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

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 p-norm pound above a high threshold. Our main result derives new large deviation principles of extremal p-blocks pound, which guide us to define and characterize spectral cluster processes in p pound. We then study cluster inference in p pound 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 p-norm pound 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 pound alpha-blocks, where alpha > 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. (c) 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).