The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 28, Number 6 (2018), 3884-3921.
Tail measure and spectral tail 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 [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.
Ann. Appl. Probab., Volume 28, Number 6 (2018), 3884-3921.
Received: October 2017
Revised: April 2018
First available in Project Euclid: 8 October 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60G70: Extreme value theory; extremal processes
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