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Zbl 1001.62029
Kantelhardt, Jan W.; Zschiegner, Stephan A.; Koscielny-Bunde, Eva; Havlin, Shlomo; Bunde, Armin; Stanley, H.Eugene
Multifractal detrended fluctuation analysis of nonstationary time series. (English)
[J] Physica A 316, No.1-4, 87-114 (2002). ISSN 0378-4371

Summary: 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.

MSC 2000:: *62M10 Time series, etc. (statistics)
37M10 Time series analysis

Keywords: scaling behavior; long-range correlations; probability density functions

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Zentralblatt MATH Berlin [Germany]