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 classicalI(0) - I(1) framework have serious size distortions when the actual data generatingprocess exhibits long-range dependencies. We prove that the limiting distributionof a CUSUM of squares based test depends on the true memory parameterif the DGP exhibits long memory. We propose adjusted critical values for the testand give finite sample response curves which allow the practitioner to easily implementthe test and to compute the relevant critical values.[...]