A test for deterministic dynamics in spatial processes

We propose a statistical procedure to determine if a spatial structure observed in the data is generated by a deterministic (even chaotic) spatial process rather than by a stochastic process. This procedure can be used as a specification test. It is robust against non-linearity and non-stationarity and can complete the toolbox for testing the diagnosis as well. The advantages of the presented methods are high power, simplicity, and ease and ample applicability for tests to be conducted, provided that weak conditions are required. Herein, we conduct several simulations to evaluate the performance of our procedure on well-known spatial processes and in situations where standard tests for spatial autocorrelation fail to detect spatial dependence. Guidelines for using the technique are also provided.