Spatio-temporal models: Estimation & testing with an application to credit default rates

Spatio-temporal datasets are becoming increasingly common, more complex and larger. Conditional Autoregressive (CAR) Models are used to analyze such data by specifying dependencies in a local, intuitive manner but estimation of their covariance structure is a critical bottleneck. This thesis proposes a novel approach to the estimation of CAR models, called L1-Min, which avoids expensive eigenvalue calculations and Monte Carlo simulations. L1-Min works using the element-wise l1-norm of a matrix and is shown to be fast, consistent and have desirable small sample properties. A subsampling extension to L1-Min provides further speedup. The predictive performance of CAR models is compared to that of autoregressive type time series models, including the Dirichlet Process Mixture Model that allows for automatic, non-parametric clustering of spatial locations. These models are estimated on simulated data and a dataset of county-level credit default rates in the United States. We find that CAR models offer superior predictions for revolving and mortgage debt default rates across different time points in the dataset