Testing for Break in Persistence Under Long Memory and Variance Break

We consider the problem of testing for a break in persistence with long memory when the long memory is subject a variance break. The limiting distribution is derived under the null and the alternative hypothesis. The CUSUM of squared-based test diverge to infinity under the against of alternative as the sample size grows. We find that the size and power of the CUSUM of squared-based test suffer severe distortions due to negligible variance break. The numerical simulation results are consistent with our theoretical analysis.