Heuristic tools for the estimation of the extremal index: a comparison of methods

Abstract

Clustering of exceedances of a critical level is a phenomenon that concerns risk managers in many areas. The extremal index θ measures the propensity of the large observations in a dataset to cluster. Thus the estimation of θ is an important issue recurrently addressed in literature. Besides a declustering parameter, inference also depends on a threshold. This choice is actually a crucial topic and is transversal to many other extremal parameters. In this paper we analyze a threshold-free heuristic procedure. We also make comparisons with other heuristic procedures already developed within the extremal index estimation. Our study is based on simulation. We illustrate with an application to environmental data.