Jiang Runze, Shang Pengjian
School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, China.
Chaos. 2024 Mar 1;34(3). doi: 10.1063/5.0197167.
The complexity-entropy curve (CEC) is a valuable tool for characterizing the structure of time series and finds broad application across various research fields. Despite its widespread usage, the original permutation complexity-entropy curve (PCEC), which is founded on permutation entropy (PE), exhibits a notable limitation: its inability to take the means and amplitudes of time series into considerations. This oversight can lead to inaccuracies in differentiating time series. In this paper, drawing inspiration from dispersion entropy (DE), we propose the dispersion complexity-entropy curve (DCEC) to enhance the capability of CEC in uncovering the concealed structures within nonlinear time series. Our approach initiates with simulated data including the logistic map, color noises, and various chaotic systems. The outcomes of our simulated experiments consistently showcase the effectiveness of DCEC in distinguishing nonlinear time series with diverse characteristics. Furthermore, we extend the application of DCEC to real-world data, thereby asserting its practical utility. A novel approach is proposed, wherein DCEC-based feature extraction is combined with multivariate support vector machine for the diagnosis of various types of bearing faults. This combination achieved a high accuracy rate in our experiments. Additionally, we employ DCEC to assess stock indices from different countries and periods, thereby facilitating an analysis of the complexity inherent in financial markets. Our findings reveal significant insights into the dynamic regularities and distinct structures of these indices, offering a novel perspective for analyzing financial time series. Collectively, these applications underscore the potential of DCEC as an effective tool for the nonlinear time series analysis.
复杂度-熵曲线（CEC）是表征时间序列结构的一种有价值的工具，在各个研究领域都有广泛应用。尽管其应用广泛，但基于排列熵（PE）的原始排列复杂度-熵曲线（PCEC）存在一个显著局限性：它无法考虑时间序列的均值和幅度。这种疏忽可能导致在区分时间序列时出现不准确的情况。在本文中，我们从离散熵（DE）中获得灵感，提出了离散复杂度-熵曲线（DCEC），以增强CEC揭示非线性时间序列中隐藏结构的能力。我们的方法首先从包括逻辑斯谛映射、色噪声和各种混沌系统的模拟数据开始。模拟实验的结果一致表明DCEC在区分具有不同特征的非线性时间序列方面的有效性。此外，我们将DCEC的应用扩展到实际数据，从而证明了其实际效用。我们提出了一种新颖的方法，即将基于DCEC的特征提取与多变量支持向量机相结合，用于诊断各种类型的轴承故障。这种结合在我们的实验中取得了很高的准确率。此外，我们使用DCEC来评估不同国家和时期的股票指数，从而便于分析金融市场中固有的复杂性。我们的研究结果揭示了这些指数的动态规律和独特结构的重要见解，为分析金融时间序列提供了一个新的视角。总的来说，这些应用强调了DCEC作为非线性时间序列分析有效工具的潜力。
