On the correlation structure of some two-dimensional stationary processes

The correlation structure of the class of stationary, unilateral, linear autoregressions defined on a plane lattice is considered. It is shown that although standard techniques for deriving the correlogram analytically are not immediately appropriate, it is, nevertheless, possible to give a simple solution in a certain region of the plane provided that the number of regressors is small. The remainder of the correlogram tends to be analytically awkward but can be very easily calculated numerically. Three specific examples arising from the literature are discussed in detail.