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Latent Process Modelling of Threshold Exceedances in Hourly Rainfall Series

Author

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  • Paola Bortot

    (Università di Bologna)

  • Carlo Gaetan

    () (Università Ca’ Foscari - Venezia)

Abstract

Abstract Two features are often observed in analyses of both daily and hourly rainfall series. One is the tendency for the strength of temporal dependence to decrease when looking at the series above increasing thresholds. The other is the empirical evidence for rainfall extremes to approach independence at high enough levels. To account for these features, Bortot and Gaetan (Scand J Stat 41:606–621, 2014) focus on rainfall exceedances above a fixed high threshold and model their dynamics through a hierarchical approach that allows for changes in the temporal dependence properties when moving further into the right tail. It is found that this modelling procedure performs generally well in analyses of daily rainfalls, but has some inherent theoretical limitations that affect its goodness of fit in the context of hourly data. In order to overcome this drawback, we develop here a modification of the Bortot and Gaetan model derived from a copula-type technique. Application of both model versions to rainfall series recorded in Camborne, England, shows that they provide similar results when studying daily data, but in the analysis of hourly data the modified version is superior.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:jagbes:v:21:y:2016:i:3:d:10.1007_s13253-016-0254-5
    DOI: 10.1007/s13253-016-0254-5
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    References listed on IDEAS

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    1. R. Huser & A. C. Davison, 2014. "Space–time modelling of extreme events," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(2), pages 439-461, March.
    2. M. E. Robinson & J. A. Tawn, 2000. "Extremal analysis of processes sampled at different frequencies," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 117-135.
    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.
    4. Emma F. Eastoe & Jonathan A. Tawn, 2009. "Modelling non-stationary extremes with application to surface level ozone," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(1), pages 25-45.
    5. Cristiano Varin & Paolo Vidoni, 2005. "A note on composite likelihood inference and model selection," Biometrika, Biometrika Trust, vol. 92(3), pages 519-528, September.
    6. 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.
    7. Christopher A. T. Ferro & Johan Segers, 2003. "Inference for clusters of extreme values," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 545-556.
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