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

Philippe Soulier (1) , Clément Dombry (2) , Enkelejd Hashorva (3)

1 MODAL'X - Modélisation aléatoire de Paris X
2 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
3 UNIL - Université de Lausanne = University of Lausanne

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.

Domaines: Probabilités [math.PR]

Philippe Soulier, Clément Dombry, Enkelejd Hashorva. The tail measure and tail spectral process of regularly varying time series. The Annals of Applied Probability, 2018, 6 (28), pp.3884-3921. ⟨10.1214/18-AAP1410⟩. ⟨hal-01686001⟩