Abstract
In this article, we have proposed a simple diagnostic statistical procedure for testing the order of dependence of a spatial process. The proposed test is of nonparametric nature, and it is able to deal with potential nonlinear spatial dependencies. An added value is that from a methodological point of view, the new test is based on symbolic dynamics and hence on information theory. We characterized the behavior of a symbolic entropy measure in the presence of spatial dependencies of order higher than 1. The good power performance of the new method in detecting higher order spatial lags is notable and gives rise to an expectation that it may form a suitable basis for constructive specification searches.
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