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

TY - JOUR

T1 - Spectral tail processes and max-stable approximations of multivariate regularly varying time series

AU - Janßen, Anja

PY - 2019/6

Y1 - 2019/6

N2 - 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.

AB - 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.

KW - Max-stable processes

KW - Regularly varying time series

KW - Spectral tail process

KW - Stationary processes

UR - http://www.scopus.com/inward/record.url?scp=85050103216&partnerID=8YFLogxK

U2 - 10.1016/j.spa.2018.06.010

DO - 10.1016/j.spa.2018.06.010

M3 - Journal article

SN - 0304-4149

VL - 129

SP - 1993

EP - 2009

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 6

ER -