Multifractal detrended fluctuation analysis of nonstationary time series

Jan W. Kantelhardt; Stephan A. Zschiegner; Eva Koscielny-Bunde; Shlomo Havlin; Armin Bunde; H. Eugene Stanley

doi:10.1016/S0378-4371(02)01383-3

Multifractal detrended fluctuation analysis of nonstationary time series

Jan W. Kantelhardt, Stephan A. Zschiegner, Eva Koscielny-Bunde, Shlomo Havlin, Armin Bunde, H. Eugene Stanley

Department of Physics - at Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

3176 Scopus citations

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.

Original language	English
Pages (from-to)	87-114
Number of pages	28
Journal	Physica A: Statistical Mechanics and its Applications
Volume	316
Issue number	1-4
DOIs	https://doi.org/10.1016/S0378-4371(02)01383-3
State	Published - 15 Dec 2002

Bibliographical note

Funding Information:
We would like to thank Yosef Ashkenazy for useful discussions and the German Academic Exchange Service (DAAD), the Deutsche Forschungsgemeinschaft (DFG), the German Israeli Foundation (GIF), the Minerva Foundation, and the NIH/National Center for Research Resources for financial support.

Funding

We would like to thank Yosef Ashkenazy for useful discussions and the German Academic Exchange Service (DAAD), the Deutsche Forschungsgemeinschaft (DFG), the German Israeli Foundation (GIF), the Minerva Foundation, and the NIH/National Center for Research Resources for financial support.

Funders	Funder number
German Israeli Foundation
National Institutes of Health
National Center for Research Resources
Deutscher Akademischer Austauschdienst
Minerva Foundation
Deutsche Forschungsgemeinschaft

Keywords

Broad distributions
Detrended fluctuation analysis
Long-range correlations
Multifractal formalism
Nonstationarities
Scaling
Time series analysis

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10.1016/S0378-4371(02)01383-3

Cite this

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title = "Multifractal detrended fluctuation analysis of nonstationary time series",

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.",

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note = "Funding Information: We would like to thank Yosef Ashkenazy for useful discussions and the German Academic Exchange Service (DAAD), the Deutsche Forschungsgemeinschaft (DFG), the German Israeli Foundation (GIF), the Minerva Foundation, and the NIH/National Center for Research Resources for financial support.",

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AU - Zschiegner, Stephan A.

AU - Koscielny-Bunde, Eva

AU - Havlin, Shlomo

AU - Bunde, Armin

AU - Stanley, H. Eugene

N1 - Funding Information: We would like to thank Yosef Ashkenazy for useful discussions and the German Academic Exchange Service (DAAD), the Deutsche Forschungsgemeinschaft (DFG), the German Israeli Foundation (GIF), the Minerva Foundation, and the NIH/National Center for Research Resources for financial support.

PY - 2002/12/15

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N2 - 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.

AB - 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.

KW - Broad distributions

KW - Detrended fluctuation analysis

KW - Long-range correlations

KW - Multifractal formalism

KW - Nonstationarities

KW - Scaling

KW - Time series analysis

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Multifractal detrended fluctuation analysis of nonstationary time series

Abstract

Bibliographical note

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Keywords

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