fracbm 0.1.1

Fractional Brownian Motion (fBM) generators in Python.

fracbm

Fractional Brownian Motion (FBM) generators in Python.

Installation

pip  install  fracbm

Usage

import  matplotlib.pyplot  as  plt

import  fracbm

# Generate with Davies–Harte method. 1000 steps with a Hurst parameter of 0.8

B  =  fracbm.daviesharte(n=1000, H=0.8)

plt.plot(B)

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).