Fractional Brownian Motion Synthesis Using the Command Line

Wavelet Toolbox

Fractional Brownian Motion Synthesis Using the Command Line

According to the value of H, the fBm exhibits for H > 0.5, long-range dependence and for H < 0.5, short or intermediate dependence.

Let us give an example of each situation using the wfbm M-file, which generates a sample path of this process.

% Generate fBm for H = 0.3 and H = 0.7

% Initialize the randn generator
randn('state',1)

% Set the parameter H and the sample length
H = 0.3; lg = 1000;
% Generate and plot wavelet-based fBm for H = 0.3
fBm03 = wfbm(H,lg,'plot');

% Reset randn generator and parameter H
randn('state',1); H = 0.7;
% Generate and plot wavelet-based fBm for H = 0.7
fBm07 = wfbm(H,lg,'plot');

% The last step is equivalent to
% Define wavelet and level of decomposition
% w = ' db10'; ns = 6;
% Generate
% fBm07 = wfbm(H,lg,'plot',w,ns);

It appears that fBm07 clearly exhibits a stronger low-frequency component and has, locally, a less irregular behavior.

One-Dimensional Fractional Brownian Motion Synthesis Fractional Brownian Motion Synthesis Using the Graphical Interface