Cluster based inference for extremes of time series

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 norma...

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Bibliographic Details
Published in:Stochastic processes and their applications 2021-12, Vol.142, p.1-33
Main Authors: Drees, Holger, Janßen, Anja, Neblung, Sebastian
Format: Article
Language:English
Subjects:
Cluster of extremes
Extreme value analysis
Projection estimator
Spectral tail process
Time series
Uniform central limit theorems
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Summary: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.
ISSN:0304-4149
1879-209X
DOI:10.1016/j.spa.2021.07.012