Vector autogressions (VARs) are widely applied when it comes to modeling and forecasting macroeconomic variables. In high dimensions, however, they are prone to overfitting. Bayesian methods, more concretely shrinkage priors, have shown to be successful in improving prediction performance. In the present paper, we introduce the semi-global framework, in which we replace the traditional global shrinkage parameter with group-specific shrinkage parameters. We show how this framework can be applied to various shrinkage priors, such as global-local priors and stochastic search variable selection priors. We demonstrate the virtues of the proposed framework in an extensive simulation study and in an empirical application forecasting data of the US economy. Further, we shed more light on the ongoing ``Illusion of Sparsity'' debate, finding that forecasting performances under sparse/dense priors vary across evaluated economic variables and across time frames. Dynamic model averaging, however, can combine the merits of both worlds.

翻译：向量自回归模型在宏观经济变量建模与预测领域得到广泛应用。然而在高维情形下，该模型容易产生过拟合问题。贝叶斯方法——更具体而言是收缩先验——已被证明能有效提升预测性能。本文提出半全局框架，该框架使用分组特异性收缩参数替代传统的全局收缩参数。我们展示了该框架如何适用于各类收缩先验，包括全局-局部先验与随机搜索变量选择先验。通过大量模拟研究和美国经济数据预测的实证应用，我们证明了所提框架的优越性。此外，我们进一步揭示了当前"稀疏性幻觉"争议的本质，发现稀疏/稠密先验下的预测性能随评估经济变量和时间范围的变化而波动。动态模型平均方法则能有效融合两类先验的优势。