Multifractal detrended $uctuation analysis of nonstationary time series
Multifractal detrended $uctuation analysis of nonstationary time series
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发表时间：
2002
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通讯作者：
J. Kantelhardt;S. Zschiegner;Eva Koscielny-Bunde;S. Havlin;A. Bunde;H. Stanley
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作者：
J. Kantelhardt;S. Zschiegner;Eva Koscielny-Bunde;S. Havlin;A. Bunde;H. Stanley
在去趋势波动分析（DFA）的基础上，提出了一种非平稳时间序列多重分形特征的方法。我们将我们的多重分形DFA方法的标准的基于配分函数的多重分形形式主义，并证明这两种方法是等价的平稳信号与紧支持。通过对几个实例的分析，表明该方法能够可靠地判定时间序列的多重分形标度行为。通过比较原始序列和Shu6ed序列的多重分形DFA结果，我们可以区分由长程相关引起的多重分形和由宽概率密度函数引起的多重分形。我们还将所得结果与小波变换模极大值法进行了比较，并证明了结果是等价的。C
We develop a method for the multifractal characterization of nonstationary time series, which is based on a generalization of the detrended $uctuation 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 shu6ed 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. c