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Extreme quantile estimation for β-mixing time series and applications

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  • Chavez-Demoulin, Valérie
  • Guillou, Armelle

Abstract

In this paper, we discuss the application of extreme value theory in the context of stationary β-mixing sequences that belong to the Fréchet domain of attraction. In particular, we propose a methodology to construct bias-corrected tail estimators. Our approach is based on the combination of two estimators for the extreme value index to cancel the bias. The resulting estimator is used to estimate an extreme quantile. In a simulation study, we outline the performance of our proposals that we compare to alternative estimators recently introduced in the literature. Also, we compute the asymptotic variance in specific examples when possible. Our methodology is applied to two datasets on finance and environment.

Suggested Citation

  • Chavez-Demoulin, Valérie & Guillou, Armelle, 2018. "Extreme quantile estimation for β-mixing time series and applications," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 59-74.
    • Handle: RePEc:eee:insuma:v:83:y:2018:i:c:p:59-74
    DOI: 10.1016/j.insmatheco.2018.09.004
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    References listed on IDEAS

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    9. Laurens Haan & Cécile Mercadier & Chen Zhou, 2016. "Adapting extreme value statistics to financial time series: dealing with bias and serial dependence," Finance and Stochastics, Springer, vol. 20(2), pages 321-354, April.
    10. M. Ivette Gomes & Laurens De Haan & Lígia Henriques Rodrigues, 2008. "Tail index estimation for heavy‐tailed models: accommodation of bias in weighted log‐excesses," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 31-52, February.
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    Cited by:

    1. Aigner, Maximilian & Chavez-Demoulin, Valérie & Guillou, Armelle, 2022. "Measuring and comparing risks of different types," Insurance: Mathematics and Economics, Elsevier, vol. 102(C), pages 1-21.

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    More about this item

    Keywords

    Asymptotic normality; β-mixing; Extreme value index; GARCH models; High quantile; Return level; Value-at-Risk;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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