A Class of Variogram Matrices for Vector Random Fields in Space and/or Time

This paper studies vector (multivariate, multiple, or multidimensional) random fields in space and/or time with second-order increments, for which the variogram matrix is an important tool to measure the dependence within each component and between each pair of distinct components. We introduce an efficient approach to construct Gaussian or non-Gaussian vector random fields from the univariate random field with higher dimensional index domain, and particularly to generate a class of variogram matrices.