Models for the extremes of Markov chains

被引:33
作者
Bortot, P [1 ]
Tawn, JA
机构
[1] Univ Padua, Dept Stat Sci, I-35121 Padua, Italy
[2] Univ Lancaster, Dept Math & Stat, Lancaster LA1 4YF, England
关键词
asymptotic independence; bivariate extreme value distribution; extremal index; extreme value theory; Gaussian process; Markov chain;
D O I
10.1093/biomet/85.4.851
中图分类号
Q [生物科学];
学科分类号
07 ; 0710 ; 09 ;
摘要
The modelling of extremes of a time series has progressed from the assumption of independent observations to more realistic forms of temporal dependence. In this paper, we focus on Markov chains, deriving a class of models for their joint tail which allows the degree of clustering of extremes to decrease at high levels, overcoming a key Limitation in current methodologies. Theoretical aspects of the model are examined and a simulation algorithm is developed through which the stochastic properties of summaries of the extremal behaviour of the chain are evaluated. The approach is illustrated through a simulation study of extremal events of Gaussian autoregressive processes and an application to temperature data.
引用
收藏
页码:851 / 867
页数:17
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