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Testing for Change in Long‐Memory Stochastic Volatility Time Series

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  • Annika Betken
  • Rafał Kulik

Abstract

In this article, change‐point problems for long‐memory stochastic volatility (LMSV) 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 LMSV 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 an analysis of Standard & Poor's 500 daily closing indices with respect to structural changes and by simulation studies which characterize the finite sample behavior of the considered testing procedures when testing for changes in mean and in variance.

Suggested Citation

  • Annika Betken & Rafał Kulik, 2019. "Testing for Change in Long‐Memory Stochastic Volatility Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 40(5), pages 707-738, September.
    • Handle: RePEc:bla:jtsera:v:40:y:2019:i:5:p:707-738
    DOI: 10.1111/jtsa.12449
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    Cited by:

    1. Zhanshou Chen & Yanting Xiao & Fuxiao Li, 2021. "Monitoring memory parameter change-points in long-memory time series," Empirical Economics, Springer, vol. 60(5), pages 2365-2389, May.

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