic theories that point to changes in inflation behavior in the early 1980s and also with recent empirical evidence against the I(1)-I(0) dichotomy.