IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v391y2012i20p4727-4739.html
   My bibliography  Save this article

The time-singularity multifractal spectrum distribution

Author

Listed:
  • Xiong, Gang
  • Zhang, Shuning
  • Liu, Qiang

Abstract

Although the multifractal singularity spectrum revealed the distribution of singularity exponent, it failed to consider the temporal information, therefore it is hard to describe the dynamic evolving process of non-stationary and nonlinear systems. In this paper, we aim for a multifractal analysis and propose a time-singularity multifractal spectrum distribution (TS-MFSD), which will hopefully reveal the spatial dynamic character of fractal systems. Similar to the Wigner–Ville time-frequency distribution, the time-delayed conjugation of fractal signals is selected as the windows function. Furthermore, the time-varying Holder exponent and the time-varying wavelet singularity exponent are deduced based on the instantaneous self-correlation fractal signal. The time-singularity exponent distribution i.e. TS-MFSD is proposed, which involves time-varying Hausdorff singularity spectrum distribution, time-varying large deviation multifractal spectrum and time-varying Legendre spectrum distribution, which exhibit the singularity exponent distribution of fractal signal at arbitrary time. Finally, we studied the algorithm of the TS-MFSD based on the wavelet transform module maxima method, analyzed and discussed the characteristic of TS-MFSD based on Devil Staircase signal, stochastic fractional motion and real sea clutter.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:20:p:4727-4739
    DOI: 10.1016/j.physa.2012.05.026
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437112003974
    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.2012.05.026?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. Telesca, Luciano & Lapenna, Vincenzo & Macchiato, Maria, 2005. "Multifractal fluctuations in seismic interspike series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 629-640.
    2. Stanley, H.E & Amaral, L.A.N & Gopikrishnan, P & Ivanov, P.Ch & Keitt, T.H & Plerou, V, 2000. "Scale invariance and universality: organizing principles in complex systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 281(1), pages 60-68.
    3. B. Lashermes & S. G. Roux & P. Abry & S. Jaffard, 2008. "Comprehensive multifractal analysis of turbulent velocity using the wavelet leaders," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 61(2), pages 201-215, January.
    4. Amir Bashan & Ronny Bartsch & Jan W. Kantelhardt & Shlomo Havlin, 2008. "Comparison of detrending methods for fluctuation analysis," Papers 0804.4081, arXiv.org.
    5. Kantelhardt, Jan W. & Zschiegner, Stephan A. & Koscielny-Bunde, Eva & Havlin, Shlomo & Bunde, Armin & Stanley, H.Eugene, 2002. "Multifractal detrended fluctuation analysis of nonstationary time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 87-114.
    6. Stanley, H.E. & Afanasyev, V. & Amaral, L.A.N. & Buldyrev, S.V. & Goldberger, A.L. & Havlin, S. & Leschhorn, H. & Maass, P. & Mantegna, R.N. & Peng, C.-K. & Prince, P.A. & Salinger, M.A. & Stanley, M., 1996. "Anomalous fluctuations in the dynamics of complex systems: from DNA and physiology to econophysics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 224(1), pages 302-321.
    7. 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.
    8. 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.
    9. 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.
    10. Castro e Silva, A. & Moreira, J.G., 1997. "Roughness exponents to calculate multi-affine fractal exponents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 235(3), pages 327-333.
    11. Peng, C.-K. & Buldyrev, S.V. & Goldberger, A.L. & Havlin, S. & Mantegna, R.N. & Simons, M. & Stanley, H.E., 1995. "Statistical properties of DNA sequences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 221(1), pages 180-192.
    12. Zunino, L. & Tabak, B.M. & Figliola, A. & Pérez, D.G. & Garavaglia, M. & Rosso, O.A., 2008. "A multifractal approach for stock market inefficiency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(26), pages 6558-6566.
    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. Lahmiri, Salim, 2017. "Multifractal analysis of Moroccan family business stock returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 183-191.
    2. Liu, Jie & Li, Qiuping & Wang, Xiaoran & Wang, Zaiquan & Lu, Shouqing & Sa, Zhanyou & Wang, Hao, 2022. "Dynamic multifractal characteristics of acoustic emission about composite coal-rock samples with different strength rock," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    3. Xi, Caiping & Zhang, Shunning & Xiong, Gang & Zhao, Huichang, 2016. "A comparative study of two-dimensional multifractal detrended fluctuation analysis and two-dimensional multifractal detrended moving average algorithm to estimate the multifractal spectrum," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 454(C), pages 34-50.
    4. Shen, Na & Chen, Jiayi, 2023. "Asymmetric multifractal spectrum distribution based on detrending moving average cross-correlation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 615(C).
    5. 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.
    6. Xiong, Gang & Zhang, Shuning & Zhao, Huichang, 2014. "Multifractal spectrum distribution based on detrending moving average," Chaos, Solitons & Fractals, Elsevier, vol. 65(C), pages 97-110.

    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. Serrano, E. & Figliola, A., 2009. "Wavelet Leaders: A new method to estimate the multifractal singularity spectra," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(14), pages 2793-2805.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Dashtian, Hassan & Jafari, G. Reza & Sahimi, Muhammad & Masihi, Mohsen, 2011. "Scaling, multifractality, and long-range correlations in well log data of large-scale porous media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(11), pages 2096-2111.
    7. Stavroyiannis, Stavros & Babalos, Vassilios & Bekiros, Stelios & Lahmiri, Salim & Uddin, Gazi Salah, 2019. "The high frequency multifractal properties of Bitcoin," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 62-71.
    8. 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.
    9. 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.
    10. Ruan, Yong-Ping & Zhou, Wei-Xing, 2011. "Long-term correlations and multifractal nature in the intertrade durations of a liquid Chinese stock and its warrant," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(9), pages 1646-1654.
    11. Gulich, Damián & Zunino, Luciano, 2012. "The effects of observational correlated noises on multifractal detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(16), pages 4100-4110.
    12. Xue Pan & Lei Hou & Mutua Stephen & Huijie Yang & Chenping Zhu, 2014. "Evaluation of Scaling Invariance Embedded in Short Time Series," PLOS ONE, Public Library of Science, vol. 9(12), pages 1-27, December.
    13. Jiang, Zhi-Qiang & Xie, Wen-Jie & Zhou, Wei-Xing, 2014. "Testing the weak-form efficiency of the WTI crude oil futures market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 235-244.
    14. Wang, Lei & Liu, Lutao, 2020. "Long-range correlation and predictability of Chinese stock prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    15. Maiorino, Enrico & Livi, Lorenzo & Giuliani, Alessandro & Sadeghian, Alireza & Rizzi, Antonello, 2015. "Multifractal characterization of protein contact networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 428(C), pages 302-313.
    16. 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.
    17. Fernandez Viviana, 2011. "Alternative Estimators of Long-Range Dependence," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 15(2), pages 1-37, March.
    18. 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.
    19. 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.
    20. 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.

    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:391:y:2012:i:20:p:4727-4739. 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.