On limiting cluster size distributions for processes of exceedances for stationary sequences
Konstantin Borovkov, Serguei Novak
STATISTICS & PROBABILITY LETTERS | ELSEVIER SCIENCE BV | Published : 2010
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. © 2010 Elsevier B.V.
Awarded by ARC
Awarded by EPSRC
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.