Extremes and local dependence in stationary sequences

Abstract

Extensions of classical extreme value theory to apply to stationary sequences generally make use of two types of dependence restriction: (a) a weak "mixing condition" restricting long range dependence (b) a local condition restricting the "clustering" of high level exceedances. The purpose of this paper is to investigate extremal properties when the local condition (b) is omitted. It is found that, under general conditions, the type of the limiting distribution for maxima is unaltered. The precise modifications and the degree of clustering of high level exceedances are found to be largely described by a parameter here called the "extremal index" of the sequence. © 1983 Springer-Verlag.