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Weak convergence of the tail empirical process for dependent sequences

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  • Rootzén, Holger

Abstract

This paper proves weak convergence in D of the tail empirical process-the renormalized extreme tail of the empirical process-for a large class of stationary sequences. The conditions needed for convergence are (i) moment restrictions on the amount of clustering of extremes, (ii) restrictions on long range dependence (absolute regularity or strong mixing), and (iii) convergence of the covariance function. We further show how the limit process is changed if exceedances of a nonrandom level are replaced by exceedances of a high quantile of the observations. Weak convergence of the tail empirical process is one key to asymptotics for extreme value statistics and its wide range of applications, from geoscience to finance.

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  • Rootzén, Holger, 2009. "Weak convergence of the tail empirical process for dependent sequences," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 468-490, February.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:2:p:468-490
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    References listed on IDEAS

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    5. Eberlein, Ernst, 1984. "Weak convergence of partial sums of absolutely regular sequences," Statistics & Probability Letters, Elsevier, vol. 2(5), pages 291-293, October.
    6. Dedecker, Jérôme & Doukhan, Paul, 2003. "A new covariance inequality and applications," Stochastic Processes and their Applications, Elsevier, vol. 106(1), pages 63-80, July.
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    Cited by:

    1. Rafal Kulik & Philippe Soulier, 2013. "Heavy tailed time series with extremal independence," Papers 1307.1501, arXiv.org, revised Oct 2014.

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