`bvar_normal_inverse_wishart` – Bayesian VAR with Normal-Inverse-Wishart prior.#

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Operational op under axis family, sub-layer L4_A_model_selection, layer l4. Standalone callable: mf.functions.bvar_niw_fit.

Function signature#

mf.functions.bvar_niw_fit(
    X: np.ndarray | pd.DataFrame,
    y: np.ndarray | pd.Series,
) -> BVARNIWFitResult

Parameters#

name	type	default	constraint	description
`X`	`np.ndarray	pd.DataFrame`	—	—
`y`	`np.ndarray	pd.Series`	—	—

Returns#

BVARNIWFitResult — frozen dataclass with fit results.

Attribute	Type	Description
`.n_lags`	`int`	VAR lag order p.
`.n_obs`	`int`	Number of observations.
`.predict(X)`	`np.ndarray`	Predictions for new data X, shape (n_samples,).
`.summary()`	`str`	Table: lag order and observation count.

Behavior#

Conjugate Normal-IW prior on (β, Σ); the posterior mean of β has the same closed form as Minnesota but with the prior tightness scaled to reflect parameter-uncertainty inflation. Slightly less aggressive than the bare Minnesota prior.

When to use

Studies preferring a fully-conjugate prior over Litterman’s hand-tuned shrinkage.

In recipe context#

Set params.family = "bvar_normal_inverse_wishart" in the relevant layer to activate this op within a recipe:

# Layer L4 recipe fragment
params:
  family: bvar_normal_inverse_wishart

References#

macroforecast design Part 2, L4: ‘forecasting model is the layer where every authoring iteration ends – pick family, tune, repeat.’
Kadiyala & Karlsson (1997) ‘Numerical Methods for Estimation and Inference in Bayesian VAR-models’, Journal of Applied Econometrics 12(2).

bvar_normal_inverse_wishart – Bayesian VAR with Normal-Inverse-Wishart prior.#