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

Borovkov, Konstantin and Novak, Serguei ORCID: https://orcid.org/0000-0001-7929-7641 (2010) On limiting cluster size distributions for processes of exceedances for stationary sequences. Statistics & Probability Letters, 80 (23-24) . pp. 1814-1818. ISSN 0167-7152 [Article] (doi:10.1016/j.spl.2010.08.006)

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.

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