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This document introduces the R package BGVAR to estimate Bayesian global vector autoregressions (GVAR) with shrinkage priors and stochastic volatility. The Bayesian treatment of GVARs allows to include large information sets by mitigating issues related to overfitting. This often improves inference as well as out-of-sample forecasts. Computational efficiency is achieved by using C++ to considerably speed up time-consuming functions. To maximize usability, the package includes numerous functions for carrying out structural inference and forecasting. These include generalized and structural impulse response functions, forecast error variance, and historical decompositions as well as conditional forecasts.