A space-time-categorical local linear smoother for predicting land/house price

A new class of data generating processes called MGWR-SAR was recently introduced, in which the regression parameters and the spatial dependence coefficient can vary over the space in order to take into account both spatial heterogeneity and spatial dependence. The estimator corresponds to a local linear smoother with a special kernel based only on Euclidean distance and a linearization of SAR regression using IV/2SLS method. Using simulated data and real price data (land, house), we proved this estimator to be more accurate than estimators integrating exclusively spatial heterogeneity or spatial autocorrelation. However, if any non-linearity exists between covariates, it would require to transform these variables to ensure linear relationship. We propose to improve that estimator using a General Product Kernel adding further smoothed variables to go beyond spatial heterogeneity. Firstly, “time” variable to consider space/time heterogeneity. Secondly, continuous variables to account for their non-linearity,and finally a categorical variable (for example number of rooms, or presence of a garden) to test the relevance of “ad hoc” market segmentation. Using a huge land/house sales spatial database in Provence, we compare prediction accuracy of the BLUP version of several models (OLS,NLS, SAR, SEM, SARAR, MGWR-SAR, REML estimator) against our proposition.