Testing for a break in persistence under long‐range dependencies

We show that tests for a break in the persistence of a time series in the classical I (0)/ I (1) framework have serious size distortions when the actual data‐generating process (DGP) exhibits long‐range dependencies. We prove that the limiting distribution of a CUSUM of squares‐based test depends on the true memory parameter if the DGP exhibits long memory. We propose adjusted critical values for the test and give finite sample response curves that allow easy implementation of the test by the practitioner and also ease in computing the relevant critical values. We furthermore prove the consistency of the test for a simple breakpoint estimator also under long memory. We show that the test has satisfying power properties when the correct critical values are used.