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

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