IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v451y2016icp63-69.html
   My bibliography  Save this article

Evenly spacing in Detrended Fluctuation Analysis

Author

Listed:
  • Almurad, Zainy M.H.
  • Delignières, Didier

Abstract

Detrended Fluctuation Analysis is a widely used method, which aims at assessing the level of self-similarity in time series. This method analyzes the diffusion properties of the signal, by computing the linear regression slope in the diffusion plot, representing in log–log coordinates the relationship between the variability of the signal and the length of the intervals over which this variability is computed. We compare in this paper the results obtained with logarithmically spaced and evenly spaced diffusion plots. The study shows the substantial benefits of evenly spacing, especially in the reduction of the variability of estimation.

Suggested Citation

  • Almurad, Zainy M.H. & Delignières, Didier, 2016. "Evenly spacing in Detrended Fluctuation Analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 63-69.
  • Handle: RePEc:eee:phsmap:v:451:y:2016:i:c:p:63-69
    DOI: 10.1016/j.physa.2015.12.155
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437116000455
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

    File URL: https://libkey.io/10.1016/j.physa.2015.12.155?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Didier Delignières & Kjerstin Torre & Pierre-Louis Bernard, 2011. "Transition from Persistent to Anti-Persistent Correlations in Postural Sway Indicates Velocity-Based Control," PLOS Computational Biology, Public Library of Science, vol. 7(2), pages 1-10, February.
    2. Fernandez Viviana, 2011. "Alternative Estimators of Long-Range Dependence," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 15(2), pages 1-37, March.
    3. Amir Bashan & Ronny Bartsch & Jan W. Kantelhardt & Shlomo Havlin, 2008. "Comparison of detrending methods for fluctuation analysis," Papers 0804.4081, arXiv.org.
    4. Cannon, Michael J. & Percival, Donald B. & Caccia, David C. & Raymond, Gary M. & Bassingthwaighte, James B., 1997. "Evaluating scaled windowed variance methods for estimating the Hurst coefficient of time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 241(3), pages 606-626.
    5. Delignières, Didier & Marmelat, Vivien, 2014. "Strong anticipation and long-range cross-correlation: Application of detrended cross-correlation analysis to human behavioral data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 47-60.
    6. Caccia, David C. & Percival, Donald & Cannon, Michael J. & Raymond, Gary & Bassingthwaighte, James B., 1997. "Analyzing exact fractal time series: evaluating dispersional analysis and rescaled range methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 246(3), pages 609-632.
    7. Bashan, Amir & Bartsch, Ronny & Kantelhardt, Jan W. & Havlin, Shlomo, 2008. "Comparison of detrending methods for fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(21), pages 5080-5090.
    8. Raymond, Gary M. & Bassingthwaighte, James B., 1999. "Deriving dispersional and scaled windowed variance analyses using the correlation function of discrete fractional Gaussian noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 265(1), pages 85-96.
    9. Gates, Deanna H. & Su, Jimmy L. & Dingwell, Jonathan B., 2007. "Possible biomechanical origins of the long-range correlations in stride intervals of walking," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 380(C), pages 259-270.
    10. 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.
    11. Anastas, Jason R. & Stephen, Damian G. & Dixon, James A., 2011. "The scaling behavior of hand motions reveals self-organization during an executive function task," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(9), pages 1539-1545.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Okano, Masahiro & Kurebayashi, Wataru & Shinya, Masahiro & Kudo, Kazutoshi, 2019. "Hybrid dynamics in a paired rhythmic synchronization–continuation task," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 625-638.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Delignières, Didier & Marmelat, Vivien, 2014. "Strong anticipation and long-range cross-correlation: Application of detrended cross-correlation analysis to human behavioral data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 47-60.
    2. Hartmann, András & Mukli, Péter & Nagy, Zoltán & Kocsis, László & Hermán, Péter & Eke, András, 2013. "Real-time fractal signal processing in the time domain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(1), pages 89-102.
    3. Klaudia Kozlowska & Miroslaw Latka & Bruce J West, 2020. "Significance of trends in gait dynamics," PLOS Computational Biology, Public Library of Science, vol. 16(10), pages 1-25, October.
    4. Zhang, Feng & Ren, Hang & Miao, Lijuan & Lei, Yadong & Duan, Mingkeng, 2019. "Simulation of daily precipitation from CMIP5 in the Qinghai-Tibet Plateau," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 15, pages 68-74.
    5. Michalski, Sebastian, 2008. "Blocks adjustment—reduction of bias and variance of detrended fluctuation analysis using Monte Carlo simulation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(1), pages 217-242.
    6. Stavros-Richard G. Christopoulos & Nicholas V. Sarlis, 2017. "An Application of the Coherent Noise Model for the Prediction of Aftershock Magnitude Time Series," Complexity, Hindawi, vol. 2017, pages 1-27, February.
    7. Ni, Xiao-Hui & Jiang, Zhi-Qiang & Gu, Gao-Feng & Ren, Fei & Chen, Wei & Zhou, Wei-Xing, 2010. "Scaling and memory in the non-Poisson process of limit order cancelation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(14), pages 2751-2761.
    8. 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.
    9. Santos, José Vicente Cardoso & Perini, Noéle Bissoli & Moret, Marcelo Albano & Nascimento, Erick Giovani Sperandio & Moreira, Davidson Martins, 2021. "Scaling behavior of wind speed in the coast of Brazil and the South Atlantic Ocean: The crossover phenomenon," Energy, Elsevier, vol. 217(C).
    10. 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.
    11. Kembro, Jackelyn M. & Flesia, Ana Georgina & Gleiser, Raquel M. & Perillo, María A. & Marin, Raul H., 2013. "Assessment of long-range correlation in animal behavior time series: The temporal pattern of locomotor activity of Japanese quail (Coturnix coturnix) and mosquito larva (Culex quinquefasciatus)," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(24), pages 6400-6413.
    12. Rybski, Diego & Bunde, Armin, 2009. "On the detection of trends in long-term correlated records," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(8), pages 1687-1695.
    13. Mante, Claude, 2007. "Application of resampling and linear spline methods to spectral and dispersional analyses of long-memory processes," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4308-4323, May.
    14. 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).
    15. Gulich, Damián & Baglietto, Gabriel & Rozenfeld, Alejandro F., 2018. "Temporal correlations in the Vicsek model with vectorial noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 590-604.
    16. Hendrik J. Blok, 2000. "On the nature of the stock market: Simulations and experiments," Papers cond-mat/0010211, arXiv.org.
    17. Leonarduzzi, R. & Wendt, H. & Abry, P. & Jaffard, S. & Melot, C. & Roux, S.G. & Torres, M.E., 2016. "p-exponent and p-leaders, Part II: Multifractal analysis. Relations to detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 448(C), pages 319-339.
    18. Xiong, Gang & Yu, Wenxian & Zhang, Shuning, 2015. "Time-singularity multifractal spectrum distribution based on detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 351-366.
    19. 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.
    20. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:451:y:2016:i:c:p:63-69. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.