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 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 in-depth Monte Carlo analysis shows that the new procedure has important power gains when compared to the local Generalized Least Squares (GLS) de-trended Dickey–Fuller type tests under various data generating processes with persistence changes. Moreover, an empirical application to OECD countries’ inflation shows that for most series analysed persistence was high in the first half of the sample and subsequently decreased. These results conform with modern macroeconomic theories that point to changes in inflation dynamics in the early 1980s and also with recent empirical evidence against the I(1)−I(0) dichotomy.