Multifractal Detrended Fluctuation Analysis of Nonstationary Time Series
Jan W. Kantelhardt,Jan W. Kantelhardt,Stephan Zschiegner,Eva Koscielny-Bunde,Eva Koscielny-Bunde,Shlomo Havlin,Shlomo Havlin,Armin Bunde,H. Eugene Stanley +8 more
TLDR
In this article, the authors developed a method for the multifractal characterization of nonstationary time series, which is based on a generalization of the detrended fluctuation analysis (DFA).Abstract:
We develop a method for the multifractal characterization of nonstationary time series, which is based on a generalization of the detrended fluctuation analysis (DFA). We relate our multifractal DFA method to the standard partition function-based multifractal formalism, and prove that both approaches are equivalent for stationary signals with compact support. By analyzing several examples we show that the new method can reliably determine the multifractal scaling behavior of time series. By comparing the multifractal DFA results for original series with those for shuffled series we can distinguish multifractality due to long-range correlations from multifractality due to a broad probability density function. We also compare our results with the wavelet transform modulus maxima method, and show that the results are equivalent.read more
Citations
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Journal ArticleDOI
Introduction to Multifractal Detrended Fluctuation Analysis in Matlab
TL;DR: The main aim of the tutorial is to give the reader a simple self-sustained guide to the implementation of MFDFA and interpretation of the resulting multifractal spectra.
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Multifractal detrended cross-correlation analysis for two nonstationary signals.
TL;DR: A method to investigate the multifractal behaviors in the power-law cross-correlations between two time series or higher-dimensional quantities recorded simultaneously is proposed, which can be applied to diverse complex systems such as turbulence, finance, ecology, physiology, geophysics, and so on.
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Modelling Financial Time Series
P. Manimaran,Jitendra C. Parikh,Prasanta K. Panigrahi,Sujit Basu,C. M. Kishtawal,M. B. Porecha +5 more
TL;DR: A new wavelet based approach is described to separate the trend from the fluctuations in a time series, and a deterministic (non-linear regression) model is constructed for the trend using genetic algorithm.
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Physical approach to complex systems
TL;DR: This review advocate some of the computational methods which in this opinion are especially fruitful in extracting information on selected–but at the same time most representative–complex systems like human brain, financial markets and natural language, from the time series representing the observables associated with these systems.
References
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Mosaic organization of DNA nucleotides
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Multifractality in human heartbeat dynamics
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TL;DR: In this paper, the authors investigate the possibility that time series generated by certain physiological control systems may be members of a special class of complex processes, termed multifractal, which require a large number of exponents to characterize their scaling properties.
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Detecting long-range correlations with detrended fluctuation analysis
TL;DR: It is shown that deviations from scaling which appear at small time scales become stronger in higher orders of detrended fluctuation analysis, and a modified DFA method is suggested to remove them.
Journal ArticleDOI
Effect of trends on detrended fluctuation analysis.
TL;DR: It is shown how to use DFA appropriately to minimize the effects of trends, how to recognize if a crossover indicates indeed a transition from one type to a different type of underlying correlation, or if the crossover is due to a trend without any transition in the dynamical properties of the noise.
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