## Term Glossary

### Fractal Dimension

Fractal dimension (capacity, Hausdorff dimension, similarity dimension) is a measure of how "complicated" a self-similar process is. Fractal dimension for a self-affine process (e.g. fractional Brownian Motion) is given by: $$D=2-H$$

$H$
Hurst exponent
A fractal dimension $1.0<D<1.5$ corresponds to a profile-like curve showing persistent behaviour, namely if the curve has been increasing for a period, it is expected to continue for another period.

A fractal dimension $1.5<D<2$ shows antipersistent behaviour. After a period of decreases, a period of increases tends to show up. The antipersistent behaviour correspondd to a very "noisy" curve (which highly fills up the plane).

###### Function Reference
portfolio_fractalDimension, position_fractalDimension