Spatio-temporal autoregressive semiparametric models


We propose a semiparametric P-Spline model for spatio-temporal data including a non-parametric trend, a spatial lag of the dependent variable, and a time series autoregressive noise. Specifically, we consider a spatio-temporal ANOVA model, disaggregating the trend into spatial and temporal main effects, as well as second-and third-order interactions between them. Algorithms based on spatial anisotropic penalties are used to estimate all the parameters in a closed form without the need for multi-dimensional optimization. Monte Carlo simulations and an empirical case show that our model represents a valid alternative to parametric methods aimed at disentangling strong and weak cross-sectional dependence.