Hurst exponent

The Hurst exponent is a key figure from chaos theory or from fractal geometry , which was named by Benoît Mandelbrot both after Harold Edwin Hurst and Otto Ludwig Hölder . It represents an index of dependency between different quantities. It can also be seen as a relative tendency of a time series . ${\displaystyle H}$

Applied to fractal surfaces, it represents a roughness coefficient that is directly related to the fractal dimension  D :

${\displaystyle H=2-D}$

The Hurst exponent varies between zero and one, with larger values ​​producing softer shapes:

${\displaystyle H\to 1\Rightarrow D\to 1}$.

swell

• Benoît Mandelbrot: The (Mis) Behavior of Markets, A Fractal View of Risk, Ruin and Reward . Basic Books, 2004, pp. 186-195 .