Bayesian Macroeconometrics and Time Series
My teaching and short courses focus on scalable Bayesian methods for macroeconomic forecasting, large Bayesian VARs, stochastic volatility, and high-dimensional state space models.
Latest: Forecasting with a VAR (how-to guides, October 2026); Which Parameters of a GDP Nowcasting Model Should Vary over Time? (tutorial, October 2026)
Start Here
If you are new to the area, I suggest four steps:
- Read the sample chapters of my forthcoming book Bayesian Macroeconometrics: Methods and Applications, or my Bayesian Macroeconometrics notes. The book comes with MATLAB, R and Python code for all 14 chapters.
- Work through the how-to guides, which show how to turn a model's equations into working MATLAB code, step by step, on small examples with generated data.
- Try the tutorials, which answer one empirical question each with the settings of a published paper, with MATLAB code that runs on your own data.
- Use the toolkits on GitHub in your own work: bvar-toolkit for large Bayesian VARs, statespace-toolkit for state space models, and trend-cycle-toolkit, which re-estimates trend inflation and output gap models every quarter.
Research overviews: Large Bayesian VARs | High-dimensional state space models | Trend inflation models.
Recent Short Courses
- A 2-day short course at the Deutsche Bundesbank
- A 5-day course at Halle Institute for Economic Research
- A 2-day short course at the European Central Bank
- A 5-day workshop at the SIDE Summer School
Core Textbooks and References
My forthcoming book Bayesian Macroeconometrics: Methods and Applications (Chapman & Hall/CRC) develops the methods on this page from the ground up. A sample containing the preface and the first four chapters is available here, and the MATLAB, R and Python code for all 14 chapters is available on GitHub.
For beginners who want to learn Bayesian econometrics and computation, I recommend Gary Koop's Bayesian Econometrics.
Our book Bayesian Econometric Methods (Second Edition) contains theoretical and programming exercises with detailed solutions.
My other textbook Statistical Modeling and Computation (Second Edition) includes chapters on Bayesian inference and Markov chain Monte Carlo methods.
Suggested Learning Path
1. Linear Gaussian State Space Models
A computational foundation is Chan and Jeliazkov (2009) (code), which develops a precision-based simulation and integrated likelihood algorithm. Chan and Strachan (2023) survey Bayesian state space models in macroeconometrics. The how-to guides of the series Getting Started with the Precision Sampler implement the algorithm step by step:
- How to Draw the States of an Unobserved Components Model
- How to Estimate a State Space Model by Gibbs Sampling
- How to Compute the Integrated Likelihood of a State Space Model
2. Stochastic Volatility
For univariate stochastic volatility models, see Chan and Hsiao (2014) (code). For more complex SV models, see Chan (2013) (code).
3. Large Bayesian VARs (shrinkage, stochastic volatility, and order invariance)
Large VARs require appropriate shrinkage priors, scalable stochastic volatility, and robustness to variable ordering. A practical entry point (with code) is my book chapter Large Bayesian VARs, and my handbook chapter BVARs and Stochastic Volatility gives an overview of the stochastic volatility specifications for large VARs.
The how-to guides of the series Getting Started with Bayesian VARs work through a small VAR step by step:
- How to Stack the Equations of a VAR
- How to Draw the VAR Coefficients under the Minnesota Prior
- How to Estimate a VAR by Gibbs Sampling
- How to Choose the Shrinkage of a VAR by the Marginal Likelihood
The series Forecasting with a VAR then sets up a Bayesian VAR for forecasting, on data simulated from a VAR fitted to US data:
- How to Simulate Data from an Estimated VAR
- How to Forecast with a Bayesian VAR
- How to Evaluate Forecasts Out of Sample
- How to Choose the Lag Length and the Shrinkage for Forecasting
- Shrinkage priors for large BVAR forecasting: Chan (2021) (code) and Chan (2022) (code). Tutorial: How Should I Choose the Shrinkage Hyperparameters of My BVAR?
- Stochastic volatility specification choice in large BVARs: Chan (2023) (code). Tutorials: Which Stochastic Volatility Specification Should My VAR Use? and Does Modeling the Volatility Improve My Forecasts?
- Order-invariant Bayesian VARs with stochastic volatility: Chan, Koop and Yu (2024) (code). Tutorial: Does the Order of the Variables Change My VAR Results?
4. Nonlinear State Space Models
For nonlinear state space models and accept-reject Metropolis-Hastings algorithms, see Chan (2017) (code). Applications to inflation modeling can be found in Chan, Koop and Potter (2013) (code) and Chan, Koop and Potter (2016) (code). The estimates page updates trend inflation estimates from Chan, Koop and Potter (2013) and three other models every quarter.
5. Structural Analysis and Mixed-Frequency Data
- Sign and ranking restrictions in large structural VARs: Chan, Matthes and Yu (2026) (code). Tutorial: Can I Use Many Sign Restrictions in My Large VAR?
- Missing and mixed-frequency data: Chan, Poon and Zhu (2023). Tutorial: How Do I Handle Missing and Mixed-Frequency Data in My VAR?
- Nowcasting with time-varying parameter MIDAS models: Chan, Poon and Zhu (2026). Tutorial: Which Parameters of a GDP Nowcasting Model Should Vary over Time?