Title: Extremal index blocks estimator: Another approach
Authors: Manuela Neves - University of Lisbon and CEAUL (Portugal)
Dora Prata Gomes - NOVA.ID.FCT FCT-UNL (Portugal) [presenting]
Abstract: The main objective of Statistics of Extremes is the estimation of probabilities and parameters related to rare events. When extending the analysis of the limiting behaviour of the extreme values from independent and identically distributed sequences to stationary sequences a key parameter appears, the extremal index, whose accurate estimation is not easy. The extremal index measures the degree of local dependence in the extremes of a stationary process. We focus on the estimation of the extremal index using blocks estimators. Blocks estimators can be constructed by using disjoint blocks or sliding blocks but both blocks estimators require the choice of a threshold and a block length. Some criteria have appeared for the choice of those nuisance parameters. The objective is to revisit another block estimation procedure that only depends on the block length, although some conditions on the underlying process need to be verified. The associated estimator presents nice asymptotic properties, and for finite samples is illustrated a stability criterion for choosing the block length and then obtaining the extremal index estimate. A simulation study has been performed to illustrate the behaviour of the blocks estimator and an application to real data is presented.