Elsevier

Statistics & Probability Letters

Volume 80, Issues 23–24, 1–15 December 2010, Pages 1814-1818
Statistics & Probability Letters

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

https://doi.org/10.1016/j.spl.2010.08.006Get rights and content

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 N, there exists a stationary sequence for which the compounding law of this limiting process of exceedances will coincide with G.

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Acknowledgements

This research was supported by ARC Grant DP0880693 and EPSRC grant EP/H006613. The authors are grateful to the referee for careful reading of their manuscript and providing useful comments that helped to improve the exposition of the paper.

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