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Space–time modelling of extreme events

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  • R. Huser
  • A. C. Davison

Abstract

type="main" xml:id="rssb12035-abs-0001"> Max-stable processes are the natural analogues of the generalized extreme value distribution when modelling extreme events in space and time. Under suitable conditions, these processes are asymptotically justified models for maxima of independent replications of random fields, and they are also suitable for the modelling of extreme measurements over high thresholds. The paper shows how a pairwise censored likelihood can be used for consistent estimation of the extremes of space–time data under mild mixing conditions and illustrates this by fitting an extension of a model due to Schlather to hourly rainfall data. A block bootstrap procedure is used for uncertainty assessment. Estimator efficiency is considered and the choice of pairs to be included in the pairwise likelihood is discussed. The model proposed fits the data better than some natural competitors.

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  • 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.
    • Handle: RePEc:bla:jorssb:v:76:y:2014:i:2:p:439-461
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    File URL: http://hdl.handle.net/10.1111/rssb.2014.76.issue-2
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    Cited by:

    1. Jonathan Jalbert & Anne-Catherine Favre & Claude Bélisle & Jean-François Angers, 2017. "A spatiotemporal model for extreme precipitation simulated by a climate model, with an application to assessing changes in return levels over North America," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(5), pages 941-962, November.
    2. Einmahl, John & Kiriliouk, A. & Segers, J.J.J., 2016. "A Continuous Updating Weighted Least Squares Estimator of Tail Dependence in High Dimensions," Other publications TiSEM a3e7350b-4773-4bd8-9c3c-6, Tilburg University, School of Economics and Management.
    3. Samuel A. Morris & Brian J. Reich & Emeric Thibaud & Daniel Cooley, 2017. "A space-time skew-t model for threshold exceedances," Biometrics, The International Biometric Society, vol. 73(3), pages 749-758, September.
    4. John H. J. Einmahl & Anna Kiriliouk & Andrea Krajina & Johan Segers, 2016. "An M-estimator of spatial tail dependence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 275-298, January.
    5. Zhong, Peng & Huser, Raphaël & Opitz, Thomas, 2024. "Exact Simulation of Max-Infinitely Divisible Processes," Econometrics and Statistics, Elsevier, vol. 30(C), pages 96-109.
    6. A. Abu-Awwad & V. Maume-Deschamps & P. Ribereau, 2021. "Semiparametric estimation for space-time max-stable processes: an F-madogram-based approach," Statistical Inference for Stochastic Processes, Springer, vol. 24(2), pages 241-276, July.
    7. Julien Hambuckers & Marie Kratz & Antoine Usseglio-Carleve, 2023. "Efficient Estimation In Extreme Value Regression Models Of Hedge Fund Tail Risks," Working Papers hal-04090916, HAL.
    8. Samuel A. Morris & Brian J. Reich & Emeric Thibaud, 2019. "Exploration and Inference in Spatial Extremes Using Empirical Basis Functions," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(4), pages 555-572, December.
    9. Hugo C. Winter & Jonathan A. Tawn, 2016. "Modelling heatwaves in central France: a case-study in extremal dependence," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 65(3), pages 345-365, April.
    10. A. Abu-Awwad & V. Maume-Deschamps & P. Ribereau, 2020. "Fitting spatial max-mixture processes with unknown extremal dependence class: an exploratory analysis tool," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 479-522, June.
    11. Buhl, Sven & Klüppelberg, Claudia, 2018. "Limit theory for the empirical extremogram of random fields," Stochastic Processes and their Applications, Elsevier, vol. 128(6), pages 2060-2082.
    12. 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.
    13. Koch, Erwan & Robert, Christian Y., 2019. "Geometric ergodicity for some space–time max-stable Markov chains," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 43-49.

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