On the Exceedance Point Process for a Stationary Sequence
Author | : T. Hsing |
Publisher | : |
Total Pages | : 23 |
Release | : 1985 |
ISBN-10 | : OCLC:227641828 |
ISBN-13 | : |
Rating | : 4/5 (28 Downloads) |
Book excerpt: It is known that the exceedance points of a high level by a stationary sequence are asymptotically Poisson as the level increases, under appropriate long range and local dependence conditions. When the local dependence conditions are relaxed, clustering of exceedances may occur, based on Poisson positions for the clusters. In this paper a detailed analysis of the exceedance point process is given, and show that, under wide conditions, any limiting point process for exceedances is necessarily compound Poisson. Sufficient conditions are also given for the existence of such a limit. The limiting distributions of extreme order statistics are derived as corollaries. Keywords include: Extreme values; stochastic processes; exceedances; point processes.