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Multifractal spectrum distribution based on detrending moving average

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  • Xiong, Gang
  • Zhang, Shuning
  • Zhao, Huichang

Abstract

The time-singularity multifractal spectrum distribution (MFSD) has been proposed recently as a generalized singularity spectrum in a time varying framework. In this paper, we aim at putting forward a new algorithm i.e. MFSD based on detrending moving average (DMA-MFSD) to determine MFSD, which is also a generalization of multifractal detrending moving average (MF-DMA) method. We relate DMA-MFSD method to the MFSD based on the standard partition function, and prove that both approaches are equivalent for fractal time series with compact support. The performance of the DMA-MFSD methods with different moving windows is studied using synthetic fractional Gaussian noise (fGn), binomial multiplicative cascades (BMC) with analytical solutions and real sea clutter data. We find that the estimated DMA-MFSD is in good accordance with the detrended fluctuation analysis based multifractal spectrum distribution (DFA-MFSD) and the theoretical analysis. Overall, the backward DMA-MFSD method has the best performance, which provides the most accurate estimates of the time-singularity MFSD, while the centered DMA-MFSD method performs worse. In addition we find that the backward DMA-MFSD algorithm even outperforms the DFA-MFSD method in the computational complexity and precision.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:65:y:2014:i:c:p:97-110
    DOI: 10.1016/j.chaos.2014.04.015
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Gao-Feng Gu & Wei-Xing Zhou, 2010. "Detrending moving average algorithm for multifractals," Papers 1005.0877, arXiv.org, revised Jun 2010.
    4. Wei-Xing Zhou, 2008. "Multifractal detrended cross-correlation analysis for two nonstationary signals," Papers 0803.2773, arXiv.org.
    5. 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.
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    Cited by:

    1. Xiong, Gang & Xiong, Ziqin & Jia, Liqiong & Truong, Trieu-Kien, 2023. "Spatial multifractal spectrum distribution method for breast ultrasonic image classification," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
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    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).

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