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

TL;DR

This paper develops central limit theorems for sliding blocks estimators of cluster indices in regularly varying time series, showing their asymptotic equivalence to disjoint blocks estimators in the Peak over Threshold framework.

Contribution

It introduces verifiable conditions for CLTs of sliding blocks estimators in multivariate regularly varying time series, extending extremal analysis methods.

Findings

Sliding blocks estimators satisfy CLTs under broad conditions.

In Peak over Threshold models, sliding and disjoint blocks estimators share the same asymptotic variance.

Theoretical results facilitate practical extremal dependence estimation.

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 Peak over Threshold framework, sliding and disjoint blocks estimators have the same limiting variance.