  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 depends only 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.
