New spatio-temporal complex covariance functions for vectorial data through positive mixtures

Abstract

In the literature, the theory of complex-valued random fields is usually recalled to describe the evolution of vector data in space, without including the temporal dimension. However, as in the real case, the development of the complex formalism in a spatio-temporal context and the construction of some new classes of spatio-temporal complex covariance models are of sure interest for the scientific community partly due to the ongoing explosion in the availability of vector observations in space–time. In this paper, after presenting the fundamental aspects of the complex formalism of a spatio-temporal random field in a complex domain and the extension of some classes of complex-valued covariance models from a spatial domain to a spatio-temporal one, a new family of spatio-temporal complex-valued models obtained through a positive mixture of an infinite number of terms is proposed and various examples are discussed. A case study on modeling the spatio-temporal complex correlation structure of vectorial data is also provided.