Fractal and Multifractal Time Series

TL;DR

This review discusses methods from Statistical Physics and Applied Mathematics for analyzing complex time series using fractal and multifractal scaling, enabling characterization, modeling, and prediction of extreme events.

Contribution

It compiles and exemplifies various fractal and multifractal analysis techniques applied to complex time series data.

Findings

Fractal and multifractal methods effectively characterize complex fluctuations.

These approaches can model and predict extreme events.

Scaling exponents reveal underlying system dynamics.

Abstract

Data series generated by complex systems exhibit fluctuations on many time scales and/or broad distributions of the values. In both equilibrium and non-equilibrium situations, the natural fluctuations are often found to follow a scaling relation over several orders of magnitude, allowing for a characterisation of the data and the generating complex system by fractal (or multifractal) scaling exponents. In addition, fractal and multifractal approaches can be used for modelling time series and deriving predictions regarding extreme events. This review article describes and exemplifies several methods originating from Statistical Physics and Applied Mathematics, which have been used for fractal and multifractal time series analysis.