  Regularly varying stochastic processes are able to model extremal dependence
between process values at locations in random fields. We investigate the
empirical extremogram as an estimator of dependence in the extremes. We provide
conditions to ensure asymptotic normality of the empirical extremogram centred
by a pre-asymptotic version. For max-stable processes with Fr{\'e}chet margins
we provide conditions such that the empirical extremogram centred by its true
version is asymptotically normal. The results of this paper apply to a variety
of spatial and space-time processes, and to time series models. We apply our
results to max-moving average processes and Brown-Resnick processes.
