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Quantitative features of multifractal subtleties in time series

Author

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  • 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
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    2. 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.
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    4. 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).
    5. 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).
    6. Meo, Marcos M. & Iaconis, Francisco R. & Del Punta, Jessica A. & Delrieux, Claudio A. & Gasaneo, Gustavo, 2024. "Multifractal information on reading eye tracking data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 638(C).
    7. Sierra-Porta, D., 2024. "A multifractal approach to understanding Forbush Decrease events: Correlations with geomagnetic storms and space weather phenomena," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    8. Marcin Wk{a}torek & Marcin Kr'olczyk & Jaros{l}aw Kwapie'n & Tomasz Stanisz & Stanis{l}aw Dro.zd.z, 2024. "Approaching multifractal complexity in decentralized cryptocurrency trading," Papers 2411.05951, arXiv.org.
    9. 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.
    10. 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).
    11. 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).
    12. Kelty-Stephen, Damian G. & Mangalam, Madhur, 2024. "Additivity suppresses multifractal nonlinearity due to multiplicative cascade dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 637(C).
    13. 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).
    14. 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).
    15. 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).
    16. R. P. Datta, 2023. "Analysis of Indian foreign exchange markets: A Multifractal Detrended Fluctuation Analysis (MFDFA) approach," Papers 2306.16162, arXiv.org.
    17. 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).
    18. Kristjanpoller, Werner & Nekhili, Ramzi & Bouri, Elie, 2024. "Blockchain ETFs and the cryptocurrency and Nasdaq markets: Multifractal and asymmetric cross-correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 637(C).

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