A frequency domain test for isotropy in spatial data models

We develop a new methodology for estimating and testing the form of anisotropy of homogeneous spatial processes. We derive a generalised version of the isotropy test proposed by Arbia et al. (2013) and analyse its properties in various settings. Expanding on this, we propose a new testing procedure in the frequency domain that allows one to estimate and test under mild conditions any form of anisotropy in homogeneous spatial processes. The power of the test is studied by means of Monte Carlo simulations performed both on regularly and irregularly spaced data. Finally, the method is used to analyse the soybean yields in the US.