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Multiscale Entropy Analysis Of Traffic Time Series

Author

Listed:
  • JING WANG

    (Department of Mathematics, Beijing Jiaotong University, No. 3 of Shangyuan Residence Haidian District, Beijing 100044, P. R. China)

  • PENGJIAN SHANG

    (Department of Mathematics, Beijing Jiaotong University, No. 3 of Shangyuan Residence Haidian District, Beijing 100044, P. R. China)

  • XIAOJUN ZHAO

    (Department of Mathematics, Beijing Jiaotong University, No. 3 of Shangyuan Residence Haidian District, Beijing 100044, P. R. China)

  • JIANAN XIA

    (Department of Mathematics, Beijing Jiaotong University, No. 3 of Shangyuan Residence Haidian District, Beijing 100044, P. R. China)

Abstract

There has been considerable interest in quantifying the complexity of different time series, such as physiologic time series, traffic time series. However, these traditional approaches fail to account for the multiple time scales inherent in time series, which have yielded contradictory findings when applied to real-world datasets. Then multi-scale entropy analysis (MSE) is introduced to solve this problem which has been widely used for physiologic time series. In this paper, we first apply the MSE method to different correlated series and obtain an interesting relationship between complexity and Hurst exponent. A modified MSE method called multiscale permutation entropy analysis (MSPE) is then introduced, which replaces the sample entropy (SampEn) with permutation entropy (PE) when measuring entropy for coarse-grained series. We employ the traditional MSE method and MSPE method to investigate complexities of different traffic series, and obtain that the complexity of weekend traffic time series differs from that of the workday time series, which helps to classify the series when making predictions.

Suggested Citation

  • Jing Wang & Pengjian Shang & Xiaojun Zhao & Jianan Xia, 2013. "Multiscale Entropy Analysis Of Traffic Time Series," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 24(02), pages 1-14.
    • Handle: RePEc:wsi:ijmpcx:v:24:y:2013:i:02:n:s012918311350006x
    DOI: 10.1142/S012918311350006X
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    References listed on IDEAS

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    1. Roberts, Evan, 2004. "John Benson and Laura Ugolini, eds. A Nation of Shopkeepers: Five Centuries of British Retailing. London and New York: I. B. Tauris, 2003. x + 269 pp. ISBN 1-86064-709-X, $65.00 (cloth); 1-86064-708-1," Enterprise & Society, Cambridge University Press, vol. 5(1), pages 140-142, March.
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    Cited by:

    1. Zhang, Yali & Shang, Pengjian & Sun, Zhenghui, 2018. "Diversity analysis based on ordered patterns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 1126-1133.
    2. Yin, Yi & Shang, Pengjian & Ahn, Andrew C. & Peng, Chung-Kang, 2019. "Multiscale joint permutation entropy for complex time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 388-402.
    3. Zhang, Ningning & Lin, Aijing & Ma, Hui & Shang, Pengjian & Yang, Pengbo, 2018. "Weighted multivariate composite multiscale sample entropy analysis for the complexity of nonlinear times series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 595-607.
    4. li, Chao & Shang, Pengjian, 2019. "Multiscale Tsallis permutation entropy analysis for complex physiological time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 10-20.
    5. Chen, Shijian & Shang, Pengjian & Wu, Yue, 2018. "Weighted multiscale Rényi permutation entropy of nonlinear time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 548-570.
    6. Li, Jinyang & Shang, Pengjian, 2018. "Time irreversibility of financial time series based on higher moments and multiscale Kullback–Leibler divergence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 248-255.
    7. Chen, Shijian & Shang, Pengjian & Wu, Yue, 2019. "Multivariate multiscale fractional order weighted permutation entropy of nonlinear time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 217-231.
    8. Zhang, Yali & Shang, Pengjian & He, Jiayi & Xiong, Hui, 2020. "Cumulative Tsallis entropy based on multi-scale permuted distribution of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 548(C).
    9. Xu, Kaiye & Shang, Pengjian & Feng, Guochen, 2015. "Multifractal time series analysis using the improved 0–1 test model," Chaos, Solitons & Fractals, Elsevier, vol. 70(C), pages 134-143.

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