The Moving Average Model for Spatial Interaction

Abstract

The paper analyses the two-dimensional moving average model as a model for the study of spatial interactions. The stationary invertible moving average model is defined and its properties are derived. Special cases are considered as particu- larly valuable for geographical study and their estimation and specification theory are discussed. A specification theory is derived based on the general structure of the autocorrelation coefficients complemented by a more formal likelihood ratio test. Cut-off points are obtained for the likelihood ratio test in the case of large and small lattices and this test is shown to be more powerful than conventional tests for spatial dependence in this more specific case of hypothesis testing. The paper also discusses the estimation theory for moving average models and concludes with a comparative study of the appropriateness of several models of dependence for given sets of data.

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