Analysis of estimation methods for the extremal index

Abstract

Many datasets present time-dependent variation and short-term clustering within extreme values. The extremal index is a primary measure to evaluate clustering of high values in a stationary sequence. Estimation procedures are based on the choice of a threshold and/or a declustering parameter or a block size. Here we revise several different methods and compare them through simulation. In particular, we will see that a recent declustering methodology may be useful for the popular runs estimator and for a new estimator that works under the validation of a local dependence condition. An application to real data is also presented.