IDEAS home Printed from https://ideas.repec.org/p/arx/papers/0907.2866.html
   My bibliography  Save this paper

Quantitative features of multifractal subtleties in time series

Author

Listed:
  • Stanislaw Drozdz
  • Jaroslaw Kwapien
  • Pawel Oswiecimka
  • Rafal Rak

Abstract

Based on the Multifractal Detrended Fluctuation Analysis (MFDFA) and on the Wavelet Transform Modulus Maxima (WTMM) methods we investigate the origin of multifractality in the time series. Series fluctuating according to a qGaussian distribution, both uncorrelated and correlated in time, are used. For the uncorrelated series at the border (q=5/3) between the Gaussian and the Levy basins of attraction asymptotically we find a phase-like transition between monofractal and bifractal characteristics. This indicates that these may solely be the specific nonlinear temporal correlations that organize the series into a genuine multifractal hierarchy. For analyzing various features of multifractality due to such correlations, we use the model series generated from the binomial cascade as well as empirical series. Then, within the temporal ranges of well developed power-law correlations we find a fast convergence in all multifractal measures. Besides of its practical significance this fact may reflect another manifestation of a conjectured q-generalized Central Limit Theorem.

Suggested Citation

  • Stanislaw Drozdz & Jaroslaw Kwapien & Pawel Oswiecimka & Rafal Rak, 2009. "Quantitative features of multifractal subtleties in time series," Papers 0907.2866, arXiv.org, revised Feb 2010.
    • Handle: RePEc:arx:papers:0907.2866
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/0907.2866
    File Function: Latest version
    Download Restriction: no
    ---><---

    Citations

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


    Cited by:

    1. Liu, Chenggong & Shang, Pengjian & Feng, Guochen, 2017. "The high order dispersion analysis based on first-passage-time probability in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 1-9.
    2. Aloui, Chaker & Shahzad, Syed Jawad Hussain & Jammazi, Rania, 2018. "Dynamic efficiency of European credit sectors: A rolling-window multifractal detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 337-349.
    3. López, J.L. & Veleva, L., 2022. "2D-DFA as a tool for non-destructive characterisation of copper surface exposed to substitute ocean water," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 586(C).
    4. Zhan, Cun & Liang, Chuan & Zhao, Lu & Jiang, Shouzheng & Niu, Kaijie & Zhang, Yaling, 2023. "Multifractal characteristics of multiscale drought in the Yellow River Basin, China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    5. 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.
    6. Li, Shuping & Li, Jianfeng & Lu, Xinsheng & Sun, Yihong, 2022. "Exploring the dynamic nonlinear relationship between crude oil price and implied volatility indices: A new perspective from MMV-MFDFA," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    7. Kristjanpoller, Werner & Minutolo, Marcel C., 2021. "Asymmetric multi-fractal cross-correlations of the price of electricity in the US with crude oil and the natural gas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).
    8. 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).
    9. Nag, Sayan & Basu, Medha & Sanyal, Shankha & Banerjee, Archi & Ghosh, Dipak, 2022. "On the application of deep learning and multifractal techniques to classify emotions and instruments using Indian Classical Music," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).
    10. Wang, Jian & Jiang, Wenjing & Wu, Xinpei & Yang, Mengdie & Shao, Wei, 2023. "Role of vaccine in fighting the variants of COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    11. R. P. Datta, 2023. "Analysis of Indian foreign exchange markets: A Multifractal Detrended Fluctuation Analysis (MFDFA) approach," Papers 2306.16162, arXiv.org.
    12. Choi, Sun-Yong, 2021. "Analysis of stock market efficiency during crisis periods in the US stock market: Differences between the global financial crisis and COVID-19 pandemic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 574(C).

    More about this item

    Statistics

    Access and download statistics

    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:arx:papers:0907.2866. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.