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The relationship between the detrendend fluctuation analysis and the autocorrelation function of a signal

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  • Marc Höll
  • Holger Kantz

Abstract

We derive an analytical expression for the fluctuation function of the detrended fluctuation analysis and state the relationship with the autocorrelation function for stationary processes. With this result we can investigate the scaling of the fluctuation function for short-range and long-range correlated processes. Furthermore we show that short-range correlated processes always exhibit a crossover between regions of different scaling. We also extend our results to processes with additive trends and discuss the effect of measurement noise. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Marc Höll & Holger Kantz, 2015. "The relationship between the detrendend fluctuation analysis and the autocorrelation function of a signal," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 88(12), pages 1-7, December.
    • Handle: RePEc:spr:eurphb:v:88:y:2015:i:12:p:1-7:10.1140/epjb/e2015-60721-1
    DOI: 10.1140/epjb/e2015-60721-1
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    Citations

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    Cited by:

    1. Bastien Berthelot & Eric Grivel & Pierrick Legrand & Audrey Giremus, 2021. "Definition of the fluctuation function in the detrended fluctuation analysis and its variants," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(11), pages 1-20, November.
    2. Stratimirovic, Djordje & Batas-Bjelic, Ilija & Djurdjevic, Vladimir & Blesic, Suzana, 2021. "Changes in long-term properties and natural cycles of the Danube river level and flow induced by damming," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    3. Igor Zyma & Sergii Tukaev & Ivan Seleznov & Ken Kiyono & Anton Popov & Mariia Chernykh & Oleksii Shpenkov, 2019. "Electroencephalograms during Mental Arithmetic Task Performance," Data, MDPI, vol. 4(1), pages 1-6, January.
    4. Yu, Zhongde & Huang, Yu & Fu, Zuntao, 2020. "Nonlinear strength quantifier based on phase correlation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
    5. Kiyono, Ken & Tsujimoto, Yutaka, 2016. "Nonlinear filtering properties of detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 807-815.
    6. Zhou, Yu & Leung, Yee & Chan, Lung Sang, 2017. "Oscillatory tendency of interevent direction in earthquake sequences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 478(C), pages 120-130.
    7. Pedro Carpena & Ana V. Coronado, 2022. "On the Autocorrelation Function of 1/ f Noises," Mathematics, MDPI, vol. 10(9), pages 1-12, April.
    8. Shen, Chenhua, 2017. "A comparison of principal components using TPCA and nonstationary principal component analysis on daily air-pollutant concentration series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 453-464.
    9. Gong, Huanhuan & Fu, Zuntao, 2022. "Beyond linear correlation: Strong nonlinear structures in diurnal temperature range variability over southern China," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

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    Keywords

    Statistical and Nonlinear Physics;

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