Estimating the multivariate extremal index function

TL;DR

This paper introduces nonparametric estimators for the multivariate extremal index function, which measures extremal clustering in multivariate stationary sequences, and demonstrates their asymptotic properties through simulations.

Contribution

It develops the first nonparametric estimators for the multivariate extremal index function with proven asymptotic normality under dependence conditions.

Findings

Estimators are consistent and asymptotically normal.

Simulation results validate theoretical properties.

Method handles long-range dependence effectively.

Abstract

The multivariate extremal index function relates the asymptotic distribution of the vector of pointwise maxima of a multivariate stationary sequence to that of the independent sequence from the same stationary distribution. It also measures the degree of clustering of extremes in the multivariate process. In this paper, we construct nonparametric estimators of this function and prove their asymptotic normality under long-range dependence and moment conditions. The results are illustrated by means of a simulation study.