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

Gloria Buriticá, Thomas Mikosch and Olivier Wintenberger

Stochastic Processes and their Applications, 2023, vol. 161, issue C, 68-101

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.

Keywords: Regularly varying time series; Large deviation principles; Cluster processes; Extremal index (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spa.2023.03.013

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