  We consider a strictly stationary random field on the two-dimensional integer
lattice with regularly varying marginal and finite-dimensional distributions.
Exploiting the regular variation, we define the spatial extremogram which takes
into account only the largest values in the random field. This extremogram is a
spatial autocovariance function. We define the corresponding extremal spectral
density and its estimator, the extremal periodogram. Based on the extremal
periodogram, we consider the Whittle estimator for suitable classes of
parametric random fields including the Brown-Resnick random field and regularly
varying max-moving averages.
