中国物理B ›› 2025, Vol. 34 ›› Issue (12): 120508-120508.doi: 10.1088/1674-1056/adea56

• • 上一篇    

Interval multiscale sample entropy: A novel tool for interval-valued time series complexity analysis

Ping Tang(唐萍), Bao-Gen Li(李宝根)†, and Yang Wang(王阳)   

  1. Huangshi Key Laboratory of Metaverse and Virtual Simulation, School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China
  • 收稿日期:2025-02-17 修回日期:2025-05-18 接受日期:2025-07-01 发布日期:2025-11-25
  • 通讯作者: Bao-Gen Li E-mail:baogenli@hbnu.edu.cn
  • 基金资助:
    Project supported by Hubei Provincial Department of Education Science and Technology Plan Project (Grant No. B2022165).

Interval multiscale sample entropy: A novel tool for interval-valued time series complexity analysis

Ping Tang(唐萍), Bao-Gen Li(李宝根)†, and Yang Wang(王阳)   

  1. Huangshi Key Laboratory of Metaverse and Virtual Simulation, School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China
  • Received:2025-02-17 Revised:2025-05-18 Accepted:2025-07-01 Published:2025-11-25
  • Contact: Bao-Gen Li E-mail:baogenli@hbnu.edu.cn
  • About author:2025-120508-250222.pdf
  • Supported by:
    Project supported by Hubei Provincial Department of Education Science and Technology Plan Project (Grant No. B2022165).

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摘要： To analyze the complexity of interval-valued time series (ITSs), a novel interval multiscale sample entropy (IMSE) methodology is proposed in this paper. To validate the effectiveness and feasibility of IMSE in characterizing ITS complexity, the method is initially implemented on simulated time series. The experimental results demonstrate that IMSE not only successfully identifies series complexity and long-range autocorrelation patterns but also effectively captures the intrinsic relationships between interval boundaries. Furthermore, the test results show that IMSE can also be applied to measure the complexity of multivariate time series of equal length. Subsequently, IMSE is applied to investigate interval temperature series (2000-2023) from four Chinese cities: Shanghai, Kunming, Chongqing, and Nagqu. The results show that IMSE not only distinctly differentiates temperature patterns across cities but also effectively quantifies complexity and long-term autocorrelation in ITSs. All the results indicate that IMSE is an alternative and effective method for studying the complexity of ITSs.

关键词: interval multiscale sample entropy, interval-valued time series

Abstract: To analyze the complexity of interval-valued time series (ITSs), a novel interval multiscale sample entropy (IMSE) methodology is proposed in this paper. To validate the effectiveness and feasibility of IMSE in characterizing ITS complexity, the method is initially implemented on simulated time series. The experimental results demonstrate that IMSE not only successfully identifies series complexity and long-range autocorrelation patterns but also effectively captures the intrinsic relationships between interval boundaries. Furthermore, the test results show that IMSE can also be applied to measure the complexity of multivariate time series of equal length. Subsequently, IMSE is applied to investigate interval temperature series (2000-2023) from four Chinese cities: Shanghai, Kunming, Chongqing, and Nagqu. The results show that IMSE not only distinctly differentiates temperature patterns across cities but also effectively quantifies complexity and long-term autocorrelation in ITSs. All the results indicate that IMSE is an alternative and effective method for studying the complexity of ITSs.

Key words: interval multiscale sample entropy, interval-valued time series

中图分类号:  (Time series analysis)

  • 05.45.Tp
02.70.Rr (General statistical methods) 02.50.Sk (Multivariate analysis) 05.45.-a (Nonlinear dynamics and chaos)