Sparse Bayesian Vector Autoregressions in Huge Dimensions

We develop a Bayesian vector autoregressive (VAR) model that is capable of handling vast dimensional information sets. Three features are introduced to permit reliable estimation of the model. First, we assume that the reduced-form errors in the VAR feature a factor stochastic volatility structure, allowing for conditional equation-by-equation estimation. Second, we apply a Dirichlet-Laplace prior to the VAR coefficients to cure the curse of dimensionality. Finally, since simulation-based methods are needed to simulate from the joint posterior distribution, we utilize recent innovations to efficiently sample from high-dimensional multivariate Gaussian distributions that improve upon recent algorithms by large margins. In the empirical exercise we apply the model to US data and evaluate its forecasting capabilities.