Modeling spatio-temporal complex covariance functions for vectorial data

The theory of complex-valued random fields was already used in Geostatistics to describe vector data with two components. However, in the literature, there are various contributions focused only on modeling their spatial evolution, while the temporal perspective was analyzed separately or used to model time-varying complex covariance models. Thus, in this context it is surely challenging to propose some advances in modeling the joint spatial and temporal behavior of vector data with a reasonable representation on a complex domain. In this paper, after introducing the fundamental aspects of the complex formalism of a spatio-temporal random field and some approaches for building new families of spatio-temporal models, the spatio-temporal complex modeling of current data observed in the US East and Gulf Coast is deeply discussed and the results regarding a comparative analysis between two different complex-valued covariance models are also presented.