VARX-L: Structured regularization for large vector autoregressions with exogenous variables

This paper introduces the VARX-L framework, a structured family of VARX models, and provides a methodology that allows for both efficient estimation and accurate forecasting in high-dimensional analysis. VARX-L adapts several prominent scalar regression regularization techniques to a vector time series context, which greatly reduces the parameter space of VAR and VARX models. We also highlight a compelling extension that allows for shrinking toward reference models, such as a vector random walk. We demonstrate the efficacy of VARX-L in both low- and high-dimensional macroeconomic forecasting applications and simulated data examples. Our methodology is easy to reproduce in a publicly available R package.