Clues for discriminating between moving average and autoregressive models in spatial processes

In this paper we try to provide additional insight into the problem of how to discriminate between the two most common spatial processes: the autoregressive and the moving average. This problem, whose analogous time series is apparently simple, acquires a certain complexity when it is considered in an irregular system of spatial units, mainly because there are few tools to carry out this discussion. Nevertheless, even with this lack, we believe that it is possible to make some progress using the methods available at present. In this paper we discuss the advantages and inconveniences of the different techniques that can help us to discriminate between both processes. We finish off the examination with a Monte Carlo exercise, and an application to the European regional income, which has enabled us to better understand the performance of several proposals such as the Lagrange Multipliers, the so-called Variance criterion and the tests of Vuong and Clarke.