bvar_minnesota – Bayesian VAR with Minnesota prior shrinkage.#

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

Function signature#

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

Parameters#

name

type

default

constraint

description

X

`np.ndarray

pd.DataFrame`

—

—

y

`np.ndarray

pd.Series`

—

—

Returns#

BVARMinnesotaFitResult — frozen dataclass with fit results.

Attribute

Type

Description

.n_lags

int

VAR lag order p.

.lambda1

float

Minnesota prior tightness.

.n_obs

int

Number of observations.

.predict(X)

np.ndarray

Predictions for new data X, shape (n_samples,).

.summary()

str

Table: lag order, tightness, observation count.

Behavior#

Litterman (1986) Minnesota prior: shrinks each equation toward a univariate random walk. params.minnesota_lambda1 controls overall tightness; params.minnesota_lambda_decay controls lag decay; params.minnesota_lambda_cross controls cross-equation shrinkage.

Returns a closed-form posterior mean – no MCMC. Cheap and deterministic.

When to use

Multi-series forecasting where standard VAR overfits; macro panels with strong unit-root behaviour.

In recipe context#

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

# Layer L4 recipe fragment
params:
  family: bvar_minnesota

References#

  • macroforecast design Part 2, L4: ‘forecasting model is the layer where every authoring iteration ends – pick family, tune, repeat.’

  • Litterman (1986) ‘Forecasting With Bayesian Vector Autoregressions – Five Years of Experience’, JBES 4(1).