Extremal clustering under moderate long range dependence and moderately heavy tails

Zaoli Chen; Gennady Samorodnitsky

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arXiv · 2003.05038

Extremal clustering under moderate long range dependence and moderately heavy tails

Zaoli Chen·Gennady Samorodnitsky

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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 $D(0,\infty)$. 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.

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Zaoli Chen, Gennady Samorodnitsky. 2020-03-10. Extremal clustering under moderate long range dependence and moderately heavy tails. https://arxiv.org/abs/2003.05038

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