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Wavelet-based discrimination of isolated singularities masquerading as multifractals in detrended fluctuation analyses

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Listed:
  • Pawe{l} O'swik{e}cimka
  • Stanis{l}aw Dro.zd.z
  • Mattia Frasca
  • Robert Gk{e}barowski
  • Natsue Yoshimura
  • Luciano Zunino
  • Ludovico Minati

Abstract

The robustness of two widespread multifractal analysis methods, one based on detrended fluctuation analysis and one on wavelet leaders, is discussed in the context of time-series containing non-uniform structures with only isolated singularities. Signals generated by simulated and experimentally-realized chaos generators, together with synthetic data addressing particular aspects, are taken into consideration. The results reveal essential limitations affecting the ability of both methods to correctly infer the non-multifractal nature of signals devoid of a cascade-like hierarchy of singularities. Namely, signals harboring only isolated singularities are found to artefactually give rise to broad multifractal spectra, resembling those expected in the presence of a well-developed underlying multifractal structure. Hence, there is a real risk of incorrectly inferring multifractality due to isolated singularities. The careful consideration of local scaling properties and the distribution of H\"older exponent obtained, for example, through wavelet analysis, is indispensable for rigorously assessing the presence or absence of multifractality.

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  • Pawe{l} O'swik{e}cimka & Stanis{l}aw Dro.zd.z & Mattia Frasca & Robert Gk{e}barowski & Natsue Yoshimura & Luciano Zunino & Ludovico Minati, 2020. "Wavelet-based discrimination of isolated singularities masquerading as multifractals in detrended fluctuation analyses," Papers 2004.03319, arXiv.org.
    • Handle: RePEc:arx:papers:2004.03319
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    References listed on IDEAS

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    7. Morales Martínez, Jorge Luis & Segovia-Domínguez, Ignacio & Rodríguez, Israel Quiros & Horta-Rangel, Francisco Antonio & Sosa-Gómez, Guillermo, 2021. "A modified Multifractal Detrended Fluctuation Analysis (MFDFA) approach for multifractal analysis of precipitation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    8. Li Wang & Xing-Lu Gao & Wei-Xing Zhou, 2023. "Testing for intrinsic multifractality in the global grain spot market indices: A multifractal detrended fluctuation analysis," Papers 2306.10496, arXiv.org.
    9. Yang, Xiaodong & Wang, Zhixiao & He, Aijun & Wang, Jun, 2020. "Identification of healthy and pathological heartbeat dynamics based on ECG-waveform using multifractal spectrum," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 559(C).

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