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Minimizing the effect of exponential trends in detrended fluctuation analysis

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  • Xu, Na
  • Shang, Pengjian
  • Kamae, Santi

Abstract

The detrended fluctuation analysis (DFA) and its extensions (MF-DFA) have been used extensively to determine possible long-range correlations in time series. However, recent studies have reported the susceptibility of DFA to trends which give rise to spurious crossovers and prevent reliable estimation of the scaling exponents. In this report, a smoothing algorithm based on the discrete laplace transform (DFT) is proposed to minimize the effect of exponential trends and distortion in the log–log plots obtained by MF-DFA techniques. The effectiveness of the technique is demonstrated on monofractal and multifractal data corrupted with exponential trends.

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  • Xu, Na & Shang, Pengjian & Kamae, Santi, 2009. "Minimizing the effect of exponential trends in detrended fluctuation analysis," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 311-316.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:1:p:311-316
    DOI: 10.1016/j.chaos.2007.12.006
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    1. Nagarajan, Radhakrishnan & Kavasseri, Rajesh G., 2005. "Minimizing the effect of periodic and quasi-periodic trends in detrended fluctuation analysis," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 777-784.
    2. Vitanov, Nikolay K. & Yankulova, Elka D., 2006. "Multifractal analysis of the long-range correlations in the cardiac dynamics of Drosophila melanogaster," Chaos, Solitons & Fractals, Elsevier, vol. 28(3), pages 768-775.
    3. Kavasseri, Rajesh G. & Nagarajan, Radhakrishnan, 2005. "A multifractal description of wind speed records," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 165-173.
    4. Kantelhardt, Jan W. & Zschiegner, Stephan A. & Koscielny-Bunde, Eva & Havlin, Shlomo & Bunde, Armin & Stanley, H.Eugene, 2002. "Multifractal detrended fluctuation analysis of nonstationary time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 87-114.
    5. Currenti, Gilda & Negro, Ciro Del & Lapenna, Vincenzo & Telesca, Luciano, 2005. "Fluctuation analysis of the hourly time variability of volcano-magnetic signals recorded at Mt. Etna Volcano, Sicily (Italy)," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1921-1929.
    6. Morariu, V.V. & Isvoran, Adriana & Zainea, Oana, 2007. "A non-linear approach to the structure–mobility relationship in protein main chains," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1305-1315.
    7. Telesca, Luciano & Balasco, Marianna & Lapenna, Vincenzo, 2007. "Investigating the time-correlation properties in self-potential signals recorded in a seismic area of Irpinia, southern Italy," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 199-211.
    8. Silva, F.E. & Gonçalves, L.L. & Fereira, D.B.B. & Rebello, J.M.A., 2005. "Characterization of failure mechanism in composite materials through fractal analysis of acoustic emission signals," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 481-494.
    9. Gerhardt, Günther J.L. & Lemke, Ney & Corso, Gilberto, 2006. "Network clustering coefficient approach to DNA sequence analysis," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 1037-1045.
    10. Peng, C.-K. & Buldyrev, S.V. & Goldberger, A.L. & Havlin, S. & Mantegna, R.N. & Simons, M. & Stanley, H.E., 1995. "Statistical properties of DNA sequences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 221(1), pages 180-192.
    11. Kantelhardt, Jan W & Koscielny-Bunde, Eva & Rego, Henio H.A & Havlin, Shlomo & Bunde, Armin, 2001. "Detecting long-range correlations with detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(3), pages 441-454.
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