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Multivariate maxima of moving multivariate maxima

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  • Ferreira, Helena
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    Abstract

    We define a class of multivariate maxima of moving multivariate maxima, generalising the M4 processes. For these stationary multivariate time series we characterise the joint distribution of extremes and compute the multivariate extremal index. We derive the bivariate upper tail dependence coefficients and the extremal coefficient of the new limiting multivariate extreme value distributions.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167715212001587
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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 82 (2012)
    Issue (Month): 8 ()
    Pages: 1489-1496

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    Handle: RePEc:eee:stapro:v:82:y:2012:i:8:p:1489-1496

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    Related research

    Keywords: Moving multivariate maxima; Multivariate extremal index; Tail dependence; Multivariate extreme value distribution;

    References

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    1. A. Martins & H. Ferreira, 2005. "The multivariate extremal index and the dependence structure of a multivariate extreme value distribution," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 14(2), pages 433-448, December.
    2. Capéraà, Philippe & Fougères, Anne-Laure & Genest, Christian, 2000. "Bivariate Distributions with Given Extreme Value Attractor," Journal of Multivariate Analysis, Elsevier, vol. 72(1), pages 30-49, January.
    3. Deheuvels, Paul, 1983. "Point processes and multivariate extreme values," Journal of Multivariate Analysis, Elsevier, vol. 13(2), pages 257-272, June.
    4. Peter Hall & Liang Peng & Qiwei Yao, 2002. "Moving-maximum models for extrema of time series," LSE Research Online Documents on Economics 6084, London School of Economics and Political Science, LSE Library.
    5. repec:sae:ecolab:v:16:y:2006:i:2:p:1-2 is not listed on IDEAS
    6. Hüsler, Jürg & Reiss, Rolf-Dieter, 1989. "Maxima of normal random vectors: Between independence and complete dependence," Statistics & Probability Letters, Elsevier, vol. 7(4), pages 283-286, February.
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