Conjugate priors allow for fast inference in large dimensional vector autoregressive (VAR) models but, at the same time, introduce the restriction that each equation features the same set of explanatory variables. This paper proposes a straightforward means of post-processing posterior estimates of a conjugate Bayesian VAR to effectively perform equation-specific covariate selection. Compared to existing techniques using shrinkage alone, our approach combines shrinkage and sparsity in both the VAR coefficients and the error variance-covariance matrices, greatly reducing estimation uncertainty in large dimensions while maintaining computational tractability. We illustrate our approach by means of two applications. The first application uses synthetic data to investigate the properties of the model across different data-generating processes, the second application analyzes the predictive gains from sparsification in a forecasting exercise for US data.

中文翻译：

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在共轭向量自回归模型中结合收缩和稀疏性

共轭先验允许在大维向量自回归 (VAR) 模型中进行快速推理，但同时引入了每个方程具有同一组解释变量的限制。本文提出了一种对共轭贝叶斯 VAR 后验估计进行后处理的简单方法，以有效地执行特定于方程的协变量选择。与单独使用收缩的现有技术相比，我们的方法将 VAR 系数和误差方差-协方差矩阵中的收缩和稀疏性结合起来，大大减少了大维度的估计不确定性，同时保持了计算的易处理性。我们通过两个应用程序来说明我们的方法。第一个应用程序使用合成数据来研究不同数据生成过程中模型的属性，第二个应用程序分析美国数据预测练习中稀疏化的预测收益。