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Weak convergence of multivariate partial maxima processes

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  • Krizmanić, Danijel

Abstract

For a strictly stationary sequence of R+d–valued random vectors we derive functional convergence of partial maxima stochastic processes under joint regular variation and weak dependence conditions. The limit process is an extremal process and the convergence takes place in the space of R+d–valued càdlàg functions on [0,1], with the Skorohod weak M1 topology. We also show that this topology in general cannot be replaced by the stronger (standard) M1 topology. The theory is illustrated on three examples, including the multivariate squared GARCH process with constant conditional correlations.

Suggested Citation

  • Krizmanić, Danijel, 2017. "Weak convergence of multivariate partial maxima processes," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 1-11.
    • Handle: RePEc:eee:jmvana:v:155:y:2017:i:c:p:1-11
    DOI: 10.1016/j.jmva.2016.11.012
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    References listed on IDEAS

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    1. Basrak, Bojan & Davis, Richard A. & Mikosch, Thomas, 2002. "Regular variation of GARCH processes," Stochastic Processes and their Applications, Elsevier, vol. 99(1), pages 95-115, May.
    2. Basrak, Bojan & Segers, Johan, 2009. "Regularly varying multivariate time series," Stochastic Processes and their Applications, Elsevier, vol. 119(4), pages 1055-1080, April.
    3. 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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    More about this item

    Keywords

    Functional limit theorem; Regular variation; Weak M1 topology; Extremal process; Weak convergence; Multivariate GARCH;
    All these keywords.

    JEL classification:

    • M1 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Administration

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