Tutorials

Each tutorial answers one empirical question with the settings of a paper, using the code of bvar-toolkit or statespace-toolkit, and comes with a script that runs the same analysis on your own data. These pages give the answer and the main figure; the full tutorials on GitHub give the method, all the results and the code that reproduces them. The how-to guides show how to use the core functions step by step, on small examples with generated data.

Newest: Which Unobserved Components Model Should I Use for Inflation? (October 2026)

Large Bayesian VARs

• Does the Order of the Variables Change My VAR Results? Under the Cholesky model of stochastic volatility it does: reversing the order of a 20-variable VAR moves one estimated correlation from about 0.82 to about 0.19, while the order-invariant model gives the same estimates in both orders. (bvar-toolkit)
• How Should I Choose the Shrinkage Hyperparameters of My BVAR? By maximizing the marginal likelihood under the asymmetric conjugate prior of Chan (2022), which in a 21-variable VAR improves the one-quarter-ahead point forecasts of 20 of the 21 variables relative to the best symmetric prior. (bvar-toolkit)
• Which Stochastic Volatility Specification Should My VAR Use? The marginal likelihoods of Chan (2023) rank five of them; in a five-variable quarterly VAR, the Cholesky specification with an outlier component fits best. (bvar-toolkit)
• Does Modeling the Volatility Improve My Forecasts? Over 140 recursive forecasts from 1990, a common volatility factor and a volatility process per equation both improve on a homoskedastic VAR in point and density forecasts, with gains in calm quarters as well as in the pandemic. (bvar-toolkit)

Structural Analysis

• Can I Use Many Sign Restrictions in My Large VAR? Yes, with the algorithm of Chan, Matthes and Yu (2026), which imposes 98 sign and 7 ranking restrictions on eight shocks in a 35-variable VAR, where the conventional accept-reject algorithm is not computationally feasible. (bvar-toolkit)

Missing and Mixed-Frequency Data

• How Do I Handle Missing and Mixed-Frequency Data in My VAR? By using data augmentation and drawing all the missing values in one block, as Chan, Poon and Zhu (2023) do. In a monthly VAR with quarterly GDP, this puts the fall in monthly GDP in April 2020 at 7.9 percent. (bvar-toolkit)

Unobserved Components Models

• Which Unobserved Components Model Should I Use for Inflation? One with stochastic volatility in the transitory component: such models beat an AR(4) in forecasting average US CPI inflation over the next year, and stochastic volatility in the trend as well does not help. (statespace-toolkit)