We define a family of local mixing conditions that enable the computation of the extremal index of periodic sequences from the joint distributions of k consecutive variables of the sequence. By applying results, under local and global mixing conditions, to the (2m - 1)-dependent periodic sequence Xn (m) = Σj=-m m-1 cjZn-j, n ≥ 1, we compute the extremal index of the periodic moving average sequence Xn = Σj=-∞ ∞ cjZn-j, n ≥ 1, of random variables with regularly varying tail probabilities.
This paper generalizes the theory for extremes of stationary moving averages with regularly varying tail probabilities.
@article{urn:eudml:doc:40456,
title = {Extremes of periodic moving averages of random variables with regularly varying tail probabilities.},
journal = {SORT},
volume = {28},
year = {2004},
pages = {161-176},
mrnumber = {MR2116189},
zbl = {1274.60168},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:40456}
}
Martins, Ana Paula; Ferreira, Helena. Extremes of periodic moving averages of random variables with regularly varying tail probabilities.. SORT, Tome 28 (2004) pp. 161-176. http://gdmltest.u-ga.fr/item/urn:eudml:doc:40456/