The Bayesian VAR path uses a conjugate normal-inverse-Wishart posterior with Minnesota-style shrinkage. The prior pulls coefficients toward simpler autoregressive dynamics, which can help when the number of variables and lags is large relative to the sample.
Prior
The default prior records:
- overall tightness
- lag decay
- own-first-lag mean
- intercept variance
- covariance prior degrees of freedom
- covariance scale
These values are included in the result so readers can see how strongly the model was shrunk.
Posterior Output
The lab reports posterior coefficient means and standard deviations by equation, residual covariance summaries, credible forecast bands, posterior sampling summaries when sampling is requested, and marginal likelihood components under the conjugate prior.
Sampling
Posterior draws are produced from the conjugate matrix-normal and inverse-Wishart forms. The draw count and seed are recorded. Forecast bands are reported at common probability levels.
Interpretation
A tight prior can reduce noisy overfit but may hide real cross-variable dynamics. A loose prior can fit more freely but may perform poorly in short samples. The posterior should be read with the prior settings, sample size, lag order, and selected variables.
References
- Litterman, 1986.
- Sims and Zha, 1998.
- Bauwens, Lubrano, and Richard, 1999.