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.
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