On Exceedance Point Processes for Stationary Sequences under Mild Oscillation Restrictions
Abstract
It is known that any point process limits for the (time normalized) exceedances of high levels by a stationary sequence is necessarily Compound Poisson, under general dependence restrictions. This results from the clustering of exceedances where the underlying Poisson points represent cluster positions, and the multiplicities correspond to cluster sizes. A class of stationary sequences satisfying a mild local dependence condition restricting the extent of local rapid oscillation is investigated. For this class, criteria are given for the existence and value of the so-called extremal index which plays a key role in determining the intensity of cluster positions. Cluster size distributions are investigated for this class and in particular shown to be asymptotically equivalent to those for lengths of runs of consecutive exceedances above the level. Relations between the point processes of exceedances, cluster centers, and upcrossings are discussed.
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1988
- Accession Number
- ADA198314
Entities
People
- M. Ross Leadbetter
- S. Nandagopalan
Organizations
- University of North Carolina at Chapel Hill