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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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    2. 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.
    3. 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).
    4. 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.
    5. 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.
    6. 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.
    7. Todorova, Neda, 2017. "The intraday directional predictability of large Australian stocks: A cross-quantilogram analysis," Economic Modelling, Elsevier, vol. 64(C), pages 221-230.
    8. Hashorva, Enkelejd, 2018. "Representations of max-stable processes via exponential tilting," Stochastic Processes and their Applications, Elsevier, vol. 128(9), pages 2952-2978.
    9. 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).
    10. 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.
    11. Y Hoga, 2018. "A structural break test for extremal dependence in β-mixing random vectors," Biometrika, Biometrika Trust, vol. 105(3), pages 627-643.
    12. Heejoon Han, 2016. "Quantile Dependence between Stock Markets and its Application in Volatility Forecasting," Papers 1608.07193, arXiv.org.
    13. 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.
    14. 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).
    15. 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).
    16. 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.
    17. Lin Han & Ivor Cribben & Stefan Trueck, 2022. "Extremal Dependence in Australian Electricity Markets," Papers 2202.09970, arXiv.org.

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