Estimation of cluster functionals for regularly varying time series: sliding blocks estimators

Abstract

Cluster indices describe extremal behaviour of stationary time series. We consider their sliding blocks estimators. Using a modern theory of multivariate, regularly varying time series, we obtain central limit theorems under conditions that can be easily verified for a large class of models. In particular, we show that in the Peaks-Over-Threshold framework, sliding and disjoint blocks estimators have the same limiting variance.