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On limiting cluster size distributions for processes of exceedances for stationary sequences

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  • Borovkov, Konstantin
  • Novak, Serguei

Abstract

It is well known that, under broad assumptions, the time-scaled point process of exceedances of a high level by a stationary sequence converges to a compound Poisson process as the level grows. The purpose of this note is to demonstrate that, for any given distribution G on , there exists a stationary sequence for which the compounding law of this limiting process of exceedances will coincide with G.

Suggested Citation

  • Borovkov, Konstantin & Novak, Serguei, 2010. "On limiting cluster size distributions for processes of exceedances for stationary sequences," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1814-1818, December.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:23-24:p:1814-1818
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    Cited by:

    1. Janssen, Anja & Segers, Johan, 2022. "Invariance properties of limiting point processes and applications to clusters of extremes," LIDAM Discussion Papers ISBA 2022020, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Janßen Anja & Segers Johan, 2024. "Invariance properties of limiting point processes and applications to clusters of extremes," Dependence Modeling, De Gruyter, vol. 12(1), pages 1-12, January.

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