12,000

We have over 12,000 students, from over 100 countries, within one of the safest campuses in the UK

97%

97% of Lancaster students go into work or further study within six months of graduating

Home > Research > Publications & Outputs > Models for the extremes of Markov chains.
View graph of relations

« Back

Models for the extremes of Markov chains.

Research output: Contribution to journalJournal article

Published

<mark>Journal publication date</mark>12/1998
<mark>Journal</mark>Biometrika
Issue4
Volume85
Number of pages17
Pages851-867
<mark>Original language</mark>English

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.