  The extremogram, proposed by Davis and Mikosch (2008), is a useful tool for
measuring extremal dependence and checking model adequacy in a time series. We
define the extremogram in the spatial domain when the data is observed on a
lattice or at locations distributed as a Poisson point process in d-dimensional
space. Under mixing and other conditions, we establish a central limit theorem
for the empirical spatial extremogram. We show these conditions are applicable
for max-moving average processes and Brown-Resnick processes and illustrate the
empirical extremogram's performance via simulation. We also demonstrate its
practical use with a data set related to rainfall in a region in Florida.
