Comparison of detrending methods for fluctuation analysis

Amir Bashan; Ronny Bartsch; Jan W. Kantelhardt; Shlomo Havlin

doi:10.1016/j.physa.2008.04.023

Comparison of detrending methods for fluctuation analysis

Amir Bashan, Ronny Bartsch, Jan W. Kantelhardt, Shlomo Havlin

Department of Physics

Martin Luther University Halle-Wittenberg

Research output: Contribution to journal › Article › peer-review

259 Scopus citations

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.

Original language	English
Pages (from-to)	5080-5090
Number of pages	11
Journal	Physica A: Statistical Mechanics and its Applications
Volume	387
Issue number	21
DOIs	https://doi.org/10.1016/j.physa.2008.04.023
State	Published - 1 Sep 2008

Bibliographical note

Funding Information:
We thank Diego Rybski for very helpful discussions. This work has been supported by the Deutsche Forschungsgemeinschaft (grant KA 1676/3) and the European Union (STREP project DAPHNet, grant 018474-2). RB acknowledges financial support from the President scholarship of Bar-Ilan University.

Funding

We thank Diego Rybski for very helpful discussions. This work has been supported by the Deutsche Forschungsgemeinschaft (grant KA 1676/3) and the European Union (STREP project DAPHNet, grant 018474-2). RB acknowledges financial support from the President scholarship of Bar-Ilan University.

Funders	Funder number
President scholarship of Bar-Ilan University
European Commission	018474-2
Deutsche Forschungsgemeinschaft	KA 1676/3

Keywords

Crossovers
Detrended fluctuation analysis
Long-range correlations
Non-stationarities
Time series analysis

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10.1016/j.physa.2008.04.023

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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.",

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Comparison of detrending methods for fluctuation analysis

Abstract

Bibliographical note

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Keywords

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