Fractal and Multifractal Time Series

Details Fractal and Multifractal Time Series Fractal and Multifractal Time Series

2008-04-04

arxiv.org/abs/0804.0747v1

Physics

Data Analysis, Statistics and Probability

59 pages, 11 figures, for Springer's Encyclopedia of Complexity and System Science

Scientific paper

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.

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