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2008 Sums of extreme values of subordinated long-range dependent sequences: moving averages with finite variance
Rafal Kulik
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Electron. J. Probab. 13: 961-979 (2008). DOI: 10.1214/EJP.v13-510

Abstract

In this paper we study the limiting behavior of sums of extreme values of long range dependent sequences defined as functionals of linear processes with finite variance. If the number of extremes in a sum is large enough, we obtain asymptotic normality, however, the scaling factor is relatively bigger than in the i.i.d case, meaning that the maximal terms have relatively smaller contribution to the whole sum. Also, it is possible for a particular choice of a model, that the scaling need not to depend on the tail index of the underlying marginal distribution, as it is well-known to be so in the i.i.d. situation. Furthermore, subordination may change the asymptotic properties of sums of extremes.

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Rafal Kulik. "Sums of extreme values of subordinated long-range dependent sequences: moving averages with finite variance." Electron. J. Probab. 13 961 - 979, 2008. https://doi.org/10.1214/EJP.v13-510

Information

Accepted: 12 June 2008; Published: 2008
First available in Project Euclid: 1 June 2016

zbMATH: 1189.60107
MathSciNet: MR2413291
Digital Object Identifier: 10.1214/EJP.v13-510

Subjects:
Primary: 60F05
Secondary: 60G70

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