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Point processes and multivariate extreme values

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  • Deheuvels, Paul
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    Abstract

    A new model for point processes is developed which assumes that the interarrival times are exponentially distributed and follow joint multivariate extreme value distributions. It is shown that such processes may arise via natural generating procedures, and that, under very weak assumptions, that they can be approximated as closely as desired by appropriate finite models.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 13 (1983)
    Issue (Month): 2 (June)
    Pages: 257-272

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    Handle: RePEc:eee:jmvana:v:13:y:1983:i:2:p:257-272

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    Related research

    Keywords: Point processes extreme values order statistics Multivariate distributions;

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    Cited by:
    1. Jouchi Nakajima & Tsuyoshi Kunihama & Yasuhiro Omori & Sylvia Fruhwirth-Schnatter, 2009. "Generalized extreme value distribution with time-dependence using the AR and MA models in state space form," CIRJE F-Series CIRJE-F-689, CIRJE, Faculty of Economics, University of Tokyo.
    2. Fougères, Anne-Laure & Mercadier, Cécile & Nolan, John P., 2013. "Dense classes of multivariate extreme value distributions," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 109-129.
    3. Zhengjun Zhang, 2008. "The estimation of M4 processes with geometric moving patterns," Annals of the Institute of Statistical Mathematics, Springer, vol. 60(1), pages 121-150, March.
    4. Jiménez, Javier Rojo & Villa-Diharce, Enrique & Flores, Miguel, 2001. "Nonparametric Estimation of the Dependence Function in Bivariate Extreme Value Distributions," Journal of Multivariate Analysis, Elsevier, vol. 76(2), pages 159-191, February.
    5. Tsuyoshi Kunihama & Yasuhiro Omori & Zhengjun Zhang, 2010. "Bayesian Estimation and Particle Filter for Max-Stable Processes," CIRJE F-Series CIRJE-F-757, CIRJE, Faculty of Economics, University of Tokyo.
    6. Zhengjun Zhang, 2009. "On approximating max-stable processes and constructing extremal copula functions," Statistical Inference for Stochastic Processes, Springer, vol. 12(1), pages 89-114, February.
    7. Ferreira, Helena, 2012. "Multivariate maxima of moving multivariate maxima," Statistics & Probability Letters, Elsevier, vol. 82(8), pages 1489-1496.
    8. A. Martins & H. Ferreira, 2014. "Extremal properties of M4 processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 23(2), pages 388-408, June.
    9. Falk, Michael, 2011. "Local asymptotic normality in a stationary model for spatial extremes," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 48-60, January.
    10. Zhang, Zhengjun & Shinki, Kazuhiko, 2007. "Extreme co-movements and extreme impacts in high frequency data in finance," Journal of Banking & Finance, Elsevier, vol. 31(5), pages 1399-1415, May.

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