Extremal clustering under moderate long range dependence and moderately heavy tails
Probability
2020-03-12 v1
Abstract
We study clustering of the extremes in a stationary sequence with subexponential tails in the maximum domain of attraction of the Gumbel We obtain functional limit theorems in the space of random sup-measures and in the space . The limits have the Gumbel distribution if the memory is only moderately long. However, as our results demonstrate rather strikingly, the "heuristic of a single big jump" could fail even in a moderately long range dependence setting. As the tails become lighter, the extremal behavior of a stationary process may depend on multiple large values of the driving noise.
Cite
@article{arxiv.2003.05038,
title = {Extremal clustering under moderate long range dependence and moderately heavy tails},
author = {Zaoli Chen and Gennady Samorodnitsky},
journal= {arXiv preprint arXiv:2003.05038},
year = {2020}
}