Semi-parametric statistical approaches for space-time process prediction

The problem of estimation and prediction of a spatial-temporal stochastic p rocess, observed at regular times and irregularly in space, is considered. A mixed formulation involving a nonparametric component, accounting for a d eterministic trend and the effect of exogenous variables, and a parametric component representing the purely spatio-temporal random variation is propo sed. 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-temp oral prediction being performed in terms of suitable spatial interpolation of the temporal variation structure. The proposed model formulation, togeth er with the estimation and prediction procedure, are applied using a Gaussi an ARMA structure for temporal modelling to space-time forecasting from rea l data of air pollution concentration levels in the region surrounding a po wer station in northwest Spain.