Naslov
Regularly varying multivariate time series

Autori
Basrak, Bojan ; Segers, Johan

Izvornik
Stochastic processes and their applications (0304-4149) 119 (2009), 4; 1055-1080

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
autoregressive process ; clusters of extremes ; extremal index ; factor

Sažetak
Extreme values of a stationary, multivariate time series may exhibit dependence across coordinates and over time. The aim of this paper is to offer a new and po- tentially useful tool called tail process to describe and model such extremes. The key property is the following fact: existence of the tail process is equivalent to mul- tivariate regular variation of finite cuts of the original process. Certain remarkable properties of the tail process are exploited to shed new light on known results on certain point processes of extremes. The theory is shown to be applicable with great ease to stationary solutions of stochastic autoregressive processes with random coef- ficient matrices, an interesting special case being a recently proposed factor GARCH model. In this class of models, the distribution of the tail process is calculated by a combination of analytical methods and a novel sampling algorithm.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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