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Fourier-detrended fluctuation analysis

Author

Listed:
  • Chianca, C.V.
  • Ticona, A.
  • Penna, T.J.P.

Abstract

Many features of natural phenomena can be observed using time records or series of observations. The time records of phenomena such as physiological and economic data or the temperature of a river can display short- and long-term time scales. These signals can also present trends which are an important aspect of their complexity. These trends can lead to difficulties in the analysis of the signals. In this short note we suggest a modified approach for the analysis of low frequency trends added to a noise in time series. We will name this method Fourier-detrended fluctuation analysis, but it is a simple high-pass filter. Using this approach, we will attempt to quantify correlations with trends in a time series. By cutting the first few coefficients of a Fourier expansion, we show that we are able to efficiently remove the globally varying trends.

Suggested Citation

  • Chianca, C.V. & Ticona, A. & Penna, T.J.P., 2005. "Fourier-detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 357(3), pages 447-454.
    • Handle: RePEc:eee:phsmap:v:357:y:2005:i:3:p:447-454
    DOI: 10.1016/j.physa.2005.03.047
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    Citations

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    Cited by:

    1. Lavička, Hynek & Kracík, Jiří, 2020. "Fluctuation analysis of electric power loads in Europe: Correlation multifractality vs. Distribution function multifractality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    2. Sarker, Alivia & Mali, Provash, 2021. "Detrended multifractal characterization of Indian rainfall records," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    3. Zhao, Xiaojun & Shang, Pengjian & Zhao, Chuang & Wang, Jing & Tao, Rui, 2012. "Minimizing the trend effect on detrended cross-correlation analysis with empirical mode decomposition," Chaos, Solitons & Fractals, Elsevier, vol. 45(2), pages 166-173.
    4. Zhao, Xiaojun & Shang, Pengjian & Lin, Aijing & Chen, Gang, 2011. "Multifractal Fourier detrended cross-correlation analysis of traffic signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(21), pages 3670-3678.
    5. Alvarez-Ramirez, J. & Rodriguez, E., 2018. "AR(p)-based detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 49-57.
    6. Shen, Chen-hua & Huang, Yi & Yan, Ya-ni, 2016. "An analysis of multifractal characteristics of API time series in Nanjing, China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 171-179.
    7. 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.
    8. Xiaohui Yuan & Bin Ji & Hao Tian & Yuehua Huang, 2014. "Multiscaling Analysis of Monthly Runoff Series Using Improved MF-DFA Approach," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(12), pages 3891-3903, September.
    9. Qian, Xi-Yuan & Gu, Gao-Feng & Zhou, Wei-Xing, 2011. "Modified detrended fluctuation analysis based on empirical mode decomposition for the characterization of anti-persistent processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4388-4395.
    10. Wang, Fang & Liao, Gui-ping & Li, Jian-hui & Li, Xiao-chun & Zhou, Tie-jun, 2013. "Multifractal detrended fluctuation analysis for clustering structures of electricity price periods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(22), pages 5723-5734.
    11. Wu, Liang & Chen, Lei & Ding, Yiming & Zhao, Tongzhou, 2018. "Testing for the source of multifractality in water level records," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 824-839.
    12. Mali, Provash & Mukhopadhyay, Amitabha & Singh, Gurmukh, 2016. "Multifractal detrended moving average analysis of particle density functions in relativistic nuclear collisions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 323-332.
    13. Jamshid Ardalankia & Mohammad Osoolian & Emmanuel Haven & G. Reza Jafari, 2019. "Scaling Features of Price-Volume Cross-Correlation," Papers 1903.01744, arXiv.org, revised Aug 2020.
    14. Yin, Yi & Wang, Xi & Li, Qiang & Shang, Pengjian, 2020. "Generalized multivariate multiscale sample entropy for detecting the complexity in complex systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).

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