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Measures of serial extremal dependence and their estimation

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  • Davis, Richard A.
  • Mikosch, Thomas
  • Zhao, Yuwei

Abstract

The goal of this paper is two-fold: (1) We review classical and recent measures of serial extremal dependence in a strictly stationary time series as well as their estimation. (2) We discuss recent concepts of heavy-tailed time series, including regular variation and max-stable processes.

Suggested Citation

  • Davis, Richard A. & Mikosch, Thomas & Zhao, Yuwei, 2013. "Measures of serial extremal dependence and their estimation," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2575-2602.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:7:p:2575-2602
    DOI: 10.1016/j.spa.2013.03.014
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    References listed on IDEAS

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    1. Davis, Richard A. & Mikosch, Thomas, 2008. "Extreme value theory for space-time processes with heavy-tailed distributions," Stochastic Processes and their Applications, Elsevier, vol. 118(4), pages 560-584, April.
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    12. Davis, Richard A. & Mikosch, Thomas & Cribben, Ivor, 2012. "Towards estimating extremal serial dependence via the bootstrapped extremogram," Journal of Econometrics, Elsevier, vol. 170(1), pages 142-152.
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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. Pushpa Dissanayake & Teresa Flock & Johanna Meier & Philipp Sibbertsen, 2021. "Modelling Short- and Long-Term Dependencies of Clustered High-Threshold Exceedances in Significant Wave Heights," Mathematics, MDPI, vol. 9(21), pages 1-33, November.
    3. Han, Heejoon & Linton, Oliver & Oka, Tatsushi & Whang, Yoon-Jae, 2016. "The cross-quantilogram: Measuring quantile dependence and testing directional predictability between time series," Journal of Econometrics, Elsevier, vol. 193(1), pages 251-270.
    4. Hashorva, Enkelejd, 2018. "Representations of max-stable processes via exponential tilting," Stochastic Processes and their Applications, Elsevier, vol. 128(9), pages 2952-2978.
    5. von Sachs, Rainer, 2019. "Spectral Analysis of Multivariate Time Series," LIDAM Discussion Papers ISBA 2019008, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Raphaël de Fondeville & Anthony C. Davison, 2022. "Functional peaks‐over‐threshold analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(4), pages 1392-1422, September.
    7. Stefan Birr & Stanislav Volgushev & Tobias Kley & Holger Dette & Marc Hallin, 2017. "Quantile spectral analysis for locally stationary time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1619-1643, November.
    8. Lin Han & Ivor Cribben & Stefan Trueck, 2022. "Extremal Dependence in Australian Electricity Markets," Papers 2202.09970, arXiv.org.
    9. Yuichi Goto & Tobias Kley & Ria Van Hecke & Stanislav Volgushev & Holger Dette & Marc Hallin, 2021. "The Integrated Copula Spectrum," Working Papers ECARES 2021-29, ULB -- Universite Libre de Bruxelles.
    10. Mikosch, Thomas & Zhao, Yuwei, 2015. "The integrated periodogram of a dependent extremal event sequence," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 3126-3169.
    11. Todorova, Neda, 2017. "The intraday directional predictability of large Australian stocks: A cross-quantilogram analysis," Economic Modelling, Elsevier, vol. 64(C), pages 221-230.
    12. Stefan Birr & Holger Dette & Marc Hallin & Tobias Kley & Stanislav Volgushev, 2016. "On Wigner-Ville Spectra and the Unicity of Time-Varying Quantile-Based Spectral Densities," Working Papers ECARES ECARES 2016-38, ULB -- Universite Libre de Bruxelles.
    13. Y Hoga, 2018. "A structural break test for extremal dependence in β-mixing random vectors," Biometrika, Biometrika Trust, vol. 105(3), pages 627-643.
    14. Heejoon Han, 2016. "Quantile Dependence between Stock Markets and its Application in Volatility Forecasting," Papers 1608.07193, arXiv.org.
    15. Segers, Johan & Zhao, Yuwei & Meinguet, Thomas, 2016. "Radial-angular decomposition of regularly varying time series in star-shaped metric spaces," LIDAM Discussion Papers ISBA 2016017, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    16. Duan, Kun & Ren, Xiaohang & Wen, Fenghua & Chen, Jinyu, 2023. "Evolution of the information transmission between Chinese and international oil markets: A quantile-based framework," Journal of Commodity Markets, Elsevier, vol. 29(C).
    17. Buhl, Sven & Klüppelberg, Claudia, 2018. "Limit theory for the empirical extremogram of random fields," Stochastic Processes and their Applications, Elsevier, vol. 128(6), pages 2060-2082.

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