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Extreme value theory for multivariate stationary sequences

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  • Hsing, Tailen

Abstract

A distributional mixing condition is introduced for stationary sequences of random vectors to study their extremes. For a sequence satisfying the condition, the following topics which concern the weak limit F of properly normalized partial maxima are studied: (1) To obtain characterizations of F. (2) To study a condition under which the partial maxima behave as they would if the sequence were i.i.d. (3) To consider problems in connection with the independence of the margins of F.

Suggested Citation

  • Hsing, Tailen, 1989. "Extreme value theory for multivariate stationary sequences," Journal of Multivariate Analysis, Elsevier, vol. 29(2), pages 274-291, May.
    • Handle: RePEc:eee:jmvana:v:29:y:1989:i:2:p:274-291
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    Citations

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    Cited by:

    1. Ferreira, H., 2011. "Dependence between two multivariate extremes," Statistics & Probability Letters, Elsevier, vol. 81(5), pages 586-591, May.
    2. Jean-David Fermanian, 2012. "An overview of the goodness-of-fit test problem for copulas," Papers 1211.4416, arXiv.org.
    3. Kabluchko, Zakhar, 2009. "Extremes of space-time Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 119(11), pages 3962-3980, November.
    4. J. Hüsler & M. G. Temido & A. Valente-Freitas, 2022. "On the Maximum of a Bivariate INMA Model with Integer Innovations," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2373-2402, December.
    5. N. Beck & C. Genest & J. Jalbert & M. Mailhot, 2020. "Predicting extreme surges from sparse data using a copula‐based hierarchical Bayesian spatial model," Environmetrics, John Wiley & Sons, Ltd., vol. 31(5), August.
    6. Segers, J.J.J., 2006. "Rare Events, Temporal Dependence and the Extremal Index," Discussion Paper 2006-7, Tilburg University, Center for Economic Research.
    7. 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.
    8. 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.
    9. Segers, J.J.J., 2006. "Rare Events, Temporal Dependence and the Extremal Index," Other publications TiSEM 04952d0f-2b24-44ad-bf07-f, Tilburg University, School of Economics and Management.
    10. Martins, A.P. & Ferreira, H., 2005. "Measuring the extremal dependence," Statistics & Probability Letters, Elsevier, vol. 73(2), pages 99-103, June.
    11. Bucher, Axel & Segers, Johan, 2013. "Extreme value copula estimation based on block maxima of a multivariate stationary time series," LIDAM Discussion Papers ISBA 2013049, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    12. Fernández, Begoña & Muriel, Nelson, 2009. "Regular variation and related results for the multivariate GARCH(p,q) model with constant conditional correlations," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1538-1550, August.

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