Regularized estimation for panel time series models with dynamic factors and local cross-sectional dependence

This paper proposes a unified approach to identifying and estimating heterogeneous spatio-temporal regression models for panel data. The framework accommodates global cross-sectional dependence by means of latent dynamic factors, local dependence arising from network structures, and regressors with unit-specific slope coefficients. The tasks of determining the number of factors, filtering dynamic factors, and parameter estimation are carried out using a unifying algorithm. It combines Expectation-Conditional Maximization with proximal optimization and likelihood maximization subject to several regularization terms. In a Monte Carlo study, we present a good performance of the algorithm in terms of determining the presence and magnitude of common factors and slope coefficients, and the degree of heterogeneity in local spillover effects. In an empirical study, we investigate monthly U.S. treasury rate excess return data on seventeen maturities over almost fifty years. After accounting for global dynamic factors and macroeconomic variables, we find evidence of grouped heterogeneous local spillover effects among neighboring maturities. We provide evidence that the resulting model with regularized coefficients can deliver significant improvements in out-of-sample prediction ability amongst a set of competitive models.