`clark_west` – Clark-West (2007) MSE-adjusted nested-model predictive ability test.#

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Operational op under axis nested_test, sub-layer L6_B_nested, layer l6. Standalone callable: mf.functions.cw_test.

Function signature#

mf.functions.cw_test(
    loss_small: np.ndarray,
    loss_large: np.ndarray,
    f_small: np.ndarray,
    f_large: np.ndarray,
) -> CWTestResult

Parameters#

name	type	default	constraint	description
`loss_small`	`np.ndarray`	—	—	Squared losses for the small (restricted) model.
`loss_large`	`np.ndarray`	—	—	Squared losses for the large (unrestricted) model.
`f_small`	`np.ndarray`	—	—	Point forecasts for the small model.
`f_large`	`np.ndarray`	—	—	Point forecasts for the large model.

Returns#

CWTestResult — frozen dataclass with fit results.

Attribute	Type	Description
`stat`	`float or None`	CW test statistic
`pvalue`	`float or None`	One-sided p-value
`decision`	`bool`	Reject H0 at 5%
`n_obs`	`int`	Observations used
`cw_adjustment`	`bool`	CW penalty applied

Behavior#

Tests whether the large (unrestricted) model significantly outperforms the small (restricted, nested) model. Constructs the CW-adjusted statistic f_t = (loss_small - loss_large) + (f_small - f_large)^2, removing the negative expected value bias that standard DM has in nested comparisons. One-sided test (H_a: large model improves on small); hln=False.

When to use

Testing whether a larger model with additional regressors beats the restricted benchmark.

When NOT to use

Non-nested model comparisons – use DM / GW (L6.A) instead. Forecast combination (use HN encompassing instead).

In recipe context#

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

# Layer L6 recipe fragment
params:
  nested_test: clark_west

References#

macroforecast design Part 3, L6: ‘tests must report (statistic, p-value, kernel, lag) and respect HAC dependence-correction.’
Clark & West (2007) ‘Approximately Normal Tests for Equal Predictive Accuracy in Nested Models’, JoE 138(2): 291-311.

clark_west – Clark-West (2007) MSE-adjusted nested-model predictive ability test.#