Dynamic Spatial Autoregressive Models with Time-Varying Spatial Weighting Matrices

We propose a new spatio--temporal model with time--varying spatial weighting matrices. The filtering procedure of the time--varying unknown parameters is performed using the information contained in the score of the conditional distribution of the observables. We provide conditions for the stationarity and ergodicity of the filtered sequence of the spatial matrices as well as for the consistency and asymptotic normality of the maximum likelihood estimator (MLE). An extensive Monte Carlo simulation study to investigate the finite sample properties of the maximum likelihood estimator is also reported. We finally analyze the association between eight European countries' perceived risk, suggesting that the economically strong countries have their perceived risk increased due to their spatial connection with the economically weaker countries. We also investigate the evolution of the spatial connection between the house prices in different areas of the UK, identifying periods when the usually adopted sparse weighting matrix is not sufficient to describe the underlying spatial process