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.
We develop a Bayesian vector autoregressive (VAR) model with multivariate stochastic volatility 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 recently developed global-local shrinkage priors to the VAR coefficients to cure the curse of dimensionality. Third, we utilize recent innovations to efficiently sample from high-dimensional multivariate Gaussian distributions . This makes simulation-based fully Bayesian inference feasible when the dimensionality is large but the time series length is moderate. We demonstrate the merits of our approach in an extensive simulation study and apply the model to US macroeconomic data to evaluate its forecasting capabilities.
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with multivariate stochastic volatility
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a Dirichlet-Laplace prior
recently developed global-local shrinkage priors
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Finally, since simulation-based methods are needed to simulate from the joint posterior distribution,
Third,
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that improve upon recent algorithms by large margins. In the empirical exercise we
. This makes simulation-based fully Bayesian inference feasible when the dimensionality is large but the time series length is moderate. We demonstrate the merits of our approach in an extensive simulation study and
R
data and
macroeconomic data to