Semi-parametric statistical approaches for space-time process prediction

The problem of estimation and prediction of a spatial-temporal stochastic process, observed at regular times and irregularly in space, is considered. A mixed formulation involving a nonparametric component, accounting for a deterministic trend and the effect of exogenous variables, and a parametric component representing the purely spatio-temporal random variation is proposed. Correspondingly, a two-step procedure, first addressing the estimation of the nonparametric component, and then the estimation of the parametric component is developed from the residual series obtained, with spatial-temporal prediction being performed in terms of suitable spatial interpolation of the temporal variation structure. The proposed model formulation, together with the estimation and prediction procedure, are applied using a Gaussian ARMA structure for temporal modelling to space-time forecasting from real data of air pollution concentration levels in the region surrounding a power station in northwest Spain.