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Markov chain models for threshold exceedances.

Smith, R. L. and Tawn, J. A. and Coles, S. G. (1997) Markov chain models for threshold exceedances. Biometrika, 84 (2). pp. 249-268. ISSN 1464-3510

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Abstract

In recent research on extreme value statistics, there has been an extensive development of threshold methods, first in the univariate case and subsequently in the multivariate case as well. In this paper, an alternative methodology for extreme values of univariate time series is developed, by assuming that the time series is Markovian and using bivariate extreme value theory to suggest appropriate models for the transition distributions. A new likelihood representation for threshold methods is presented which we apply to a Markovian time series. An important motivation for developing this kind of theory is the possibility of calculating probability distributions for functionals of extreme events. We address this issue by showing how a theory of compound Poisson limits for additive functionals can be combined with simulation to obtain numerical solutions for problems of practical interest. The methods are illustrated by application to temperature data.

Item Type: Article
Journal or Publication Title: Biometrika
Uncontrolled Keywords: Extreme value theory • Generalised Pareto distribution • Markov chain • Threshold model
Subjects: Q Science > QA Mathematics
Departments: Faculty of Science and Technology > Mathematics and Statistics
Faculty of Science and Technology > Lancaster Environment Centre
ID Code: 19516
Deposited By: ep_ss_importer
Deposited On: 14 Nov 2008 11:45
Refereed?: Yes
Published?: Published
Last Modified: 09 Oct 2013 15:40
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/19516

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