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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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