medae – Median absolute error – median |y_t - ŷ_t|.#

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

Function signature#

mf.functions.medae(
    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 medae. Maximally robust point-forecast metric: substitution by median completely insulates the score from a constant-share of extreme residuals. Common in robust-statistics papers; rarer in mainstream forecasting.

When to use

Pathologically heavy-tailed errors (financial crises, regime shifts).

When NOT to use

Standard reporting – mean-based metrics are the convention.

In recipe context#

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

# Layer L5 recipe fragment
params:
  point_metrics: medae

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