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Long-term correlations and multifractality of toll-free calls in China

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  • Gui, Jun
  • Zheng, Zeyu
  • Fu, Dianzheng
  • Fu, Yang
  • Liu, Zhi

Abstract

In the recent decades, calling activities have been studied from different perspectives in social physics field. In diverse studies, call frequencies and call durations have been widely used to quantify calling activity. However, they have been rarely studied. In this work, long-term correlations as well as the multifractality of toll-free call frequency (TFCF) and toll-free call duration (TFCD) time series were investigated with multifractal detrended fluctuation analysis (MFDFA). The results show that these two time series have a similar crossover, which is approximately 36 h, and they have different long-term correlations as well as sophisticated multifractality below and above the crossover. The TFCF time series below the crossover is non-stationary and small fluctuations contribute more to its strong multifractality than large fluctuations. The TFCF time series above the crossover is stationary with long-term anti-correlation and its weak multifractality is only caused by small fluctuations. The TFCD time series below the crossover is non-stationary and large fluctuations contribute more to its strong multifractality than small fluctuations. The TFCD time series above the crossover is stationary with long-term correlation and its weak multifractality is mainly caused by small fluctuations. Moreover, we found that the multifractality of the TFCF time series is primarily caused by correlations, but that of the TFCD time series is caused by a combination of correlations and broad distribution of data. We also discussed the possible factors in the sophisticated multifractality with comparative analysis.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:567:y:2021:i:c:s0378437120309316
    DOI: 10.1016/j.physa.2020.125633
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    References listed on IDEAS

    as
    1. Todd Zorick & Mark A Mandelkern, 2013. "Multifractal Detrended Fluctuation Analysis of Human EEG: Preliminary Investigation and Comparison with the Wavelet Transform Modulus Maxima Technique," PLOS ONE, Public Library of Science, vol. 8(7), pages 1-7, July.
    2. Zhang, Xie & Liu, Hongzhi & Zhao, Yifei & Zhang, Xingchen, 2019. "Multifractal detrended fluctuation analysis on air traffic flow time series: A single airport case," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 531(C).
    3. Chattopadhyay, Anirban & Khondekar, Mofazzal H. & Bhattacharjee, Anup Kumar, 2018. "Fractality and singularity in CME linear speed signal: Cycle 23," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 542-550.
    4. 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.
    5. Talayeh Aledavood & Eduardo López & Sam G B Roberts & Felix Reed-Tsochas & Esteban Moro & Robin I M Dunbar & Jari Saramäki, 2015. "Daily Rhythms in Mobile Telephone Communication," PLOS ONE, Public Library of Science, vol. 10(9), pages 1-14, September.
    6. 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.
    7. Yang, Yan-Hong & Xie, Wen-Jie & Li, Ming-Xia & Jiang, Zhi-Qiang & Zhou, Wei-Xing, 2017. "Statistical properties of user activity fluctuations in virtual worlds," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 271-278.
    8. Shang, Pengjian & Lu, Yongbo & Kamae, Santi, 2008. "Detecting long-range correlations of traffic time series with multifractal detrended fluctuation analysis," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 82-90.
    9. Mali, P. & Manna, S.K. & Mukhopadhyay, A. & Haldar, P.K. & Singh, G., 2018. "Multifractal analysis of multiparticle emission data in the framework of visibility graph and sandbox algorithm," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 493(C), pages 253-266.
    10. Dai, Meifeng & Hou, Jie & Ye, Dandan, 2016. "Multifractal detrended fluctuation analysis based on fractal fitting: The long-range correlation detection method for highway volume data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 722-731.
    11. Wu, Wenlu & Yuan, Naiming & Xie, Fenghua & Qi, Yanjun, 2019. "Understanding long-term persistence and multifractal behaviors in river runoff: A detailed study over eastern China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 533(C).
    12. Jun Gui & Zeyu Zheng & Dianzheng Fu & Zihao Yang & Yuan Gao & Zhi Liu, 2020. "Dynamics of calling activity to toll-free numbers in China," PLOS ONE, Public Library of Science, vol. 15(3), pages 1-16, March.
    13. Albert-László Barabási, 2005. "The origin of bursts and heavy tails in human dynamics," Nature, Nature, vol. 435(7039), pages 207-211, May.
    14. 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).
    15. Sadegh Movahed, M. & Hermanis, Evalds, 2008. "Fractal analysis of river flow fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(4), pages 915-932.
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