statsmodels.stats.diagnostic.pesaran_timmermann

statsmodels.stats.diagnostic.pesaran_timmermann(actual, predicted, alternative='two-sided')

Pesaran-Timmermann test of directional predictive accuracy.

Parameters:

actualarray_like

Realized values. The direction is classified by actual > 0.

predictedarray_like

Forecasted or predicted values. The direction is classified by predicted > 0.

alternative{“two-sided”, “larger”, “smaller”}

Alternative hypothesis for the directional accuracy statistic.

Returns:

PesaranTimmermannResult

A NamedTuple with fields:

statisticfloat

Normal test statistic.

pvaluefloat

P-value for the chosen alternative.

res_storeResultsStore or None

Intermediate results.

Notes

The Pesaran-Timmermann test evaluates whether the realized and predicted signs are independent. Let

\[\hat{p} = n^{-1}\sum_{t=1}^n 1\{\operatorname{sign}(y_t) = \operatorname{sign}(\hat{y}_t)\}\]

be the observed success rate, and let

\[\hat{p}_* = \hat{p}_y \hat{p}_z + (1 - \hat{p}_y)(1 - \hat{p}_z)\]

denote the success rate implied by independence, where \(\hat{p}_y\) and \(\hat{p}_z\) are the sample proportions of positive realizations and positive predictions. The test statistic is

\[S_n = \frac{\hat{p} - \hat{p}_*} {\sqrt{\hat{v} - \hat{w}}},\]

where

\[\hat{v} = \hat{p}_* (1 - \hat{p}_*) / n\]

and

\[\hat{w} = \left[(2\hat{p}_y - 1)^2 \hat{p}_z (1 - \hat{p}_z) + (2\hat{p}_z - 1)^2 \hat{p}_y (1 - \hat{p}_y)\right] / n.\]

Under the null of no directional predictive ability, the statistic is asymptotically standard normal.

References

[1]

Pesaran, M. H., and Timmermann, A. “A Simple Nonparametric Test of Predictive Performance.” Journal of Business & Economic Statistics 10, no. 4 (1992): 461-465.