Testing for change in stochastic volatility with long range dependence

Abstract

In this paper we consider a change point problem for long memory stochastic volatility models. We show that the limiting behavior for the CUSUM test statistics may not be affected by long memory, unlike the Wilcoxon test statistic which is infuenced by long range dependence. We compare our results to subordinated long memory Gaussian processes. Theoretical properties are accompanied by simulation studies.