A class of valid Matérn cross-covariance functions for multivariate spatio-temporal random fields

Abstract We extend a current result in the literature by introducing a parametric family of matrix-valued cross-covariance functions, which would help describe multivariate space–time dependence structures for any number of variables. All the direct and cross-covariance functions belong to the Matern class. The smoothness, space–time separability and scale parameters are allowed to be different for each variable.