r2_oos – Out-of-sample R² (Campbell-Thompson 2008) – 1 - SSE_model / SSE_benchmark.#

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Operational op under axis relative_metrics, sub-layer L5_A_metric_specification, layer l5. Standalone callable: mf.functions.r2_oos.

Function signature#

mf.functions.r2_oos(
    y_true: np.ndarray | pd.Series,
    y_model: np.ndarray | pd.Series,
    y_benchmark: np.ndarray | pd.Series,
) -> float

Parameters#

name

type

default

constraint

description

y_true

`np.ndarray

pd.Series`

—

—

y_model

`np.ndarray

pd.Series`

—

—

y_benchmark

`np.ndarray

pd.Series`

—

—

Returns#

float — scalar result.

Behavior#

Relative-loss metric r2_oos. Standard return-predictability metric in finance (and increasingly in macro). Identical formula to mse_reduction when the benchmark is the historical mean. Campbell & Thompson (2008) popularised the metric for the empirical-asset-pricing literature.

When to use

Macro / financial forecasting tradition; literature-compatibility with CT-2008-era papers.

In recipe context#

Set params.relative_metrics = "r2_oos" in the relevant layer to activate this op within a recipe:

# Layer L5 recipe fragment
params:
  relative_metrics: r2_oos

References#

  • macroforecast design Part 3, L5: ‘evaluation = (metric × benchmark × aggregation × decomposition × ranking).’

  • Campbell & Thompson (2008) ‘Predicting Excess Stock Returns Out of Sample: Can Anything Beat the Historical Average?’, Review of Financial Studies 21(4): 1509-1531. (doi:10.1093/rfs/hhm055)