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The multivariate Gaussian tail model: an application to oceanographic data

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  • P. Bortot
  • S. Coles
  • J. Tawn

Abstract

Optimal design of sea‐walls requires the extreme value analysis of a variety of oceanographic data. Asymptotic arguments suggest the use of multivariate extreme value models, but empirical studies based on data from several UK locations have revealed an inadequacy of this class for modelling the types of dependence that are often encountered in such data. This paper develops a specific model based on the marginal transformation of the tail of a multivariate Gaussian distribution and examines its utility in overcoming the limitations that are encountered with the current methodology. Diagnostics for the model are developed and the robustness of the model is demonstrated through a simulation study. Our analysis focuses on extreme sea‐levels at Newlyn, a port in south‐west England, for which previous studies had given conflicting estimates of the probability of flooding. The novel diagnostics suggest that this discrepancy may be due to the weak dependence at extreme levels between wave periods and both wave heights and still water levels. The multivariate Gaussian tail model is shown to resolve the conflict and to offer a convincing description of the extremal sea‐state process at Newlyn.

Suggested Citation

  • P. Bortot & S. Coles & J. Tawn, 2000. "The multivariate Gaussian tail model: an application to oceanographic data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 49(1), pages 31-049.
    • Handle: RePEc:bla:jorssc:v:49:y:2000:i:1:p:31-049
    DOI: 10.1111/1467-9876.00177
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    Cited by:

    1. Ranoua Bouchouicha, 2010. "Dépendance entre risques extrêmes : Application aux Hedge Funds," Working Papers 1013, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
    2. JOOCHEOl KIM & SUNGHO KIM, 2014. "Multivariate Tail Dependence in Financial Markets," Working papers 2014rwp-71, Yonsei University, Yonsei Economics Research Institute.
    3. Rockinger, Michael & Poon, Ser-Huang & Tawn, Jonathan, 2001. "New Extreme-Value Dependence Measures and Finance Applications," CEPR Discussion Papers 2762, C.E.P.R. Discussion Papers.
    4. Schlather, Martin, 2001. "Examples for the coefficient of tail dependence and the domain of attraction of a bivariate extreme value distribution," Statistics & Probability Letters, Elsevier, vol. 53(3), pages 325-329, June.
    5. Padoan, Simone A., 2013. "Extreme dependence models based on event magnitude," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 1-19.
    6. J. L. Wadsworth & J. A. Tawn & A. C. Davison & D. M. Elton, 2017. "Modelling across extremal dependence classes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(1), pages 149-175, January.
    7. Alexandra Ramos & Anthony Ledford, 2009. "A new class of models for bivariate joint tails," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 219-241, January.
    8. Manaf Ahmed & Véronique Maume‐Deschamps & Pierre Ribereau, 2022. "Recognizing a spatial extreme dependence structure: A deep learning approach," Environmetrics, John Wiley & Sons, Ltd., vol. 33(4), June.

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