Towards an automatic procedure for modeling multivariate space–time data

In many environmental sciences, several correlated variables are observed at some locations of the domain of interest and over a certain period of time. In this context, appropriate modeling and prediction techniques for multivariate space–time data as well as interactive software packages are necessary. In this paper, a new automatic procedure for fitting the space–time linear coregionalization model (ST-LCM) using the product–sum variogram model is discussed. This procedure, based on the simultaneous diagonalization of the sample matrix variograms, allows the identification of the ST-LCM parameters in a very flexible way. The fitting process is analytically described by a main flow chart and all steps are specified by four subprocedures. An application of this procedure is illustrated through a case study concerning the daily concentrations of three air pollutants measured in an urban area. Then the fitted space–time coregionalization model is applied to predict the variable of interest using a recent GSLib routine, named “COK2ST.”