Extremal clustering under moderate long range dependence and moderately heavy tails

Zaoli Chen and Gennady Samorodnitsky

Stochastic Processes and their Applications, 2022, vol. 145, issue C, 86-116

Abstract: We study clustering of the extremes in a stationary sequence with subexponential tails in the maximum domain of attraction of the Gumbel distribution. We obtain functional limit theorems in the space D[0,∞) and in the space of random sup-measures. 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.

Keywords: Long range dependence; Random sup-measure; Stable regenerative set; Subexponential tails; Extremal clustering; Gumbel domain of attraction (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spa.2021.12.001

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