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Adapting extreme value statistics to financial time series: dealing with bias and serial dependence

Author

Listed:
  • Laurens Haan

    (Erasmus University Rotterdam)

  • Cécile Mercadier

    (Université Claude Bernard—Lyon 1)

  • Chen Zhou

    (De Nederlandsche Bank)

Abstract

We handle two major issues in applying extreme value analysis to financial time series, bias and serial dependence, jointly. This is achieved by studying bias correction methods when observations exhibit weak serial dependence, in the sense that they come from β $\beta$ -mixing series. For estimating the extreme value index, we propose an asymptotically unbiased estimator and prove its asymptotic normality under the β $\beta$ -mixing condition. The bias correction procedure and the dependence structure have a joint impact on the asymptotic variance of the estimator. Then we construct an asymptotically unbiased estimator of high quantiles. We apply the new method to estimate the value-at-risk of the daily return on the Dow Jones Industrial Average index.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:finsto:v:20:y:2016:i:2:d:10.1007_s00780-015-0287-6
    DOI: 10.1007/s00780-015-0287-6
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    References listed on IDEAS

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    1. Armelle Guillou & Peter Hall, 2001. "A diagnostic for selecting the threshold in extreme value analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 293-305.
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    3. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
    4. Drees, Holger & Kaufmann, Edgar, 1998. "Selecting the optimal sample fraction in univariate extreme value estimation," Stochastic Processes and their Applications, Elsevier, vol. 75(2), pages 149-172, July.
    5. 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.
    6. Sun, Pengfei & Zhou, Chen, 2014. "Diagnosing the distribution of GARCH innovations," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 287-303.
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    Citations

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    Cited by:

    1. Daouia, Abdelaati & Girard, Stéphane & Stupfler, Gilles, 2017. "Extreme M-quantiles as risk measures: From L1 to Lp optimization," TSE Working Papers 17-841, Toulouse School of Economics (TSE).
    2. H. Kaibuchi & Y. Kawasaki & G. Stupfler, 2022. "GARCH-UGH: a bias-reduced approach for dynamic extreme Value-at-Risk estimation in financial time series," Quantitative Finance, Taylor & Francis Journals, vol. 22(7), pages 1277-1294, July.
    3. Daouia, Abdelaati & Girard, Stéphane & Stupfler, Gilles, 2018. "Tail expectile process and risk assessment," TSE Working Papers 18-944, Toulouse School of Economics (TSE).
    4. Jurgen Spaanderman, 2018. "An urgent call to get better prepared for unexpected events," DNB Occasional Studies 1602, Netherlands Central Bank, Research Department.
    5. Gloria Buriticá & Philippe Naveau, 2023. "Stable sums to infer high return levels of multivariate rainfall time series," Environmetrics, John Wiley & Sons, Ltd., vol. 34(4), June.
    6. 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.
    7. Buriticá, Gloria & Mikosch, Thomas & Wintenberger, Olivier, 2023. "Large deviations of ℓp-blocks of regularly varying time series and applications to cluster inference," Stochastic Processes and their Applications, Elsevier, vol. 161(C), pages 68-101.
    8. Osman Doğan & Süleyman Taşpınar & Anil K. Bera, 2021. "Bayesian estimation of stochastic tail index from high-frequency financial data," Empirical Economics, Springer, vol. 61(5), pages 2685-2711, November.

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    More about this item

    Keywords

    Hill estimator; Bias correction; β $beta$ -mixing condition; Tail quantile process;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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