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Cascade-Driven Series with Narrower Multifractal Spectra Than Their Surrogates: Standard Deviation of Multipliers Changes Interactions across Scales

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  • Jun Taek Lee
  • Damian G. Kelty-Stephen

Abstract

Multifractal (or singularity) spectra widths allow diagnosing cascade structure through comparing original series’ widths to surrogate series’ widths . However, interpretations of have been ambiguous. Stochastic multipliers generate cascades with by diversifying cross-scale interactions using white-noise multipliers. Multifractal detrended fluctuation analysis (MF-DFA) and Chhabra and Jensen’s method provided two estimates of for 200 simulated series at each value incrementing by 0.05. Increasing σ draws away from and towards for both methods but more for MF-DFA. indicates cascades with cross-scale interactions more diverse than in cascades with .

Suggested Citation

  • Jun Taek Lee & Damian G. Kelty-Stephen, 2017. "Cascade-Driven Series with Narrower Multifractal Spectra Than Their Surrogates: Standard Deviation of Multipliers Changes Interactions across Scales," Complexity, Hindawi, vol. 2017, pages 1-8, January.
    • Handle: RePEc:hin:complx:7015243
    DOI: 10.1155/2017/7015243
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    References listed on IDEAS

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    1. Zhou, Wei-Xing, 2012. "Finite-size effect and the components of multifractality in financial volatility," Chaos, Solitons & Fractals, Elsevier, vol. 45(2), pages 147-155.
    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. Stephen, Damian G. & Dixon, James A., 2011. "Strong anticipation: Multifractal cascade dynamics modulate scaling in synchronization behaviors," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 160-168.
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    Cited by:

    1. Damian G Kelty-Stephen, 2018. "Multifractal evidence of nonlinear interactions stabilizing posture for phasmids in windy conditions: A reanalysis of insect postural-sway data," PLOS ONE, Public Library of Science, vol. 13(8), pages 1-21, August.
    2. 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.
    3. Kelty-Stephen, Damian G., 2017. "Threading a multifractal social psychology through within-organism coordination to within-group interactions: A tale of coordination in three acts," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 363-370.

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