A new blocks estimator for the extremal index

TL;DR

This paper introduces a new extremal index estimator that depends on only one parameter, simplifying the estimation process and potentially improving accuracy, demonstrated through simulations and financial data application.

Contribution

The paper proposes a novel extremal index estimator that reduces parameter dependence, enhancing robustness and ease of use compared to existing methods.

Findings

The new estimator performs well in simulations.

Application to financial data demonstrates practical utility.

Reduces parameter tuning complexity.

Abstract

The occurrence of successive extreme observations can have an impact on society. In extreme value theory there are parameters to evaluate the effect of clustering of high values, such as the extremal index. The estimation of the extremal index is a recurrent theme in the literature and there are several methodologies for this purpose. The majority of existing methods depend on two parameters whose choice affects the performance of the estimators. Here we consider a new estimator depending only on one of the parameters, thus contributing to a decrease in the degree of uncertainty. A simulation study presents motivating results. An application to financial data will also be presented.