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A Latent Process Model for Temporal Extremes

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  • Paola Bortot
  • Carlo Gaetan

Abstract

type="main" xml:id="sjos12051-abs-0001"> This paper presents a hierarchical approach to modelling extremes of a stationary time series. The procedure comprises two stages. In the first stage, exceedances over a high threshold are modelled through a generalized Pareto distribution, which is represented as a mixture of an exponential variable with a Gamma distributed rate parameter. In the second stage, a latent Gamma process is embedded inside the exponential distribution in order to induce temporal dependence among exceedances. Unlike other hierarchical extreme-value models, this version has marginal distributions that belong to the generalized Pareto family, so that the classical extreme-value paradigm is respected. In addition, analytical developments show that different choices of the underlying Gamma process can lead to different degrees of temporal dependence of extremes, including asymptotic independence. The model is tested through a simulation study in a Markov chain setting and used for the analysis of two datasets, one environmental and one financial. In both cases, a good flexibility in capturing different types of tail behaviour is obtained.

Suggested Citation

  • Paola Bortot & Carlo Gaetan, 2014. "A Latent Process Model for Temporal Extremes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(3), pages 606-621, September.
    • Handle: RePEc:bla:scjsta:v:41:y:2014:i:3:p:606-621
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    File URL: http://hdl.handle.net/10.1111/sjos.12051
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    References listed on IDEAS

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    1. Cristiano Varin & Paolo Vidoni, 2005. "A note on composite likelihood inference and model selection," Biometrika, Biometrika Trust, vol. 92(3), pages 519-528, September.
    2. Joe, Harry & Lee, Youngjo, 2009. "On weighting of bivariate margins in pairwise likelihood," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 670-685, April.
    3. S. G. Walker, 2000. "A Note on the Innovation Distribution of a Gamma Distributed Autoregressive Process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(3), pages 575-576, September.
    4. Paola Bortot & Stuart Coles, 2003. "Extremes of Markov chains with tail switching potential," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(4), pages 851-867, November.
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    1. Rishikesh Yadav & Raphaël Huser & Thomas Opitz, 2021. "Spatial hierarchical modeling of threshold exceedances using rate mixtures," Environmetrics, John Wiley & Sons, Ltd., vol. 32(3), May.
    2. Valentin Courgeau & Almut E.D. Veraart, 2022. "Asymptotic theory for the inference of the latent trawl model for extreme values," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(4), pages 1448-1495, December.
    3. Paola Bortot & Carlo Gaetan, 2016. "Latent Process Modelling of Threshold Exceedances in Hourly Rainfall Series," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(3), pages 531-547, September.

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