Families of spatio-temporal stationary covariance models

Abstract

This paper provides simple methods for constructing new families of spatio-temporal stationary covariance models from purely spatial (or purely temporal) stationary covariance models. As the application of the methods developed, we introduce spatio-temporal stationary covariance models with the Gaussian and related spatial margins, and develop the Heine family and the Whittle–Matérn family of spatio-temporal stationary covariance models.