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Detrending fluctuation analysis based on moving average filtering

Author

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  • Alvarez-Ramirez, Jose
  • Rodriguez, Eduardo
  • Carlos Echeverría, Juan

Abstract

Detrended fluctuation analysis (DFA) is a scaling method commonly used for detecting long-range correlations in nonstationary time series. Applications range from financial time series to physiological data. However, as the removal of trends in DFA is based on discontinuous polynomial fitting, oscillations in the fluctuation function and significant errors in crossover locations can be introduced. To reduce the problems induced by discontinuous fitting, moving average (MA) methods have been proposed previously by Alesio et al. (Eur. J. Phys. B 27 (2002) 197). In this work, a variant of such MA methods is studied; specifically, the performance and characteristics of a MA method based on central differences is studied. Some important properties of this MA method are analyzed and illustrated with several artificial and real time series.

Suggested Citation

  • Alvarez-Ramirez, Jose & Rodriguez, Eduardo & Carlos Echeverría, Juan, 2005. "Detrending fluctuation analysis based on moving average filtering," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 199-219.
    • Handle: RePEc:eee:phsmap:v:354:y:2005:i:c:p:199-219
    DOI: 10.1016/j.physa.2005.02.020
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    Cited by:

    1. Xiong, Gang & Zhang, Shuning & Yang, Xiaoniu, 2012. "The fractal energy measurement and the singularity energy spectrum analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6347-6361.
    2. Tong, Shanbao & Jiang, Dineng & Wang, Ziming & Zhu, Yisheng & Geocadin, Romeryko G. & Thakor, Nitish V., 2007. "Long range correlations in the heart rate variability following the injury of cardiac arrest," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 380(C), pages 250-258.
    3. Schumann, Aicko Y. & Kantelhardt, Jan W., 2011. "Multifractal moving average analysis and test of multifractal model with tuned correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(14), pages 2637-2654.
    4. Kristoufek, Ladislav, 2010. "On spurious anti-persistence in the US stock indices," Chaos, Solitons & Fractals, Elsevier, vol. 43(1), pages 68-78.
    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. Kristoufek, Ladislav, 2009. "R/S analysis and DFA: finite sample properties and confidence intervals," MPRA Paper 16446, University Library of Munich, Germany.
    7. Xiong, Gang & Zhang, Shuning & Liu, Qiang, 2012. "The time-singularity multifractal spectrum distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(20), pages 4727-4739.
    8. Gulich, Damián & Zunino, Luciano, 2014. "A criterion for the determination of optimal scaling ranges in DFA and MF-DFA," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 397(C), pages 17-30.
    9. Kristoufek, Ladislav, 2009. "Procesy s dlouhou pamětí a jejich vývoj ve výnosech indexu PX v letech 1999 – 2009 [Long-term memory and its evolution in returns of PX between 1999 and 2009]," MPRA Paper 16435, University Library of Munich, Germany.
    10. Ladislav Krištoufek, 2010. "Dlouhá paměť a její vývoj ve výnosech burzovního indexu PX v letech 1997-2009 [Long-Term Memory and Its Evolution in Returns of Stock Index PX Between 1997 and 2009]," Politická ekonomie, Prague University of Economics and Business, vol. 2010(4), pages 471-487.
    11. Barunik, Jozef & Kristoufek, Ladislav, 2010. "On Hurst exponent estimation under heavy-tailed distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(18), pages 3844-3855.
    12. Zhongxing Wang & Yan Yan & Xiaosong Chen, 2016. "Long-range Correlation and Market Segmentation in Bond Market," Papers 1610.09812, arXiv.org.
    13. Xiong, Gang & Yu, Wenxian & Zhang, Shuning, 2015. "Singularity power spectrum distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 431(C), pages 63-73.
    14. Gómez-Águila, A. & Sánchez-Granero, M.A., 2021. "A theoretical framework for the TTA algorithm," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 582(C).
    15. 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.
    16. Fernandez Viviana, 2011. "Alternative Estimators of Long-Range Dependence," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 15(2), pages 1-37, March.
    17. Kristoufek, Ladislav, 2019. "Are the crude oil markets really becoming more efficient over time? Some new evidence," Energy Economics, Elsevier, vol. 82(C), pages 253-263.
    18. Ladislav Krištoufek, 2010. "Rescaled Range Analysis and Detrended Fluctuation Analysis: Finite Sample Properties and Confidence Intervals," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 4(3), pages 315-329, November.
    19. 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.
    20. Wang, Zhongxing & Yan, Yan & Chen, Xiaosong, 2017. "Long-range correlation and market segmentation in bond market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 477-485.

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