The Annals of Applied Probability

Tail measure and spectral tail process of regularly varying time series

Clément Dombry, Enkelejd Hashorva, and Philippe Soulier

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Abstract

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 [Stochastic Process. Appl. 119 (2009) 1055–1080]. Our main result is to prove in an abstract framework that there is a one-to-one correspondence between these two objects, 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 nonnegative time series, we recover results explicitly or implicitly known in the theory of max-stable processes.

Article information

Source
Ann. Appl. Probab., Volume 28, Number 6 (2018), 3884-3921.

Dates
Received: October 2017
Revised: April 2018
First available in Project Euclid: 8 October 2018

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1538985638

Digital Object Identifier
doi:10.1214/18-AAP1410

Mathematical Reviews number (MathSciNet)
MR3861829

Zentralblatt MATH identifier
06994409

Subjects
Primary: 60G70: Extreme value theory; extremal processes

Keywords
Regularly varying time series tail measure spectral tail process time change formula

Citation

Dombry, Clément; Hashorva, Enkelejd; Soulier, Philippe. Tail measure and spectral tail process of regularly varying time series. Ann. Appl. Probab. 28 (2018), no. 6, 3884--3921. doi:10.1214/18-AAP1410. https://projecteuclid.org/euclid.aoap/1538985638


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