Dynamic Spatial Autoregressive Models with Time-varying Spatial Weighting Matrices

We propose a new spatio-temporal model with time-varying spatial weighting matrices. We allow for a general parameterization of the spatial matrix, such as: (i) a function of the inverse distances among pairs of units to the power of an unknown time-varying distance decay parameter, and (ii) a negative exponential function of the time-varying parameter as in (i). The filtering procedure of the time-varying parameters is performed using the information in the score of the conditional distribution of the observables. An extensive Monte Carlo simulation study to investigate the finite sample properties of the ML estimator is reported. We 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, and we investigates 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.