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Multiscale multifractal detrended fluctuation analysis of multivariate time series

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  • Fan, Qingju
  • Liu, Shuanggui
  • Wang, Kehao

Abstract

This work extends the multivariate multifractal detrended fluctuation analysis(MV-MFDFA) method to multiscale case, named multiscale multivariate multifractal detrended fluctuation analysis (MMV-MFDFA). The benefits of the proposed approach are illustrated by numerical simulations on synthetic multivariate processes. Furthermore, the proposed MMV-MFDFA method is applied to the fractal auto-correlation analysis of six pollutants’ (PM2.5, PM10, SO2, NO2, CO and O3) hourly data in different seasons. The results show that the seasonal periodicity has robust impact on the auto-correlation of pollutants in spring and summer. Besides, we also find that the pollutants in the four seasons possess strong multifractal auto-correlation nature, even after the removal of the seasonal pattern. Finally, the source of multifractality among more than two series is also discussed, and some interesting results are obtained. PM2.5 not only dominates the underlying evolution process in fall and winter, but also is more correlated to the other pollutants than the other ones to each other except in spring. The proposed MMV-MFDFA methodology can provide reliable ways of measuring the fractal auto-correlation properties of multivariate series, and it can be applied to any system with multiple data channels.

Suggested Citation

  • Fan, Qingju & Liu, Shuanggui & Wang, Kehao, 2019. "Multiscale multifractal detrended fluctuation analysis of multivariate time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 532(C).
    • Handle: RePEc:eee:phsmap:v:532:y:2019:i:c:s0378437119310921
    DOI: 10.1016/j.physa.2019.121864
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    Citations

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    Cited by:

    1. Gui, Jun & Zheng, Zeyu & Fu, Dianzheng & Fu, Yang & Liu, Zhi, 2021. "Long-term correlations and multifractality of toll-free calls in China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    2. Vogl, Markus, 2023. "Hurst exponent dynamics of S&P 500 returns: Implications for market efficiency, long memory, multifractality and financial crises predictability by application of a nonlinear dynamics analysis framewo," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    3. Meo, Marcos M. & Iaconis, Francisco R. & Del Punta, Jessica A. & Delrieux, Claudio A. & Gasaneo, Gustavo, 2024. "Multifractal information on reading eye tracking data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 638(C).
    4. Zhang, Jiao & Li, Youping & Liu, Chunqiong & Wu, Bo & Shi, Kai, 2022. "A study of cross-correlations between PM2.5 and O3 based on Copula and Multifractal methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 589(C).
    5. Li, Shuping & Li, Jianfeng & Lu, Xinsheng & Sun, Yihong, 2022. "Exploring the dynamic nonlinear relationship between crude oil price and implied volatility indices: A new perspective from MMV-MFDFA," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    6. Wang, Fang & Han, Guosheng, 2023. "Coupling correlation adaptive detrended analysis for multiple nonstationary series," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    7. 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).
    8. Cao, Guangxi & Xie, Wenhao, 2022. "Detrended multiple moving average cross-correlation analysis and its application in the correlation measurement of stock market in Shanghai, Shenzhen, and Hong Kong," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 590(C).
    9. Meraz, M. & Alvarez-Ramirez, J. & Rodriguez, E., 2022. "Multivariate rescaled range analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 589(C).
    10. Milena Kojić & Petar Mitić & Marko Dimovski & Jelena Minović, 2021. "Multivariate Multifractal Detrending Moving Average Analysis of Air Pollutants," Mathematics, MDPI, vol. 9(7), pages 1-17, March.
    11. Telli, Şahin & Chen, Hongzhuan & Zhao, Xufeng, 2022. "Detecting multifractality and exposing distributions of local fluctuations: Detrended fluctuation analysis with descriptive statistics pooling," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).

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