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Beyond Benford's Law: Distinguishing Noise from Chaos

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  • Qinglei Li
  • Zuntao Fu
  • Naiming Yuan

Abstract

Determinism and randomness are two inherent aspects of all physical processes. Time series from chaotic systems share several features identical with those generated from stochastic processes, which makes them almost undistinguishable. In this paper, a new method based on Benford's law is designed in order to distinguish noise from chaos by only information from the first digit of considered series. By applying this method to discrete data, we confirm that chaotic data indeed can be distinguished from noise data, quantitatively and clearly.

Suggested Citation

  • Qinglei Li & Zuntao Fu & Naiming Yuan, 2015. "Beyond Benford's Law: Distinguishing Noise from Chaos," PLOS ONE, Public Library of Science, vol. 10(6), pages 1-11, June.
    • Handle: RePEc:plo:pone00:0129161
    DOI: 10.1371/journal.pone.0129161
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    References listed on IDEAS

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    1. P.-M. Binder & R. M. Pipes, 2014. "How chaos forgets and remembers," Nature, Nature, vol. 510(7505), pages 343-344, June.
    2. Chih-hao Hsieh & Sarah M. Glaser & Andrew J. Lucas & George Sugihara, 2005. "Distinguishing random environmental fluctuations from ecological catastrophes for the North Pacific Ocean," Nature, Nature, vol. 435(7040), pages 336-340, May.
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    Cited by:

    1. Whyman, G. & Ohtori, N. & Shulzinger, E. & Bormashenko, Ed., 2016. "Revisiting the Benford law: When the Benford-like distribution of leading digits in sets of numerical data is expectable?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 595-601.
    2. Wang, Fang & Wang, Lin & Chen, Yuming, 2022. "Multi-affine visible height correlation analysis for revealing rich structures of fractal time series," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    3. Ausloos, Marcel & Castellano, Rosella & Cerqueti, Roy, 2016. "Regularities and discrepancies of credit default swaps: a data science approach through Benford's law," Chaos, Solitons & Fractals, Elsevier, vol. 90(C), pages 8-17.
    4. Alexandre Donizeti Alves & Horacio Hideki Yanasse & Nei Yoshihiro Soma, 2016. "An analysis of bibliometric indicators to JCR according to Benford’s law," Scientometrics, Springer;Akadémiai Kiadó, vol. 107(3), pages 1489-1499, June.
    5. Fu, Shu & Huang, Yu & Feng, Tao & Nian, Da & Fu, Zuntao, 2019. "Regional contrasting DTR’s predictability over China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 282-292.
    6. da Silva, A.J. & Floquet, S. & Santos, D.O.C. & Lima, R.F., 2020. "On the validation of the Newcomb−Benford Law and the Weibull distribution in neuromuscular transmission," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).

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