A major part of my recent work develops computationally efficient Bayesian methods for high-dimensional state space models. These models are widely used in macroeconomics for nowcasting, handling missing and mixed-frequency data, modeling time variation, and producing density forecasts. The key practical challenge is computation: naive Kalman-based approaches can become prohibitively expensive as the dimension grows or when missing data patterns are complex.
Start here
For beginners, chapters 6 and 7 of my teaching notes on linear and nonlinear state space models provide a gentle introduction. Chan and Strachan (2023) surveys modern Bayesian state space models used in macroeconomics and discusses scalable computation.
Recommended citations
If you use the papers, code, or algorithms below, please cite the most relevant default reference(s) from the list. In particular, the underlying precision-based simulation and integrated likelihood engine that powers many of these high-dimensional UC / state space applications builds on Chan and Jeliazkov (2009).
- Underlying computation (precision-based simulation and integrated likelihood): 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)
- High-dimensional conditionally Gaussian state space models with missing data (default cite): Chan, Poon and Zhu (2023), High-Dimensional Conditionally Gaussian State Space Models with Missing Data, Journal of Econometrics, 236(1): 105468
- Time-varying parameter MIDAS state space models for nowcasting (default cite): Chan, Poon and Zhu (2025), Time-Varying Parameter MIDAS Models: Application to Nowcasting US Real GDP, Journal of Econometrics, forthcoming
- Large Bayesian VARs with stochastic volatility (specification choice / default cite): Chan (2023), Comparing Stochastic Volatility Specifications for Large Bayesian VARs, Journal of Econometrics, 235(2): 1419-1446 (code)
- Efficient estimation of nonlinear state space models (default cite): Chan (2017), The Stochastic Volatility in Mean Model with Time-Varying Parameters: An Application to Inflation Modeling, Journal of Business and Economic Statistics, 35(1): 17-28 (code)
How these models are typically used
- Nowcasting and real-time measurement: incorporating mixed-frequency predictors and ragged-edge datasets.
- Missing data and data revisions: sampling missing observations efficiently and coherently within the Bayesian posterior.
- Time variation: allowing parameters, states, and volatility to evolve over time in a scalable way.
- Density forecasting: producing predictive distributions that adapt to changing volatility and tail risk.
- Structural and economic interpretation: combining state space modeling with macroeconomic restrictions or interpretable components.
Precision-based computation for state space models
Chan and Jeliazkov (2009) develop a conceptually transparent derivation of the posterior distribution of the state vector that leads to a modular and scalable precision-based simulation algorithm. The same framework also yields a convenient approach for evaluating the integrated likelihood (marginal of the states), which is useful for model comparison and hyperparameter selection.
High-dimensional state space models with missing and mixed-frequency data
Chan, Poon and Zhu (2023) develop computational methods for high-dimensional conditionally Gaussian state space models with missing observations, exploiting sparse/banded precision structures to draw missing values and latent states efficiently. This is particularly useful for macroeconomic datasets with ragged edges and mixed frequencies.
Chan, Poon and Zhu (2025) extend these ideas to time-varying parameter MIDAS state space models and apply them to nowcasting US real GDP.
Time-varying volatility and time variation in macroeconomic state space models
Chan (2023) compares alternative multivariate stochastic volatility specifications for large Bayesian VARs and develops model comparison tools to guide specification choice in high-dimensional forecasting settings.
Chan (2017) studies the stochastic volatility-in-mean model with time-varying parameters, with an application to inflation modeling, linking time variation and volatility dynamics to macroeconomic interpretation.