Estimation of cluster functionals for regularly varying time series: runs estimators

TL;DR

This paper develops central limit theorems for runs estimators of cluster indices in regularly varying time series, showing their asymptotic equivalence in variance and providing a theoretical foundation for analyzing extremal dependence.

Contribution

It introduces verifiable conditions for CLTs of runs estimators in multivariate regularly varying time series, establishing their asymptotic properties.

Findings

Blocks and runs estimators have the same limiting variance.

Central limit theorems are established under verifiable conditions.

Theoretical framework applies to a large class of models.

Abstract

Cluster indices describe extremal behaviour of stationary time series. We consider runs estimators of cluster indices. 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 blocks and runs estimators have the same limiting variance.