Spectral tail processes and max-stable approximations of multivariate regularly varying time series

Publikation: Bidrag til tidsskriftTidsskriftartikelfagfællebedømt

Dokumenter

  • Anja Janßen
A regularly varying time series as introduced in Basrak and Segers (2009) is a (multivariate) time series such that all finite dimensional distributions are multivariate regularly varying. The extremal behavior of such a process can then be described by the index of regular variation and the so-called spectral tail process, which is the limiting distribution of the rescaled process, given an extreme event at time 0. As shown in Basrak and Segers (2009), the stationarity of the underlying time series implies a certain structure of the spectral tail process, informally known as the "time change formula". In this article, we show that on the other hand, every process which satisfies this property is in fact the spectral tail process of an underlying stationary max-stable process. The spectral tail process and the corresponding max-stable process then provide two complementary views on the extremal behavior of a multivariate regularly varying stationary time series.
OriginalsprogEngelsk
TidsskriftStochastic Processes and Their Applications
Vol/bind129
Udgave nummer6
Sider (fra-til)1993-2009
ISSN0304-4149
DOI
StatusUdgivet - 2019

ID: 202239716