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Extremal clustering under moderate long range dependence and moderately heavy tails

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  • Chen, Zaoli
  • Samorodnitsky, Gennady

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.

Suggested Citation

  • Chen, Zaoli & Samorodnitsky, Gennady, 2022. "Extremal clustering under moderate long range dependence and moderately heavy tails," Stochastic Processes and their Applications, Elsevier, vol. 145(C), pages 86-116.
    • Handle: RePEc:eee:spapps:v:145:y:2022:i:c:p:86-116
    DOI: 10.1016/j.spa.2021.12.001
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    References listed on IDEAS

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    1. Resnick, Sidney & Samorodnitsky, Gennady & Xue, Fang, 2000. "Growth rates of sample covariances of stationary symmetric [alpha]-stable processes associated with null recurrent Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 85(2), pages 321-339, February.
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