A formal test for nonstationarity of spatial stochastic processes

In this manuscript, we consider the problem of testing a given spatial process for stationarity and isotropy. The approach is based on a spatial spectral analysis, this means spectral functions which are space dependent. The proposed method consists essentially in testing the homogeneity of a set of spatial spectra evaluated at different locations. In addition to testing stationarity and isotropy, the analysis provides also a method for testing whether the observed process fits a uniformly modulated model, and a test for randomness (white noise). Applications include modeling and testing for nonstationary of air pollution concentrations over different geo-political boundaries.