Title: Testing for Change in Stochastic Volatility with Long Range Dependence,
Abstract: In this paper, change-point problems for long memory stochastic volatility
models are considered. A general testing problem which includes various
alternative hypotheses is discussed. Under the hypothesis of stationarity the
limiting behavior of CUSUM- and Wilcoxon-type test statistics is derived. In
this context, a limit theorem for the two-parameter empirical process of long
memory stochastic volatility time series is proved. In particular, it is shown
that the asymptotic distribution of CUSUM test statistics may not be affected
by long memory, unlike Wilcoxon test statistics which are typically influenced
by long range dependence. To avoid the estimation of nuisance parameters in
applications, the usage of self-normalized test statistics is proposed. The
theoretical results are accompanied by simulation studies which characterize
the finite sample behavior of the considered testing procedures when testing
for changes in mean, in variance, and in the tail index.