Weak convergence of the tail empirical function for dependent sequences
Journal article, 2009

This paper proves weak convergence in D of the tail empirical process – the renormalized extreme tail of the empirical process – for a large class of stationary sequences. The conditions needed for convergence are (i) moment restrictions on the amount of clustering of extremes, (ii) restrictions on long range dependence (absolute regularity or strong mixing), and (iii) convergence of the covariance function. We further show how the limit process is changed if exceedances of a nonrandom level are replaced by exceedances of a high quantile of the observations. Weak convergence of the tail empirical process is one key to asymptotics for extreme value statistics and its wide range of applications, from geoscience to finance.

Strong mixing

Clustering of extremes

Tail distribution function

Absolute regularity



Holger Rootzen

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematical Statistics

Stoch. Proc. Appl.

Vol. 119 2 468-490

Subject Categories

Other Mathematics

More information