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Models for the extremes of Markov chains.

Research output: Contribution to journalJournal article

Published

Journal publication date12/1998
JournalBiometrika
Journal number4
Volume85
Number of pages17
Pages851-867
Original languageEnglish

Abstract

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 txhaviour 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.