My current research develops scalable Bayesian methods for large vector autoregressions (VARs) used in macroeconomic forecasting and structural analysis. The key design goal is to make rich features that are important in small VARs (shrinkage, stochastic volatility, and time variation) practical in high-dimensional systems.
Start here
If you are new to large Bayesian VARs, two good entry points are my book chapter on large Bayesian VARs (with examples and code) and my handbook chapter BVARs and Stochastic Volatility, which provides an overview of stochastic volatility specifications for large VARs. A suggested reading order is: (i) shrinkage priors, (ii) flexible covariance structures, and then (iii) stochastic volatility specification choice and time variation.
Recommended citations
To make it easier for readers to cite the most relevant entry point, I list below a small set of default references. If you use the code on this page, please cite the umbrella paper(s) most closely aligned with your model choice.
- Large BVARs with stochastic volatility (specification choice / default cite): Chan (2023b), Comparing Stochastic Volatility Specifications for Large Bayesian VARs, Journal of Econometrics, 235(2): 1419-1446 (code)
- Order-invariant VARs with stochastic volatility (default cite): Chan, Koop and Yu (2024), Large Order-Invariant Bayesian VARs with Stochastic Volatility, Journal of Business and Economic Statistics, 42(2): 825-837 (code)
- Large BVAR covariance structures / heavy tails / flexible innovations: Chan (2020), Large Bayesian VARs: A Flexible Kronecker Error Covariance Structure, Journal of Business and Economic Statistics, 38(1), 68-79 (code)
- Default shrinkage prior for large BVAR forecasting: Chan (2021), Minnesota-Type Adaptive Hierarchical Priors for Large Bayesian VARs, International Journal of Forecasting, 37(3): 1212-1226 (code)
- Asymmetric cross-variable shrinkage and closed-form marginal likelihood: Chan (2022), Asymmetric Conjugate Priors for Large Bayesian VARs, Quantitative Economics, 13(3): 1145-1169 (code)
- Hybrid time variation in large VARs (automatic sparsification): Chan (2023a), Large Hybrid Time-Varying Parameter VARs, Journal of Business and Economic Statistics, 41(3): 890-905 (code)
Below I organize my work around two themes.
Hierarchical shrinkage priors
Large VARs have many parameters, and strong shrinkage is essential for good forecasting and stable inference. I have developed flexible hierarchical priors that are easy to use and perform well in high-dimensional macroeconomic forecasting problems.
1. Chan (2022) proposes an asymmetric conjugate prior for large Bayesian VARs. Unlike the standard natural conjugate prior that rules out cross-variable shrinkage, this prior allows coefficients on lags of other variables to be shrunk more aggressively than coefficients on own lags. The marginal likelihood is available in closed form, which makes selecting lag length and shrinkage hyperparameters straightforward (e.g., by maximizing the marginal likelihood).
2. Chan (2021) introduces Minnesota-type adaptive hierarchical priors that combine useful features of global-local shrinkage and Minnesota priors. These priors strongly shrink only small coefficients towards zero while leaving large coefficients relatively intact. They also naturally incorporate cross-variable shrinkage and stronger shrinkage on higher lags.
Time variation and stochastic volatility
In many macroeconomic applications, time-varying parameters and stochastic volatility are empirically important. My coauthors and I have developed scalable models and estimation algorithms that can be used in large systems.
1. Chan (2023a) develops an efficient Bayesian sparsification method for large hybrid time-varying parameter VARs with stochastic volatility. The method decides, equation by equation, whether VAR coefficients and contemporaneous relations are constant or time-varying. Using US datasets of various dimensions, we find evidence that parameters in some (but not all) equations are time varying.
2. Chan (2023b) compares several stochastic volatility specifications for large Bayesian VARs, including common stochastic volatility, Cholesky stochastic volatility, and factor stochastic volatility, and develops Bayesian model comparison methods to select among them. This paper is intended to be a default reference for selecting SV specifications in large BVARs.
3. Chan, Koop and Yu (2024) develop an order-invariant Bayesian VAR with stochastic volatility, addressing the well-known sensitivity of multivariate stochastic volatility models to variable ordering. This issue becomes particularly severe in large VARs. We propose a specification that is invariant to ordering and scalable to high dimensions. In a macroeconomic forecasting exercise involving VARs with 20 variables, the order-invariant approach delivers superior forecast performance relative to conventional, order-dependent specifications.
4. Chan (2020) introduces a family of large VARs with flexible covariance structures, allowing for non-Gaussian, heteroscedastic, and serially dependent innovations. In particular, the version with common stochastic volatility and t-distributed innovations can handle large outliers such as those observed during the COVID-19 pandemic.
5. Chan, Eisenstat and Strachan (2020) develop a large time-varying parameter structural VAR where the VAR coefficients and multivariate stochastic volatility are formulated as a singular state space model. The singular representation reduces the state dimension and implies a factor-like structure, which makes the model more parsimonious and computationally tractable in large systems.