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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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G70: Extreme value theory; extremal processes

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


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.

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