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Biometrika 1998 85(4):851-867; doi:10.1093/biomet/85.4.851
© 1998 by Biometrika Trust
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Models for the extremes of Markov chains

PAOLA BORTOT and JONATHAN A. TAWN

Department of Statistical Sciences, University of Padova 35121 Padova, Italybortot{at}hal.stat.unipd.it
Department of Mathematics and Statistics, Lancaster University University, Lancaster LA1 4YF, U.K.j.tawn{at}lancaster.ac.uk

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.

Key Words: Asymptotic independence • Bivariate extreme value distribution • Extremal index • Extreme value theory • Gaussian process • Markov chain


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