Sparse Bayesian vector autoregressions in huge dimensions

Abstract

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.

References in corpus (6)

• Ancillarity-Sufficiency Interweaving Strategy (ASIS) for Boosting MCMC Estimation of Stochastic Volatility Models
• Dealing with Stochastic Volatility in Time Series Using the R Package stochvol
• Sparse Bayesian time-varying covariance estimation in many dimensions
• Efficient Bayesian Inference for Multivariate Factor Stochastic Volatility Models
• Should I stay or should I go? A latent threshold approach to large-scale mixture innovation models
• A Flexible Mixed-Frequency Vector Autoregression with a Steady-State Prior

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