SAR models with nonparametric spatial trends : A P-spline approach

This article proposes a model which includes a global spatial trend in an SAR specification to take into account both large-scale spatial dependencies and local spatial autocorrelation. We use penalized splines to estimate the model, as they can be represented as mixed models. As a result we can (i) deal with complex nonlinear trends, which are very common in spatial phenomena, (ii) estimate shortrange spatial correlation together with the large-scale spatial trend, (iii) decompose the systematic spatial variation into these two components and (iv) estimate the smoothing parameters together with the other parameters of the model. We call this model the P-spline-SAR model. Based on the simulation of 2000 datasets generated by a P-spline-SAR (using both linear and non-linear and non-separable global spatial trends), we conclude that (i) the P-spline-SAR model provides much better estimates of both the global spatial trend and also the spatial autocorrelation term than the pure P-spline or SAR specifications, irrespective of whether the true trend is linear or non-linear; (ii) the estimations of the observed values yielded by the P-Spline-SAR model are equally as accurate as those provided by the best competing alternative. We also empirically illustrate how well the P-spline-SAR model performs using the augmented Harrison and Rubinfeld (1978) hedonic pricing data for Boston SMSA.

SAR models with nonparametric spatial trends : A P-spline approach Articles