fracbm 0.3.0

Fractional Brownian Noise (fGN) and Fractional Brownian Motion (fBM) generators in Python.

fracbm

Fractional Gaussian Noise (fGN) and Fractional Brownian Motion (fBM) tools.

Installation

pip  install  fracbm

Usage

import matplotlib.pyplot as plt
import fracbm

# Parameters
n = 10000      # number of steps
H = 0.7       # Hurst parameter

# Fractional Brownian motion using Davies–Harte
fbm_path = fracbm.daviesharte.motion(n, H)      # cumulative sum of fGN
fgn_increments = fracbm.daviesharte.noise(n, H) # fractional Gaussian noise

# Wavelet based estimation of Hurst exponent
estimated_hurst = fracbm.invhurst(fbm_path)
print(f'Estimated Hurst Exponent = {estimated_hurst}')

# Plot the full fBm path
plt.figure(figsize=(10, 4))
plt.plot(fbm_path, label="fBM path (Davies–Harte)")
plt.xlabel("Step")
plt.ylabel("Value")
plt.title("Fractional Brownian Motion (H=0.8, Davies–Harte)")
plt.legend()
plt.show()

Features

Generate exact fractional Brownian motion using:

• Cholesky decomposition, order $\mathcal{O}(n^3)$

• Davies-Harte method, order $\mathcal{O}(n \log n)$ (recommended)

• Vary the Hurst parameter $H \in [0,1]$:

• $H = 0.5$ is regular Brownian motion.

• $H > 0.5$ causes slowly decaying positive autocorrelations (positive increments tend to follow positive increments - increments follow a trend).

• $H < 0.5$ causes fast-decaying negative autocorrelations (negative increments tend to follow positive increments - increments revert to the mean).

Determine the Hurst exponent of a time series:

• Wavelet transform method
• For n ~ 10000 or greater