MATLAB code associated with our new book Bayesian Econometric Methods (Second Edition) can be found at the book website. MATLAB and R code for Statistical Modeling and Computation is available here.

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If you use code from this page, please cite the most relevant default reference(s) below. These papers form a coherent toolkit for scalable Bayesian time series and state space methods.

• Precision-based state space simulation (computational engine): Chan and Jeliazkov (2009), Efficient Simulation and Integrated Likelihood Estimation in State Space Models, International Journal of Mathematical Modelling and Numerical Optimisation, 1, 101-120 (code)
• SV specification choice for large Bayesian VARs: Chan (2023), Comparing Stochastic Volatility Specifications for Large Bayesian VARs, Journal of Econometrics, 235(2): 1419-1446 (code)
• Order-invariant Bayesian VARs with SV: Chan, Koop and Yu (2024), Large Order-Invariant Bayesian VARs with Stochastic Volatility, Journal of Business and Economic Statistics, 42(2): 825-837 (code)
• Default shrinkage prior for large BVARs: Chan (2021), Chan (2021), Minnesota-Type Adaptive Hierarchical Priors for Large Bayesian VARs, International Journal of Forecasting, 37(3): 1212-1226 (code)
• Large conditionally Gaussian state space models with mixed-frequency data: Chan, Poon and Zhu (2023), High-Dimensional Conditionally Gaussian State Space Models with Missing Data, Journal of Econometrics, 236(1): 105468
• Trend inflation with long-run inflation expectations: Chan, Clark and Koop (2018), A New Model of Inflation, Trend Inflation, and Long-Run Inflation Expectations Journal of Money, Credit and Banking, 50(1), 5-53 (code)

Research overviews: Large Bayesian VARs | High-dimensional state space models | Trend inflation models.

If you want to download the code associated with a particular paper, it will be easier to locate it at my research page. Below I organize the code by topics.

Please contact me if you find any errors.

Vector Autoregressions and VARMAs

See here for more information about my recent projects on large Bayesian VARs.

• A new hybrid TVP-VAR with SV where each equation can have either constant or time-varying coefficients
• A large order-invariant Bayesian VAR with SV
• A large TVP-VAR with SV where the time-varying parameters and stochastic volatilities are formulated as a singular state space model
• Estimation code of a standard, large reduced-form Bayesian VAR with SV
• A new family of Minnesota-type adaptive hierarchical priors for Large Bayesian VARs with SV
• A large Bayesian VAR with a new asymmetric conjugate prior; the application estimates a 15-variable VAR identified with sign restrictions
• Forecasting using large BVARs with various shrinkage priors
• Large Bayesian VARs with non-Gaussian, heteroscedastic and serially dependent innovations
• Forecasting using time-varying parameter VARMAs with stochastic volatility
• Time-varying parameter VAR with SV and stochastic model specification search
• Time-varying parameter VAR with constant volatility

Stochastic Volatility and GARCH Models

• Seven pairs of SV and GARCH models, including the SV in mean model and the SV model with leverage
• Time-varying parameter VAR with SV and stochastic model specification search
• Three univariate SV models: standard SV, SV with MA(1) Gaussian errors and SV with MA(1) Student's t errors
• Stochastic volatility in mean model with time-varying parameters
• Four stochastic volatility models with moving average errors

Marginal Likelihood and Deviance Information Criterion

• Marginal likelihood computation for large VARs with 4 different types of SV
• Marginal likelihood computation for hybrid TVP-VARs with SV
• Marginal likelihood and DIC computation for 10 VARs, including time-varying parameter VARs with SV and regime-switching VARs
• Bayes factor computation for time-varying coefficients vs constant coefficients
• Observed-data and conditional DICs computation for 7 SV models
• Marginal likelihood computation for 7 SV and 7 GARCH models
• Three variants of the DIC for three latent variable models: static factor model, TVP-VAR and semiparametric regression
• Marginal likelihood computation for 6 models using the cross-entropy method: VAR, dynamic factor VAR, TVP-VAR, probit, logit and t-link

Models for Inflation

See here for more information about my research on trend inflation models.

• A new bivariate UC model for measuring long-run inflation expectations uncertainty using both monthly inflation and daily break-even inflation data.
• A new trend inflation model using both inflation data and long-run inflation expectations
• Stock and Watson (2007) model: unobserved components model with 2 SVs
• Unobserved components model with inflation volatility feedback
• Unobserved components model with a bounded inflation trend and SV
• Bivariate unobserved components model with bounded inflation trend and NAIRU
• Unobserved components models with stochastic volatility and moving average errors

Models for Output Gap

• Output gap from a trivariate unobserved components model using stochastic model specification search
• Output gap from extensions of the HP filter by allowing serial correlation in the cyclical component
• Output gaps from eight unobserved components models, including models with correlated trend and cycle innovations and breaks in trend output growth

Other Models

• A regime switching skew-normal model of contagion
• A partially identified instrumental variable model

Other Sources

A number of econometricians have provided code associated with their books or papers:

• MATLAB code associated with Gary Koop's books, papers and short courses can be found on his website.
• Dimitris Korobilis provides code for estimating a wide variety of models, including Bayesian VARs, TVP-VARs and factor models.
• Jouchi Nakajima provides MATLAB and R code for estimating various stochastic volatility models, including a TVP-VAR with SV.