The linear coregionalization model and the product-sum space-time variogram

The product covariance model, the product-sum covariance model, and the integrated product and integrated product-sum models have the advantage of being easily fitted by the use of "marginal" variograms. These models and the use of the marginals are described in a series of papers by De Iaco, Myers, and Posa. Such models allow not only estimating values at nondata locations but also prediction in future times, hence, they are useful for analyzing air pollution data, meteorological data, or ground water data. These three kinds of data are nearly always multivariate and because the processes determining the deposition or dynamics will affect all variates, a multivariate approach is desirable. It is shown that the use of marginal variograms for space-time modeling can be extended to the multivariate case and in particular to the use of the Linear Coregionalization Model (LCM) for cokriging in space-time. An application to an environmental data set is given.