Change-point tests for the tail parameter of Long Memory Stochastic Volatility time series

TL;DR

This paper develops a change-point test for detecting structural shifts in the tail index of Long Memory Stochastic Volatility time series, using the Hill estimator and a novel uniform reduction principle, with applications to financial data.

Contribution

It introduces a new change-point testing method based on the Hill estimator for long memory volatility models, supported by theoretical proofs and empirical analysis.

Findings

The test accurately detects changes in tail index.

The asymptotic distribution depends on the Hurst parameter and tail index.

Simulation studies confirm the method's effectiveness.

Abstract

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.