Prediction for spatio-temporal models with autoregression in errors

In various environmental studies spatio-temporal correlated data are involved, so there has been an increasing demand for spatio-temporal prediction methods that capture spatio-temporal correlation so as to improve the accuracy of prediction. In this paper we propose a nonparametric iteration procedure for spatio-temporal models with specific autocorrelation structures. We extended the local linear method for spatial data to spatio-temporal local linear models, taking both spatial and temporal characteristics into consideration. The asymptotic normality of the predictors is established under mild conditions. The results of a simulation and case study also show that our predictors perform better than the traditional local linear method.