Likelihood-based inference for multivariate space-time wrapped-Gaussian fields

Directional spatial data, typically represented through angles, are of central importance in many scientific disciplines, such as environmental sciences, oceanography and meteorology, among others. We propose a wrapped-Gaussian field to model directions in a multivariate spatial or spatio-temporal context. The n-dimensional distributions of a wrapped Gaussian field can be written as a sum over the n-dimensional lattice of ℝⁿ , making likelihood-based inference impracticable. We adopt a parametric approach and develop composite likelihood methods to estimate the parameters associated with location, as well as the spatial or spatio-temporal dependence. Our approach outperforms the analytical and computational limitations of full likelihood, because it works with the marginal bivariate distributions of the random field. We study the performance of the method through simulation experiments and by analysing a real data set of wave directions from the Adriatic coast of Italy.