IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v392y2013i23p5845-5864.html
   My bibliography  Save this article

On the multifractal effects generated by monofractal signals

Author

Listed:
  • Grech, Dariusz
  • Pamuła, Grzegorz

Abstract

We study quantitatively the level of false multifractal signal one may encounter while analyzing multifractal phenomena in time series within multifractal detrended fluctuation analysis (MF-DFA). The investigated effect appears as a result of finite length of used data series and is additionally amplified by the long-term memory the data eventually may contain. We provide the detailed quantitative description of such apparent multifractal background signal as a threshold in spread of generalized Hurst exponent values Δh or a threshold in the width of multifractal spectrum Δα below which multifractal properties of the system are only apparent, i.e. do not exist, despite Δα≠0 or Δh≠0. We find this effect quite important for shorter or persistent series and we argue it is linear with respect to autocorrelation exponent γ. Its strength decays according to power law with respect to the length of time series. The influence of basic linear and nonlinear transformations applied to initial data in finite time series with various levels of long memory is also investigated. This provides additional set of semi-analytical results. The obtained formulas are significant in any interdisciplinary application of multifractality, including physics, financial data analysis or physiology, because they allow to separate the ‘true’ multifractal phenomena from the apparent (artificial) multifractal effects. They should be a helpful tool of the first choice to decide whether we do in particular case with the signal with real multiscaling properties or not.

Suggested Citation

  • Grech, Dariusz & Pamuła, Grzegorz, 2013. "On the multifractal effects generated by monofractal signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(23), pages 5845-5864.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:23:p:5845-5864
    DOI: 10.1016/j.physa.2013.07.045
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437113006559
    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.2013.07.045?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.

    Citations

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


    Cited by:

    1. Chen, Feier & Tian, Kang & Ding, Xiaoxu & Miao, Yuqi & Lu, Chunxia, 2016. "Finite-size effect and the components of multifractality in transport economics volatility based on multifractal detrending moving average method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 1058-1066.
    2. Kukacka, Jiri & Kristoufek, Ladislav, 2020. "Do ‘complex’ financial models really lead to complex dynamics? Agent-based models and multifractality," Journal of Economic Dynamics and Control, Elsevier, vol. 113(C).
    3. Schadner, Wolfgang, 2022. "U.S. Politics from a multifractal perspective," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    4. Olivares, Felipe & Sun, Xiaoqian & Wandelt, Sebastian & Zanin, Massimiliano, 2023. "Measuring landing independence and interactions using statistical physics," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 170(C).
    5. 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.
    6. Olivares, Felipe & Zanin, Massimiliano, 2022. "Corrupted bifractal features in finite uncorrelated power-law distributed data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    7. Sarker, Alivia & Mali, Provash, 2021. "Detrended multifractal characterization of Indian rainfall records," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    8. Hongtao Chang & Rui Ren & Yaqiong Wang & Jiaqi Li, 2022. "Evaluation of Air Pollutants in Extra-Long Road Tunnel with the Combination of Pollutants Nonlinear Evolution and Machine Learning Method," Sustainability, MDPI, vol. 14(17), pages 1-20, August.
    9. Zhuang, Xiaoyang & Wei, Dan, 2022. "Asymmetric multifractality, comparative efficiency analysis of green finance markets: A dynamic study by index-based model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 604(C).
    10. Marcin Wk{a}torek & Stanis{l}aw Dro.zd.z & Jaros{l}aw Kwapie'n & Ludovico Minati & Pawe{l} O'swik{e}cimka & Marek Stanuszek, 2020. "Multiscale characteristics of the emerging global cryptocurrency market," Papers 2010.15403, arXiv.org, revised Mar 2021.
    11. Li, Tingyi & Xue, Leyang & Chen, Yu & Chen, Feier & Miao, Yuqi & Shao, Xinzeng & Zhang, Chenyi, 2018. "Insights from multifractality analysis of tanker freight market volatility with common external factor of crude oil price," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 374-384.
    12. Schadner, Wolfgang, 2021. "On the persistence of market sentiment: A multifractal fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).

    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:392:y:2013:i:23:p:5845-5864. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.