Comparison of detrending methods for fluctuation analysis

By Amir Bashan, R. Bartsch, Jan W. Kantelhardt, Shlomo Havlin. 2008

307 citations recorded by the source corpus.

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.

Subfields: Condensed Matter Physics, Economics and Econometrics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/1b8f8243689aa1332e5f9cde0677e35469954436

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Citations in the corpus

p-exponent and p-leaders, Part II: Multifractal Analysis. Relations to Detrended Fluctuation Analysis (2015, methodology): “In the MFDFA method, increasing NP also brings some form of robustness to additive noise, however, this far more depends on the nature of the trend [66, 67, 68, 69] (see also the numerical illustrations in Section 5.”
On the computational complexity of the empirical mode decomposition algorithm (2014, methodology): “During the last decade, the EMD/EEMDwas shown to bemore effective than the traditional Fourier method inmany problems from various fields such as physics [4], biomedicine [5–8], mechanical health diagnosis [9], image analysis [10] and others.”