Joint Modelling and Estimation of Global and Local Cross-Sectional Dependence in Large Panels

Abstract

We propose a new unified approach to identifying and estimating spatio-temporal dependence structures in large panels. The model accommodates global cross-sectional dependence due to global dynamic factors as well as local cross-sectional dependence, which may arise from local network structures. Model selection, filtering of the dynamic factors, and estimation are carried out iteratively using a new algorithm that combines the Expectation-Maximization algorithm with coordinate descent and gradient descent, allowing us to efficiently maximize an l1- and l2-penalized state space likelihood function. A Monte Carlo simulation study illustrates the good performance of the algorithm in terms of determining the presence and magnitude of global and/or local cross-sectional dependence. In an empirical application, we investigate monthly US interest rate data on 15 maturities over almost 40 years. We find that besides a changing number of global dynamic factors, there is heterogeneous local dependence among neighboring maturities. Taking this heterogeneity into account substantially improves out-of-sample forecasting performance.