`factor_augmented_ar` – Factor-augmented AR (PCA factors + AR lags on target).#

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

Function signature#

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

Parameters#

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

Returns#

FARFitResult — frozen dataclass with fit results.

Attribute	Type	Description
`.n_factors`	`int`	Number of PCA factors extracted from X.
`.n_lags`	`int`	AR lag order p.
`.predict(X)`	`np.ndarray`	Predictions for new data X, shape (n_samples,).
`.summary()`	`str`	Table: factor count and lag order.

Behavior#

Stock-Watson (2002) FAR: extract the first params.n_factors principal components from the predictor panel, augment with AR(params.n_lag) lags of the target, run OLS. Standard high-dimensional macro forecasting baseline.

When to use

High-dimensional macro panels (FRED-MD/QD); diffusion-index baselines.

In recipe context#

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

# Layer L4 recipe fragment
params:
  family: factor_augmented_ar

References#

macroforecast design Part 2, L4: ‘forecasting model is the layer where every authoring iteration ends – pick family, tune, repeat.’
Stock & Watson (2002) ‘Forecasting Using Principal Components from a Large Number of Predictors’, JASA 97(460).

factor_augmented_ar – Factor-augmented AR (PCA factors + AR lags on target).#