  We consider a change-point test based on the Hill estimator to test for
structural changes in the tail index of Long Memory Stochastic Volatility time
series. In order to determine the asymptotic distribution of the corresponding
test statistic, we prove a uniform reduction principle for the tail empirical
process in a two-parameter Skorohod space. It is shown that such a process
displays a dichotomous behavior according to an interplay between the Hurst
parameter, i.e., a parameter characterizing the dependence in the data, and the
tail index. Our theoretical results are accompanied by simulation studies and
the analysis of financial time series with regard to structural changes in the
tail index.
