Forecasting macroeconomic data with Bayesian VARs: Sparse or dense? It depends!
提出半全局框架，用分组收缩参数替代全局收缩参数，适用于多种收缩先验，通过模拟和预测美国经济数据展示其优势，并揭示稀疏与密集先验的预测效果因变量和时间而异。
Vector autoregressions (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 been shown to be successful at 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 on 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.