The tail measure and tail spectral process of regularly varying time series

The goal of this paper is an exhaustive investigation of the link between the tail measure of a regularly varying time series and its spectral tail process, independently introduced in Owada and Samorodnitsky (2012) and Basrak and Segers (2009). Our main result is to prove in an abstract framework t...

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Bibliographic Details
Published in:The Annals of applied probability 2018, Vol.6 (28), p.3884-3921
Main Authors: Soulier, Philippe, Dombry, Clément, Hashorva, Enkelejd
Format: Article
Language:English
Subjects:
Mathematics
Probability
Online Access:Get full text
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Summary:The goal of this paper is an exhaustive investigation of the link between the tail measure of a regularly varying time series and its spectral tail process, independently introduced in Owada and Samorodnitsky (2012) and Basrak and Segers (2009). Our main result is to prove in an abstract framework that there is a one to one correspondance between these two objets, and given one of them to show that it is always possible to build a time series of which it will be the tail measure or the spectral tail process. For non negative time series, we recover results explicitly or implicitly known in the theory of max-stable processes.
ISSN:1050-5164
2168-8737
DOI:10.1214/18-AAP1410