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Cluster based inference for extremes of time series

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  • Drees, Holger
  • Janßen, Anja
  • Neblung, Sebastian

Abstract

We introduce a new type of estimator for the spectral tail process of a regularly varying time series. The approach is based on a characterizing invariance property of the spectral tail process, which is incorporated into the new estimator via a projection technique. We show uniform asymptotic normality of this estimator, both in the case of known and of unknown index of regular variation. In a simulation study the new procedure shows a more stable performance than previously proposed estimators.

Suggested Citation

  • Drees, Holger & Janßen, Anja & Neblung, Sebastian, 2021. "Cluster based inference for extremes of time series," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 1-33.
    • Handle: RePEc:eee:spapps:v:142:y:2021:i:c:p:1-33
    DOI: 10.1016/j.spa.2021.07.012
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    References listed on IDEAS

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    1. Janssens, Anja & Segers, Johan, 2015. "Markov tail chains," LIDAM Reprints ISBA 2015010, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Basrak, Bojan & Davis, Richard A. & Mikosch, Thomas, 2002. "Regular variation of GARCH processes," Stochastic Processes and their Applications, Elsevier, vol. 99(1), pages 95-115, May.
    3. Kulik, Rafał & Soulier, Philippe & Wintenberger, Olivier, 2019. "The tail empirical process of regularly varying functions of geometrically ergodic Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 129(11), pages 4209-4238.
    4. Drees, Holger & Segers, Johan & Warchol, Michal, 2015. "Statistics for Tail Processes of Markov Chains," LIDAM Reprints ISBA 2015023, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Davis, Richard A. & Drees, Holger & Segers, Johan & WarchoÅ‚, MichaÅ‚, 2018. "Inference on the tail process with application to financial time series modelling," LIDAM Reprints ISBA 2018022, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Basrak, Bojan & Segers, Johan, 2009. "Regularly varying multivariate time series," Stochastic Processes and their Applications, Elsevier, vol. 119(4), pages 1055-1080, April.
    7. Davis, Richard A. & Drees, Holger & Segers, Johan & Warchoł, Michał, 2018. "Inference on the tail process with application to financial time series modeling," Journal of Econometrics, Elsevier, vol. 205(2), pages 508-525.
    8. Eberlein, Ernst, 1984. "Weak convergence of partial sums of absolutely regular sequences," Statistics & Probability Letters, Elsevier, vol. 2(5), pages 291-293, October.
    9. Davis, Richard & Drees, Holger & Segers, Johan & Warchol, Michal, 2018. "Inference on the tail process with application to financial time series modelling," LIDAM Discussion Papers ISBA 2018002, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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    Cited by:

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    2. 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.

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