In this paper, weighted link entropy (WLE) and multiscale weighted link entropy (MWLE) are proposed as novel measures to quantify complexity of nonlinear time series. MWLE is different from traditional weighted permutation entropy (WPE) in that its proposal is based on the combination of symbolic ordinal analysis and networks. Besides, the analysis of MWLE takes into account multiple time scales inherent in complex systems. The advantages of the proposed methods are investigated by simulations on synthetic signals and real-world data. Based on the study of synthetic data, we find that a significant advantage of WLE is its reduced sensitivity to noise. WLE shows the trend of more chaotic of system as the variance of Gaussian white noise increases. In addition, WLE has a wider range of variations when the system is in a chaotic state and can detect minute changes of complexity in complex systems as control parameters vary. To further show the utility of MWLE and WLE methods, we provide new evidences of their application in financial time series. By comparing WLE with the mean and variance of closing price data, WLE can predict the occurrence of financial crisis in advance. Furthermore, MWLE is capable of helping mark off different regions of stock markets, detecting their multiscale structure and reflects more information containing in financial time series.

在本文中，加权链接熵（WLE）和多尺度加权链接熵（MWLE）被提出作为量化非线性时间序列复杂性的新方法。MWLE 与传统的加权置换熵 (WPE) 不同，它的提议是基于符号序数分析和网络的结合。此外，MWLE 的分析考虑了复杂系统中固有的多个时间尺度。通过对合成信号和真实世界数据的模拟来研究所提出方法的优点。基于对合成数据的研究，我们发现 WLE 的一个显着优势是其对噪声的敏感性降低。随着高斯白噪声方差的增加，WLE 表现出系统更加混乱的趋势。此外，当系统处于混沌状态时，WLE 具有更广泛的变化范围，并且可以随着控制参数的变化检测复杂系统中复杂性的微小变化。为了进一步展示 MWLE 和 WLE 方法的实用性，我们提供了它们在金融时间序列中应用的新证据。通过将WLE与收盘价数据的均值和方差进行比较，WLE可以提前预测金融危机的发生。此外，MWLE 能够帮助标记股票市场的不同区域，检测其多尺度结构并反映金融时间序列中包含的更多信息。通过将WLE与收盘价数据的均值和方差进行比较，WLE可以提前预测金融危机的发生。此外，MWLE 能够帮助标记股票市场的不同区域，检测其多尺度结构并反映金融时间序列中包含的更多信息。通过将WLE与收盘价数据的均值和方差进行比较，WLE可以提前预测金融危机的发生。此外，MWLE 能够帮助标记股票市场的不同区域，检测其多尺度结构并反映金融时间序列中包含的更多信息。