  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.
