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On spurious and corrupted multifractality: The effects of additive noise, short-term memory and periodic trends

Author

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  • Ludescher, Josef
  • Bogachev, Mikhail I.
  • Kantelhardt, Jan W.
  • Schumann, Aicko Y.
  • Bunde, Armin

Abstract

We study the performance of multifractal detrended fluctuation analysis (MF-DFA) applied to long-term correlated and multifractal data records in the presence of additive white noise, short-term memory and periodicities. Such additions and disturbances that can be typically found in the observational records of various complex systems ranging from climate dynamics to physiology, network traffic, and finance. In monofractal records, we find that (i) additive white noise hardly results in spurious multifractality, but causes underestimated generalized Hurst exponents h(q) for all q values; (ii) short-range correlations lead to pronounced crossovers in the generalized fluctuation functions Fq(s) at positions that decrease with increasing moment q, thus causing significantly overestimated h(q) for small q and spurious multifractality; (iii) periodicities like seasonal trends (with standard deviations comparable with the one of the studied process) result in spurious “reversed” multifractality where h(q) increases with increasing q (except for very short time windows). We also show that in multifractal cascades moderate additions of noise, short-range memory, or periodic trends cause flawed results for h(q) with q<2, while h(q) with q>2 remains nearly unchanged.

Suggested Citation

  • Ludescher, Josef & Bogachev, Mikhail I. & Kantelhardt, Jan W. & Schumann, Aicko Y. & Bunde, Armin, 2011. "On spurious and corrupted multifractality: The effects of additive noise, short-term memory and periodic trends," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(13), pages 2480-2490.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:13:p:2480-2490
    DOI: 10.1016/j.physa.2011.03.008
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    Cited by:

    1. Sarker, Alivia & Mali, Provash, 2021. "Detrended multifractal characterization of Indian rainfall records," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    2. Krenar Avdulaj & Ladislav Kristoufek, 2020. "On Tail Dependence and Multifractality," Mathematics, MDPI, vol. 8(10), pages 1-13, October.
    3. Ruan, Qingsong & Zhou, Mi & Yin, Linsen & Lv, Dayong, 2021. "Hedging effectiveness of Chinese Treasury bond futures: New evidence based on nonlinear analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    4. Cristina Sattarhoff & Marc Gronwald, 2018. "How to Measure Financial Market Efficiency? A Multifractality-Based Quantitative Approach with an Application to the European Carbon Market," CESifo Working Paper Series 7102, CESifo.
    5. Shen, Chen-hua & Huang, Yi & Yan, Ya-ni, 2016. "An analysis of multifractal characteristics of API time series in Nanjing, China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 171-179.
    6. 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.
    7. 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.
    8. Stan, Cristina & Cristescu, Cristina Maria & Alexandroaei, D. & Cristescu, C.P., 2014. "The effect of Gaussian white noise on the fractality of fluctuations in the plasma of a symmetrical discharge," Chaos, Solitons & Fractals, Elsevier, vol. 61(C), pages 46-55.
    9. Jovanovic, Tijana & Mejía, Alfonso & Gall, Heather & Gironás, Jorge, 2016. "Effect of urbanization on the long-term persistence of streamflow records," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 208-221.
    10. Gulich, Damián & Baglietto, Gabriel & Rozenfeld, Alejandro F., 2018. "Temporal correlations in the Vicsek model with vectorial noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 590-604.
    11. Gulich, Damián & Zunino, Luciano, 2012. "The effects of observational correlated noises on multifractal detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(16), pages 4100-4110.
    12. Balkissoon, Sarah & Fox, Neil & Lupo, Anthony, 2020. "Fractal characteristics of tall tower wind speeds in Missouri," Renewable Energy, Elsevier, vol. 154(C), pages 1346-1356.
    13. Olivares, Felipe & Sun, Xiaoqian & Wandelt, Sebastian & Zanin, Massimiliano, 2023. "Measuring landing independence and interactions using statistical physics," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 170(C).
    14. Paradisi, Paolo & Allegrini, Paolo, 2015. "Scaling law of diffusivity generated by a noisy telegraph signal with fractal intermittency," Chaos, Solitons & Fractals, Elsevier, vol. 81(PB), pages 451-462.
    15. Stan, Cristina & Marmureanu, Luminita & Marin, Cristina & Cristescu, Constantin P., 2020. "Investigation of multifractal cross-correlation surfaces of Hurst exponents for some atmospheric pollutants," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    16. Mukli, Peter & Nagy, Zoltan & Eke, Andras, 2015. "Multifractal formalism by enforcing the universal behavior of scaling functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 417(C), pages 150-167.
    17. 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).

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