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Inference for clusters of extreme values

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  • Christopher A. T. Ferro
  • Johan Segers
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    Abstract

    Inference for clusters of extreme values of a time series typically requires the identification of independent clusters of exceedances over a high threshold. The choice of declustering scheme often has a significant effect on estimates of cluster characteristics. We propose an automatic declustering scheme that is justified by an asymptotic result for the times between threshold exceedances. The scheme relies on the extremal index, which we show may be estimated before declustering, and supports a bootstrap procedure for assessing the variability of estimates. Copyright 2003 Royal Statistical Society.

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    Bibliographic Info

    Article provided by Royal Statistical Society in its journal Journal of the Royal Statistical Society: Series B (Statistical Methodology).

    Volume (Year): 65 (2003)
    Issue (Month): 2 ()
    Pages: 545-556

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    Handle: RePEc:bla:jorssb:v:65:y:2003:i:2:p:545-556

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    Cited by:
    1. Omey, Edward & Mallor, Fermin & Nualart, Eulalia, 2009. "An introduction to statistical modelling of extreme values. Application to calculate extreme wind speeds," Working Papers 2009/36, Hogeschool-Universiteit Brussel, Faculteit Economie en Management.
    2. Marco Moscadelli, 2004. "The modelling of operational risk: experience with the analysis of the data collected by the Basel Committee," Temi di discussione (Economic working papers) 517, Bank of Italy, Economic Research and International Relations Area.
    3. Beirlant, J. & Schoutens, W. & Segers, J.J.J., 2004. "Mandelbrot's Extremism," Discussion Paper 2004-125, Tilburg University, Center for Economic Research.
    4. Zhao, Xin & Scarrott, Carl John & Oxley, Les & Reale, Marco, 2011. "GARCH dependence in extreme value models with Bayesian inference," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(7), pages 1430-1440.
    5. J. SebastiĆ£o & A. Martins & H. Ferreira & L. Pereira, 2013. "Estimating the upcrossings index," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 22(4), pages 549-579, November.
    6. F. Laurini & J. A. Tawn, 2006. "The extremal index for GARCH(1,1) processes with t-distributed innovations," Economics Department Working Papers 2006-SE01, Department of Economics, Parma University (Italy).
    7. Xin Zhao & Carl John Scarrott & Marco Reale & Les Oxley, 2009. "Bayesian Extreme Value Mixture Modelling for Estimating VaR," Working Papers in Economics 09/15, University of Canterbury, Department of Economics and Finance.
    8. John G. Galbraith & Serguei Zernov, 2006. "Extreme Dependence In The Nasdaq And S&P Composite Indexes," Departmental Working Papers 2006-14, McGill University, Department of Economics.
    9. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.

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