Non-stationary spatial autoregressive modeling for the prediction of lattice data

Spatial autoregressive models are usually used for stationary lattice random fields with a zero or fixed mean. However, many lattice random fields are non-stationary, because they have a non-fixed mean, a non-fixed covariance function, or both. In non-stationary time series, subtracting a fitted trend and differencing are two methods to reach a stationary model. In this paper, these methods have been generalized for non-stationary spatial lattice data. Then, we provide a spatial prediction for each method. By using a simulation study and real data set, we compare the prediction accuracy of the two methods. The results show that predictions made by the trend estimation method are better than differencing method.