Thomas Mikosch, Laboratory of Actuarial Mathematics, University of Copenhagen 	

The extremogram: A correllogram for extreme events

Abstract

We consider a strictly stationary sequence of random vectors whose finite-dimensional
distributions are jointly regularly varying with some positive index. This class of processes includes
among others ARMA processes with regularly varying noise, GARCH processes with normally or
student distributed noise, and stochastic volatility models with regularly varying multiplicative
noise. We define an analog of the autocorrelation function, the extremogram, which only depends
on the extreme values in the sequence. We also propose a natural estimator for the extremogram
and study its asymptotic properties under alpha-mixing. We show asymptotic normality, calculate the
extremogram for various examples and consider spectral analysis related to the extremogram