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.

中文翻译：

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大维稀疏贝叶斯向量自回归

我们开发了一个贝叶斯向量自回归 (VAR) 模型，该模型能够处理大量维度信息集。引入了三个特征以允许对模型进行可靠的估计。首先，我们假设 VAR 中的简化形式误差具有因子随机波动率结构，允许条件方程逐方程估计。其次，我们在 VAR 系数之前应用 Dirichlet-Laplace 来解决维数灾难。最后，由于需要基于模拟的方法来模拟联合后验分布，因此我们利用最近的创新从高维多元高斯分布中有效地采样，这些高维多变量高斯分布大大改进了最近的算法。在实证练习中，我们将模型应用于美国数据并评估其预测能力。