`mse` – Mean squared error – `(1/N) Σ (y_t - ŷ_t)²`.#

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Operational op under axis point_metrics, sub-layer L5_A_metric_specification, layer l5. Standalone callable: mf.functions.mse.

Function signature#

mf.functions.mse(
    y_true: np.ndarray | pd.Series,
    y_pred: np.ndarray | pd.Series,
) -> float

Parameters#

name	type	default	constraint	description
`y_true`	`np.ndarray	pd.Series`	—	—
`y_pred`	`np.ndarray	pd.Series`	—	—

Returns#

float — scalar result.

Behavior#

Point-forecast metric mse. The classical quadratic-loss metric. Optimal under Gaussian-residual / squared-loss decision theory; the L4 fit objective for OLS / ridge / elastic net is its in-sample version. MSE penalises large residuals super-linearly, so a single outlier in the OOS sample can dominate the score.

When to use

Default for Gaussian-residual problems; horse-race ranking under squared-loss decision rules.

When NOT to use

Heavy-tailed forecast errors – a single outlier dominates the score; consider MAE or MedAE instead.

In recipe context#

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

# Layer L5 recipe fragment
params:
  point_metrics: mse

References#

macroforecast design Part 3, L5: ‘evaluation = (metric × benchmark × aggregation × decomposition × ranking).’
Diebold (2017) ‘Forecasting in Economics, Business, Finance and Beyond’, University of Pennsylvania (free online). https://www.sas.upenn.edu/~fdiebold/Textbooks.html

mse – Mean squared error – (1/N) Σ (y_t - ŷ_t)².#