Model Specification in Stationary Random Fields

The problems of model specification in one- and two-dimensional stationary random fields are considered, with particular reference to the class of spatial autoregressions. The role of the autocorrelation function is discussed and it is shown to have a valuable exploratory use, especially in identifying directional bias in random fields. It is recommended that this analysis be supplemented by a likelihood-ratio test, which permits more precise tests of hypotheses about the form of the underlying model.