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Point processes and multivariate extreme values

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  • Deheuvels, Paul

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.

Suggested Citation

  • Deheuvels, Paul, 1983. "Point processes and multivariate extreme values," Journal of Multivariate Analysis, Elsevier, vol. 13(2), pages 257-272, June.
    • Handle: RePEc:eee:jmvana:v:13:y:1983:i:2:p:257-272
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    Citations

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    Cited by:

    1. Jouchi Nakajima & Tsuyoshi Kunihama & Yasuhiro Omori, 2017. "Bayesian modeling of dynamic extreme values: extension of generalized extreme value distributions with latent stochastic processes," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(7), pages 1248-1268, May.
    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. Isao Ishida & Virmantas Kvedaras, 2015. "Modeling Autoregressive Processes with Moving-Quantiles-Implied Nonlinearity," Econometrics, MDPI, vol. 3(1), pages 1-53, January.
    4. Hürlimann, Werner, 2003. "Hutchinson-Lai's conjecture for bivariate extreme value copulas," Statistics & Probability Letters, Elsevier, vol. 61(2), pages 191-198, January.
    5. Kereszturi, Mónika & Tawn, Jonathan, 2017. "Properties of extremal dependence models built on bivariate max-linearity," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 52-71.
    6. Zhengjun Zhang, 2008. "The estimation of M4 processes with geometric moving patterns," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(1), pages 121-150, March.
    7. 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.
    8. Nakajima, Jouchi & Kunihama, Tsuyoshi & Omori, Yasuhiro & Frühwirth-Schnatter, Sylvia, 2012. "Generalized extreme value distribution with time-dependence using the AR and MA models in state space form," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3241-3259.
    9. Marta Ferreira, 2024. "Extremal index: estimation and resampling," Computational Statistics, Springer, vol. 39(5), pages 2703-2720, July.
    10. Ferreira, Helena, 2012. "Multivariate maxima of moving multivariate maxima," Statistics & Probability Letters, Elsevier, vol. 82(8), pages 1489-1496.
    11. Zhang, Zhengjun & Zhu, Bin, 2016. "Copula structured M4 processes with application to high-frequency financial data," Journal of Econometrics, Elsevier, vol. 194(2), pages 231-241.
    12. Stefan Aulbach & Michael Falk & Timo Fuller, 2019. "Testing for a $$\delta $$ δ -neighborhood of a generalized Pareto copula," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(3), pages 599-626, June.
    13. 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.
    14. Tsuyoshi Kunihama & Yasuhiro Omori & Zhengjun Zhang, 2012. "Efficient estimation and particle filter for max‐stable processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(1), pages 61-80, January.
    15. 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.
    16. 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.
    17. 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.
    18. 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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