Extremes and local dependence in stationary sequences
a weak “mixing condition” restricting long range dependence
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.
KeywordsPoint Process Stationary Sequence Local Dependence Extremal Index Dependent Random Variable
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