Comparison of detrending methods for fluctuation analysis
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TLDR
A detailed comparison between the regular DFA and two recently suggested methods: the Centered Moving Average (CMA) Method and a Modified Detrended Fluctuation Analysis (MDFA) is presented, finding that CMA performs the same as DFA in long data with weak trends and is slightly superior to D FA in short data with strong trends.Abstract:
We examine several recently suggested methods for the detection of long-range correlations in data series based on similar ideas as the well-established Detrended Fluctuation Analysis (DFA). In particular, we present a detailed comparison between the regular DFA and two recently suggested methods: the Centered Moving Average (CMA) Method and a Modified Detrended Fluctuation Analysis (MDFA). We find that CMA performs the same as DFA in long data with weak trends and is slightly superior to DFA in short data with weak trends. When comparing standard DFA to MDFA we observe that DFA performs slightly better in almost all examples we studied. We also discuss how several types of trends affect different types of DFA. For weak trends in the data, the new methods are comparable with DFA in these respects. However, if the functional form of the trend in data is not a-priori known, DFA remains the method of choice. Only a comparison of DFA results, using different detrending polynomials, yields full recognition of the trends. A comparison with independent methods is recommended for proving long-range correlations.read more
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TL;DR: In this paper, a solution of the problem of determining the reservoir storage required on a given stream, to guarantee a given draft, is presented, where a long-time record of annual total...
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Mosaic organization of DNA nucleotides
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TL;DR: This work analyzes two classes of controls consisting of patchy nucleotide sequences generated by different algorithms--one without and one with long-range power-law correlations, finding that both types of sequences are quantitatively distinguishable by an alternative fluctuation analysis method.
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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
TL;DR: 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).
Journal ArticleDOI
Multifractal detrended fluctuation analysis of nonstationary time series
Jan W. Kantelhardt,Stephan Zschiegner,Eva Koscielny-Bunde,Armin Bunde,Shlomo Havlin,H. Eugene Stanley +5 more
TL;DR: 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).