Title: A nonparametric estimator of the extremal index
Authors: Juan Juan Cai - Delft University of Technology (Netherlands) [presenting]
Andrea Krajina - Rabobank (Netherlands)
Abstract: Clustering of extremes usually has a large societal impact. The extremal index, a number in the unit interval, is a key parameter in modelling the clustering of extremes. We use a tool from multivariate extreme value theory to represent the extremal index, that is, we build a connection between the extremal index and the stable tail dependence function, which enables us to compute the value of extremal indices for some time series models. We also construct a nonparametric estimator of the extremal index using this connection. We prove that the estimator is consistent and asymptotically normal. The simulation study compares our estimator to the existing ones, which shows that our method has good finite sample properties. We also illustrate our method to a real data set on the daily maximum temperature in the Netherlands.