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Testing for Spatial Autocorrelation: Moving Average versus Autoregressive Processes

In this paper I try to provide an answer to a simple question: how can we distinguish between a spatial autoregressive process and a spatial moving average process. This problem, which is apparently simple in a more general context, acquires a certain complexity when it is considered over an irregular, rather than homogeneous, space, so that the available instruments are somewhat scarce. In the light of this shortcoming, I develop an identification regime based on the Lagrange multipliers tests, one which is relatively simple to implement and which gives rise to significant results. This strategy tends to minimise the probability of commiting identification errors, albeit at the price of assuming some areas of uncertainty.