Spatio-Temporal weight with simultaneous effect for environmental data

In this work we present space-time models with simultaneous effect in which the relations between phenomenon measured in different sites are not determined on the base of an a priori structure, but are estimated in the model’s estimation procedure. This approach avoids superimposition of a priori space fixed structure so that the spatial weights are not bound at being symmetrical and have not to be constant over time. In this way, spatial weights will then take into account the intensity and the direction of influence that a single station, in a given time including the contemporaneous one, has on the whole spatial system and vice versa. To reduce the increase in the number of parameters a procedure for constrained estimation is presented.