Extremal Index: estimation and resampling

Abstract

The duration of extremes in time leads to a phenomenon known as clustering of high values, with a strong impact on risk assessment. The extremal index is a measure developed within Extreme ValueTheory that quanties the degree of clustering of high values. In this work we will consider the cycles estimator introduced in Ferreira & Ferreira (2018). A reduced bias estimator based on the Jackknife methodology will be presented. The bootstrap technique will also be considered in the inference and will allow to obtain con dence intervals. The performance will be analyzed based on simulation. We foundour proposal eective in reducing bias and it compares favorably with some well-known methods. An application of the methods to real data will also be presented.