Space-time analysis using a general product-sum model

A generalization of the product-sum covariance model introduced by De Cesare et al. (Statist. Probab. Lett. 51 (2001) 9) is given in this paper. This generalized model is non-separable and in general is non-integrable, hence, it cannot be obtained from the Cressie-Huang representation. Moreover, the product-sum model does not correspond to the use of a metric in space-time. It is shown that there are simple methods for estimating and modeling the covariance or variogram components of the product-sum model using data from realizations of spatial-temporal random fields.