用贝叶斯VAR预测宏观经济数据：稀疏还是稠密？取决于具体情况！
Forecasting macroeconomic data with Bayesian VARs: Sparse or dense? It depends!
AI总结：
本文提出半全局框架，用组特定收缩参数替代全局参数，应用于多种贝叶斯收缩先验，通过模拟和实证发现稀疏与稠密先验的预测性能因变量和时间而异，动态模型平均可兼得两者优势。
摘要：
向量自回归（VAR）模型在建模和预测宏观经济变量时被广泛应用。然而，在高维情况下，它们容易过拟合。贝叶斯方法，更具体地说是收缩先验，已被证明能有效提高预测性能。在本文中，我们引入了半全局框架，用组特定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应用于各种收缩先验，如全局-局部先验和随机搜索变量选择先验。我们通过广泛的模拟研究和预测美国经济数据的实证应用来展示所提出框架的优点。此外，我们进一步阐明了持续的“稀疏幻觉”争论，发现稀疏/稠密先验下的预测性能因评估的经济变量和时间段而异。然而，动态模型平均可以结合两者的优点。
英文摘要：
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.
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