On the Prediction of the Subpopulation Total Based on Spatially Correlated Longitudinal Data

In a special case of the general linear mixed model, one random component obeys a spatial autoregressive process and another a temporal autoregressive process. The population and any affiliations to subpopulations may change in time. The empirical best linear unbiased predictor is derived and may be used even if the sample size in the subpopulation is null in the period of interest. The mean squared error and its estimator are expressed. The accuracy of the predictor and the bias of the mean squared error estimator are addressed through simulations.