Asymptotic Properties of the Empirical Spatial Extremogram

The extremogram 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. 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 and ground‐level ozone in the eastern United States.