Smooth Transition Spatial Autoregressive Models

Abstract

This paper introduces a new model for spatial time series in which cross-sectional dependence varies nonlinearly over space by means of smooth transitions. We refer to our model as the Smooth Transition Spatial Autoregressive (ST-SAR). We establish consistency and asymptotic Gaussianity for the MLE under misspecification and provide additional conditions for geometric ergodicity of the model. Simulation results justify the use of limit theory in empirically relevant settings. The model is applied to study spatio-temporal dynamics in two cases that differ in spatial and temporal extent. We study clustering in urban densities in a large number of neighborhoods in the Netherlands over a 10-year period. We pay particular focus to the advantages of the ST-SAR as an alternative to linear spatial models. In our second study, we apply the ST-SAR to monthly long term interest rates of 15 European sovereigns over 25-year period. We develop a strategy to assess financial stability across the Eurozone based on attraction of individual sovereigns toward the common stochastic trend. Our estimates reveal that stability attained a low during the Greek sovereign debt crisis, and that the Eurozone has remained to struggle in attaining stability since the onset of the financial crisis. The results suggest that the European Monetary System has not fully succeeded in aligning the economies of Ireland, Portugal, Italy, Spain, and Greece with the rest of the Eurozone, while attraction between other sovereigns has continued to increase. In our applications linearity of spatial dependence is overwhelmingly rejected in terms of model fit and forecast accuracy, estimates of control variables improve, and residual correlation is better neutralized.