mfbm 0.1.5

Multivariate fractional Brownian motion

Multivariate fractional Brownian motion (mfBm)

This package provides implementation for the multivariate fractional Brownian motion and simple fractional brownian motion with the method described in [1].

Installation

The mfbm package is available on PyPI and can be install via pip with the following command:

pip install mfbm

Example usage

import numpy as np
from mfbm import MFBM

p = 5
H = np.linspace(0.6, 0.9, 5)
n = 100
T = 100

rho = 0.7 * np.ones((p, p))
np.fill_diagonal(rho, 1)

eta = np.ones_like(rho)
sigma = np.ones(len(H))

mfbm = MFBM(H, rho, eta, sigma)
ts = mfbm.sample(n, T)

Explanation of the parameters:

• H: np.ndarray is a one dimensional array of the Hurst parameters, where all Hursts are in the range (0, 1).
• rho: np.ndarray is a two dimensional array of the cross correlations between the multiple fBms, default is the identity matrix.
• sigma: np.ndarray is a one dimensional array of the standard deviations of the single fBms, default is all ones.
• n: int is the number of increaments to generate for the multivariate fractional Gaussian noise.
• T: float is the time horizon of the mfBm, default is n.

[1] Andrew T. A. Wood & Grace Chan (1994): Simulation of Stationary Gaussian Processes in [0, 1]^d , Journal of Computational and Graphical Statistics, 3:4, 409-432