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Testing for changes in (extreme) VaR

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  • Yannick Hoga

Abstract

In this paper, we develop tests for a change in an unconditional small quantile (Value‐at‐Risk, VaR, in financial time series analysis) based on an estimator motivated by extreme value theory. This so‐called Weissman estimator allows tests to be applied for extreme VaR, where extant tests mostly fail. In view of applications, we allow for weakly dependent observations. Our test statistics rely on self‐normalization, which obviates the need to estimate the complicated asymptotic variance. Consistency is shown under local alternatives, where multiple breaks can occur. A simulation study shows that in finite samples our tests compare favourably in the tail region with extant tests based on order statistic estimators and also with tail index break tests. Two empirical examples serve to illustrate the practical use of our tests.

Suggested Citation

  • Yannick Hoga, 2017. "Testing for changes in (extreme) VaR," Econometrics Journal, Royal Economic Society, vol. 20(1), pages 23-51, February.
    • Handle: RePEc:wly:emjrnl:v:20:y:2017:i:1:p:23-51
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    File URL: http://hdl.handle.net/10.1111/ectj.12080
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    Cited by:

    1. Lazar, Emese & Wang, Shixuan & Xue, Xiaohan, 2023. "Loss function-based change point detection in risk measures," European Journal of Operational Research, Elsevier, vol. 310(1), pages 415-431.
    2. Enzo D'Innocenzo & Andre Lucas & Bernd Schwaab & Xin Zhang, 2024. "Joint extreme Value-at-Risk and Expected Shortfall dynamics with a single integrated tail shape parameter," Tinbergen Institute Discussion Papers 24-069/III, Tinbergen Institute.
    3. Tobias Fissler & Yannick Hoga, 2021. "Backtesting Systemic Risk Forecasts using Multi-Objective Elicitability," Papers 2104.10673, arXiv.org, revised Feb 2022.
    4. Y Hoga, 2018. "A structural break test for extremal dependence in β-mixing random vectors," Biometrika, Biometrika Trust, vol. 105(3), pages 627-643.
    5. Yun Feng & Weijie Hou & Yuping Song, 2024. "Tail risk forecasting and its application to margin requirements in the commodity futures market," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 43(5), pages 1513-1529, August.
    6. Lazar, Emese & Pan, Jingqi & Wang, Shixuan, 2024. "On the estimation of Value-at-Risk and Expected Shortfall at extreme levels," Journal of Commodity Markets, Elsevier, vol. 34(C).

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