Fast Hurst exponent calculation

fast_husrt.py

import pandas as pd
import numpy as np
from numba import jit

def calc_hurst(series: pd.Series, n_wins: int = 300):
    changes = series.diff().dropna().astype(np.float32).values
    max_w = changes.shape[0] - 1

    win_sizes = np.linspace(np.log10(10), np.log10(max_w), num=n_wins)
    win_sizes = np.unique(np.power(10, win_sizes).astype(np.int16))

    rs = _calc(changes, win_sizes)
    hurst, const = np.polyfit(np.log10(win_sizes), np.log10(rs), 1)
    rs /= np.power(10, const)

    return hurst, win_sizes, rs


@jit(nopython=True)
def _calc(changes, win_sizes):
    rs = np.empty_like(win_sizes, dtype=np.float32)
    for k, ws in enumerate(win_sizes):
        total: float = 0.0
        n: int = changes.shape[0]-ws+1

        for i in range(0, n):
            Z = (changes[i:i+ws] - changes[i:i+ws].mean()).cumsum()
            R = max(Z) - min(Z)
            S = changes[i:i+ws].std()
            total += R/S

        rs[k] = total/n

    return rs