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Large deviations of ℓp-blocks of regularly varying time series and applications to cluster inference

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  • Buriticá, Gloria
  • Mikosch, Thomas
  • Wintenberger, Olivier

Abstract

In the regularly varying time series setting, a cluster of exceedances is a short period for which the supremum norm exceeds a high threshold. We propose to study a generalization of this notion considering short periods, or blocks, with ℓp−norm above a high threshold. Our main result derives new large deviation principles of extremal ℓp−blocks, which guide us to define and characterize spectral cluster processes in ℓp. We then study cluster inference in ℓp to motivate our results. We design consistent disjoint blocks methods to infer features of cluster processes. Our inferential setting promotes the use of large empirical quantiles from the ℓp−norm of blocks as threshold levels which eases implementation and also facilitates comparison for different p>0. Our approach highlights the advantages of cluster inference based on extremal ℓα−blocks, where α>0 is the index of regular variation of the series. We focus on inference of important indices in extreme value theory, e.g., the extremal index.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:161:y:2023:i:c:p:68-101
    DOI: 10.1016/j.spa.2023.03.013
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    References listed on IDEAS

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    1. Janßen, Anja, 2019. "Spectral tail processes and max-stable approximations of multivariate regularly varying time series," Stochastic Processes and their Applications, Elsevier, vol. 129(6), pages 1993-2009.
    2. Segers, Johan & Zhao, Yuwei & Meinguet, Thomas, 2017. "Polar decomposition of regularly varying time series in star-shaped metric spaces," LIDAM Reprints ISBA 2017029, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. 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.
    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. Basrak, Bojan & Krizmanić, Danijel & Segers, Johan, 2012. "A functional limit theorem for dependent sequences with infinite variance stable limits," LIDAM Reprints ISBA 2012034, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    9. 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.
    10. 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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