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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 to 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 (WTMM)
method, and show that the results are equivalent.