`ar_p` – Autoregressive AR(p) on the target.#

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

Function signature#

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

Parameters#

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

Returns#

ARFitResult — frozen dataclass with fit results.

Attribute	Type	Description
`.n_lags`	`int`	AR lag order p.
`.coef_`	`np.ndarray`	Fitted AR coefficients, shape (n_lags,).
`.intercept_`	`float`	Fitted intercept.
`.predict(X)`	`np.ndarray`	Predictions for new data X, shape (n_samples,).
`.summary()`	`str`	Table: AR order, intercept, per-lag coefficients.

Behavior#

Pure autoregression – predictor matrix is the lagged target (no exogenous regressors). params.n_lag sets p. Useful as a non-trivial benchmark in macro forecasting where the lagged target captures most of the predictability.

When to use

Default benchmark in any forecasting horse race; replication of papers reporting AR baselines.

In recipe context#

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

# Layer L4 recipe fragment
params:
  family: ar_p

References#

macroforecast design Part 2, L4: ‘forecasting model is the layer where every authoring iteration ends – pick family, tune, repeat.’
Stock & Watson (2007) ‘Why Has US Inflation Become Harder to Forecast?’, JMCB 39.

ar_p – Autoregressive AR(p) on the target.#