harvey_newbold_encompassing – Harvey-Leybourne-Newbold (1998) forecast-encompassing test.#

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Operational op under axis equal_predictive_test, sub-layer L6_A_equal_predictive, layer l6. Standalone callable: mf.functions.hn_test.

Function signature#

mf.functions.hn_test(
    e_a: np.ndarray,
    e_b: np.ndarray,
) -> HNTestResult

Parameters#

name

type

default

constraint

description

e_a

np.ndarray

—

—

Forecast errors for model A (actual - forecast_a).

e_b

np.ndarray

—

—

Forecast errors for model B (actual - forecast_b).

Returns#

HNTestResult — frozen dataclass with fit results.

Attribute

Type

Description

stat

float or None

HN test statistic

pvalue

float or None

One-sided p-value

decision

bool

Reject H0 at 5%

n_obs

int

Observations used

encompassing

str

Direction: a_over_b

Behavior#

Tests the null that forecast f_1 encompasses f_2 – i.e. the optimal linear combination of the two forecasts puts zero weight on f_2’s error. Constructs d_t = e_a (e_a - e_b) from the per-period forecast errors and tests its mean against zero with a Newey-West HAC long-run variance and an HLN small-sample correction at horizon h>1. Asymmetric by construction (f_1 encompasses f_2 ≠ f_2 encompasses f_1).

When to use

Deciding whether one forecast contains all the information of another.

When NOT to use

Symmetric equal-MSE comparison – use dm_diebold_mariano instead.

In recipe context#

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

# Layer L6 recipe fragment
params:
  equal_predictive_test: harvey_newbold_encompassing

References#

  • macroforecast design Part 3, L6: ‘tests must report (statistic, p-value, kernel, lag) and respect HAC dependence-correction.’

  • Harvey, Leybourne & Newbold (1998) ‘Tests for Forecast Encompassing’, JBES 16(2): 254-259.