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December 2018 Tail measure and spectral tail process of regularly varying time series
Clément Dombry, Enkelejd Hashorva, Philippe Soulier
Ann. Appl. Probab. 28(6): 3884-3921 (December 2018). DOI: 10.1214/18-AAP1410


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.


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Clément Dombry. Enkelejd Hashorva. Philippe Soulier. "Tail measure and spectral tail process of regularly varying time series." Ann. Appl. Probab. 28 (6) 3884 - 3921, December 2018.


Received: 1 October 2017; Revised: 1 April 2018; Published: December 2018
First available in Project Euclid: 8 October 2018

zbMATH: 06994409
MathSciNet: MR3861829
Digital Object Identifier: 10.1214/18-AAP1410

Primary: 60G70

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

Rights: Copyright © 2018 Institute of Mathematical Statistics


Vol.28 • No. 6 • December 2018
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