Testing axial symmetry and separability of lattice processes

Data collected on a rectangular lattice are common in many areas, and models used often make simplifying assumptions. These assumptions include axial symmetry in the spatial process and separability. Some different methods for testing axial symmetry and separability are considered. Using the sample periodogram is shown to provide some simple satisfactory tests of both hypotheses, but tests for separability given axial symmetry have low power for small lattices.