Fractal and Multifractal Time Series
Definition of the Subject
Data series generated by complex systems exhibit fluctuations on a wide range of time scales and/or broad distributions of the values. In both equilibrium and nonequilibrium situations, the natural fluctuations are often found to follow a scaling relation over several orders of magnitude. Such scaling laws allow for a characterization of the data and the generating complex system by fractal (or multifractal) scaling exponents, which can serve as characteristic fingerprints of the systems in comparison with other systems and with models. Fractal scaling behavior has been observed, e.g., in many data series from experimental physics, geophysics, medicine, physiology, and even social sciences. Although the underlying causes of the observed fractal scaling are often not known in detail, the fractal or multifractal characterization can be used for generating surrogate (test) data, modeling the time series, and deriving predictions regarding extreme events or future...
KeywordsEmpirical Mode Decomposition Hurst Exponent Scaling Behavior Detrended Fluctuation Analysis Return Interval
We thank Ronny Bartsch, Amir Bashan, Mikhail Bogachev, Armin Bunde, Jan Eichner, Shlomo Havlin, Diego Rybski, Aicko Schumann, and Stephan Zschiegner for the helpful discussions and contributions. This work has been supported by the Deutsche Forschungsgemeinschaft (grants KA 1676/3 and KA 1676/4) and the European Union (FP6 project DAPHNet, grant 018474-2, and FP7 project SOCIONICAL, grant 231288).
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