A Python implementation of the Directional Accuracy Score and Pesaran-Timmermann statistic.

pttest.py

import numpy as np
import scipy.stats as stats


def pttest(y, yhat):
    """Given NumPy arrays with predictions and with true values, 
    return Directional Accuracy Score, Pesaran-Timmermann statistic and its p-value
    """
    size = y.shape[0]
    pyz = np.sum(np.sign(y) == np.sign(yhat))/size
    py = np.sum(y > 0)/size
    qy = py*(1 - py)/size
    pz = np.sum(yhat > 0)/size
    qz = pz*(1 - pz)/size
    p = py*pz + (1 - py)*(1 - pz)
    v = p*(1 - p)/size
    w = ((2*py - 1)**2) * qz + ((2*pz - 1)**2) * qy + 4*qy*qz
    pt = (pyz - p) / (np.sqrt(v - w))
    pval = 1 - stats.norm.cdf(pt, 0, 1)
    return pyz, pt, pval


if __name__ == "__main__":
    a = np.array([23, -2, 56, 51, 4, -45, -12, -24, -51, 78, -6, -7, -39, 31, 35])
    b = np.array([14, 3, 45, 23, -5, -56, 4, -11, -34, 29, 3, -11, -12, 24, 3])
    dac, pt, pval = pttest(a, b)
    print(f"Directional Accuracy: {dac}, PT stat: {pt}, p-value: {pval}")