pesaran_timmermann_metric – Pesaran-Timmermann (1992) directional-accuracy statistic.#

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

Function signature#

mf.functions.pesaran_timmermann_metric(
    y_true: np.ndarray | pd.Series,
    y_pred: np.ndarray | pd.Series,
    *,
    threshold: float = 0.0,
) -> float

Parameters#

name

type

default

constraint

description

y_true

`np.ndarray

pd.Series`

—

—

y_pred

`np.ndarray

pd.Series`

—

—

threshold

float

0.0

—

Threshold for computing directional binary series. A forecast above threshold = directional ‘up’.

Returns#

float — scalar result.

Behavior#

Directional-accuracy metric pesaran_timmermann_metric. Adjusts the success ratio for the joint probability of agreement under independence (so a constant-sign forecast no longer scores high). Asymptotically standard normal under the null of no directional skill; the L6.F test computes the corresponding p-value.

When to use

Formal directional-accuracy reporting (paired with the L6 PT test).

In recipe context#

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

# Layer L5 recipe fragment
params:
  direction_metrics: pesaran_timmermann_metric

References#

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

  • Pesaran & Timmermann (1992) ‘A simple nonparametric test of predictive performance’, JBES 10(4): 461-465.