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 Electronic Journal of Probability > Vol. 13 (2008) > Paper 32 open journal systems 


Sums of extreme values of subordinated long-range dependent sequences: moving averages with finite variance

Rafal Kulik, University of Ottawa


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.


Full text: PDF

Pages: 961-979

Published on: June 12, 2008
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Electronic Journal of Probability. ISSN: 1083-6489