Complex Covariance Models

The aim of this work is to introduce the theoretical background regarding the complex formalism of a spatial and spatio-temporal random field and to present some families of complex-valued covariance models. In geostatistical literature, the study of the evolution of vector data with two components in space and space-time is often developed in the framework of the theory of complex-valued random fields. However, some efforts are required in the multivariate context. The computational details of their fitting are discussed through an environmental case study.