BigVAR User ’ s Guide Dimension Reduction Procedures for Multivariate Time Series

The R package BigVAR allows for the simultaneous estimation of high-dimensional time series by applying structured penalties to the conventional vector autoregression (VAR) and vector autoregression with exogenous variables (VARX) frameworks. Our methods can be utilized in many applications that make use of time-dependent data, such as macroeconomics, finance, and internet traffic. Our package adapts solution algorithms from the regularization literature to a multivariate time series setting, allowing for the computationally efficient estimation of high-dimensional VARs with the option to additionally incorporate unmodeled exogenous series. The conventional VAR and VARX are heavily overparameterized, often forcing practitioners to arbitrarily specify a reduced subset of series to model. BigVAR allows for the incorporation of many potentially useful series by imposing zero restrictions in a data-driven manner. Moreover, if forecasts are only desired from a subset of included series, using the VARXL framework (Nicholson et al. [2015]), BigVAR can effectively leverage the information from the unmodeled exogenous series to improve the forecasts of the modeled endogenous series. We additionally offer a class of Hierarchical Vector Autoregression (HVAR) procedures (Nicholson et al. [2014]) that address the issue of lag order selection in VAR models. This document presents a brief overview of our notation, the models that comprise BigVAR, and the functionality of the package. For more detail, we refer you to the original papers. Section 2 provides a brief overview of the notation, the VARX-L penalties presented in Nicholson et al. [2015] and the HVAR methodology detailed in Nicholson et al. [2014], and Section 3 details practical implementation of BigVAR with a macroeconomic data example.