Term Glossary

Metrics, Models & Concepts

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: \begin{equation} D=2-H \end{equation}

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