On space-time variograms: estimation and modeling choices

Space-time correlation modeling is one of the crucial steps of traditional structural analysis, since spacetime models are used for prediction purposes. There are significant problems to overcome in both the estimation and the modeling stages for space-time analysis. A covariance function must be strictly positive definite and a variogram must be strictly conditionally negative definite to ensure that the kriging equations have a unique solution. In the spatial-temporal context the list of possible models is likely to be much greater and model type selection more difficult. Hence, in the estimation stage there are two separate problems, one is to determine the appropriate model type and the other is to estimate the model parameters. De Iaco, Myers and Posa have shown that the use of marginal variograms is one way to attack this problem. A comparative study among some classes of space-time variogram functions is proposed.