Abstract
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.
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