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Models for the extremes of Markov chains. (English) Zbl 0926.60044
The theoretical background of this paper includes a very useful survey of current statistical approaches to the tail behaviour of a stationary first-order Markov chain. The authors focus on the joint tail approach which models the behaviour of asymptotically independent Markov chains over high threshold. Special attention is given to produce threshold-dependent within-cluster characteristics and a simulation algorithm for their evaluating is developed. At the end, the joint tail method is illustrated by a simulation study for Gaussian processes and applied to statistical analysis of temperature data.
Reviewer: E.Pancheva (Sofia)

MSC:
60G70 Extreme value theory; extremal stochastic processes
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
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