TAIL MEASURE AND SPECTRAL TAIL PROCESS OF REGULARLY VARYING TIME SERIES

• 成果类型: Article
• 署名作者: Dombry, Clement; Hashorva, Enkelejd; Soulier, Philippe
• 署名单位: Universite Marie et Louis Pasteur; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Lausanne
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/18-AAP1410
• 发表日期: 2018
• 页码: 3884-3921
• 关键词: metric-spaces; infinite variance; CONVERGENCE; SEQUENCES; THEOREM; MODEL

摘要

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.