Conjugate VAR#
ConjugateVAR is the sibling estimator to VAR. It pairs a natural-conjugate
Normal-Inverse-Wishart prior (NIWPrior) with the VAR likelihood, so the
coefficient and covariance posterior is available in closed form and no PyMC
model is ever built; Monte Carlo is reserved for the single low-dimensional
Minnesota tightness hyperparameter, which the data selects by marginal
likelihood [Giannone et al., 2015]. Prefer it over the
NUTS-sampled VAR when the system is large, when the fit has to be repeated
many times (rolling windows, real-time exercises), or when the closed-form
marginal likelihood is itself the quantity of interest. Stay on VAR when you
need per-equation own/cross shrinkage asymmetry, stochastic volatility, or a
prior the conjugate Kronecker structure cannot express. Both paths return the
same FittedVAR, so identification, impulse responses, variance
decompositions, and forecasting behave identically downstream.
Time-varying volatility on the conjugate path is deterministic rather than
latent, which is what keeps the posterior closed-form. ConjugateVolatility
is the adapter surface a conjugate fit attaches when the residual scale
breaks: it reports a per-period multiplier s_t on a base Cholesky factor, so
Sigma_t = s_t**2 * Sigma_base. PandemicBreak is the concrete adapter, the
COVID-19 break of Lenza and Primiceri [2022] — free outbreak scales for
March, April, and May 2020 followed by a geometric decay back toward the
pre-break scale. The latent volatility processes used by the VAR path live
on the volatility page.
Closed-form conjugate (Normal-Inverse-Wishart) Bayesian VAR estimator. |
Natural-conjugate Normal-Inverse-Wishart Minnesota prior (Giannone-Lenza-Primiceri, 2015). |
Query-surface adapter for a deterministically time-varying conjugate VAR. |
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Lenza-Primiceri (2020) deterministic COVID-19 volatility break. |