Asymptotic expansions for blocks estimators: PoT framework

TL;DR

This paper develops asymptotic expansions for block estimators of cluster indices in multivariate time series, clarifying their limiting behavior and differences between sliding and disjoint blocks within the Peak-over-Threshold framework.

Contribution

It provides a detailed asymptotic analysis of block estimators, extending existing convergence results and revealing behavior differences based on block size.

Findings

Asymptotic expansions depend on internal and boundary clusters.

Dichotomous behavior observed between small and large blocks.

Extended convergence results for cluster measures.

Abstract

We consider disjoint and sliding blocks estimators of cluster indices for multivariate, regularly varying time series in the Peak-over-Threshold framework. We aim to provide a complete description of the limiting behaviour of these estimators. This is achieved by a precise expansion for the difference between the sliding and the disjoint blocks statistics. The rates in the expansion stem from internal clusters and boundary clusters. To obtain these rates we need to extend the existing results on vague convergence of cluster measures. We reveal dichotomous behaviour between small blocks and large blocks scenario.