Markov chain models for threshold exceedances.

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Markov chain models for threshold exceedances. / Smith, R. L.; Tawn, J. A.; Coles, S. G.
In: Biometrika, Vol. 84, No. 2, 1997, p. 249-268.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Smith, RL, Tawn, JA & Coles, SG 1997, 'Markov chain models for threshold exceedances.', Biometrika, vol. 84, no. 2, pp. 249-268. https://doi.org/10.1093/biomet/84.2.249

APA

Smith, R. L., Tawn, J. A., & Coles, S. G. (1997). Markov chain models for threshold exceedances. Biometrika, 84(2), 249-268. https://doi.org/10.1093/biomet/84.2.249

Vancouver

Smith RL, Tawn JA, Coles SG. Markov chain models for threshold exceedances. Biometrika. 1997;84(2):249-268. doi: 10.1093/biomet/84.2.249

Author

Smith, R. L. ; Tawn, J. A. ; Coles, S. G. / Markov chain models for threshold exceedances. In: Biometrika. 1997 ; Vol. 84, No. 2. pp. 249-268.

Bibtex

@article{aabacc6f08fe4186813539a19fc4dec7,

title = "Markov chain models for threshold exceedances.",

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.",

keywords = "Extreme value theory • Generalised Pareto distribution • Markov chain • Threshold model",

author = "Smith, {R. L.} and Tawn, {J. A.} and Coles, {S. G.}",

year = "1997",

doi = "10.1093/biomet/84.2.249",

language = "English",

volume = "84",

pages = "249--268",

journal = "Biometrika",

issn = "1464-3510",

publisher = "Oxford University Press",

number = "2",

}

RIS

TY - JOUR

T1 - Markov chain models for threshold exceedances.

AU - Smith, R. L.

AU - Tawn, J. A.

AU - Coles, S. G.

PY - 1997

Y1 - 1997

N2 - 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.

AB - 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.

KW - Extreme value theory • Generalised Pareto distribution • Markov chain • Threshold model

U2 - 10.1093/biomet/84.2.249

DO - 10.1093/biomet/84.2.249

M3 - Journal article

VL - 84

SP - 249

EP - 268

JO - Biometrika

JF - Biometrika

SN - 1464-3510

IS - 2

ER -

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