A Class of Convolution-Based Models for Spatio-Temporal Processes with Non-Separable Covariance Structure

In this article, we propose a new parametric family of models for real-valued spatio-temporal stochastic processes S(x, t) and show how low-rank approximations can be used to overcome the computational problems that arise in fitting the proposed class of models to large datasets. Separable covariance models, in which the spatio-temporal covariance function of S(x, t) factorizes into a product of purely spatial and purely temporal functions, are often used as a convenient working assumption but are too inflexible to cover the range of covariance structures encountered in applications. We define positive and negative non-separability and show that in our proposed family we can capture positive, zero and negative non-separability by varying the value of a single parameter.