Bayesian vector autoregressions (BVARs) are the workhorse in macroeconomic forecasting. Research in the last decade has established the importance of allowing time-varying volatility to capture both secular and cyclical variations in macroeconomic uncertainty. This recognition, together with the growing availability of large datasets, has propelled a surge in recent research in building stochastic volatility models suitable for large BVARs. Some of these new models are also equipped with additional features that are especially desirable for large systems, such as order invariance--i.e., estimates are not dependent on how the variables are ordered in the BVAR--and robustness against COVID-19 outliers. Estimation of these large, flexible models is made possible by the recently developed equation-by-equation approach that drastically reduces the computational cost of estimating large systems. Despite these recent advances, there remains much ongoing work, such as the development of parsimonious approaches for time-varying coefficients and other types of nonlinearities in large BVARs.

翻译：贝叶斯向量自回归（BVARs）是宏观经济预测的核心工具。过去十年的研究已证实，允许时变波动性对于捕捉宏观经济不确定性中的长期趋势与周期波动至关重要。这一认识，加之大规模数据集的日益可得，推动近期研究涌现出大量适用于大型BVARs的随机波动模型构建方法。部分新型模型还具备特别适用于大型系统的附加特性，例如顺序不变性——即估计结果不依赖于变量在BVAR中的排序方式——以及对COVID-19异常值的稳健性。通过近期开发的逐方程估计方法，这些大规模、灵活模型的估计成为可能，该方法大幅降低了大型系统的计算成本。尽管取得上述进展，相关研究仍面临诸多挑战，例如如何在大规模BVARs中发展出简洁的时变系数处理方法及其他非线性建模策略。