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Multivariate maxima of moving multivariate maxima

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  • Ferreira, Helena

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.

Suggested Citation

  • Ferreira, Helena, 2012. "Multivariate maxima of moving multivariate maxima," Statistics & Probability Letters, Elsevier, vol. 82(8), pages 1489-1496.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:8:p:1489-1496
    DOI: 10.1016/j.spl.2012.04.015
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    References listed on IDEAS

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    1. Hall, Peter & Peng, Liang & Yao, Qiwei, 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.
    2. Deheuvels, Paul, 1983. "Point processes and multivariate extreme values," Journal of Multivariate Analysis, Elsevier, vol. 13(2), pages 257-272, June.
    3. 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.
    4. 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.
    5. 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;Sociedad de Estadística e Investigación Operativa, vol. 14(2), pages 433-448, December.
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    1. A. Martins & H. Ferreira, 2014. "Extremal properties of M4 processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 388-408, June.

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