标题： 具有可见性图方法的持久性和反持久时间序列分析 显示英文标题

标题： Analysis of persistent and antipersistent time series with the Visibility Graph method

摘要： 在本工作中，我们使用可视图（VG）方法研究了一系列时间序列，包括高斯噪声（白噪声、粉红噪声和蓝噪声）、随机过程（奥恩斯坦-乌伦贝克过程、分数布朗运动和莱维飞行）以及混沌系统（逻辑斯蒂映射）。 我们关注使用VG所需的最小数据点数以及两个关键描述符：度分布P(k)，它通常遵循幂律P(k) ~ k^-gamma，以及赫斯特指数H，它用于识别持久性和反持久性时间序列。 尽管VG方法近年来引起了越来越多的关注，但其在不同动力系统中一致表征时间序列的能力仍不明确。 我们的分析表明，VG方法的可靠应用需要至少1000个数据点。 此外，我们发现对于赫斯特指数H <= 0.5的时间序列，相应的临界指数满足gamma >= 2。 这些结果明确了VG方法的敏感性，并为其在随机和混沌时间序列分析中的应用提供了实用指南。 显示英文摘要

摘要： In this work, we investigate a range of time series, including Gaussian noises (white, pink, and blue), stochastic processes (Ornstein-Uhlenbeck, fractional Brownian motion, and Levy flights), and chaotic systems (the logistic map), using the Visibility Graph (VG) method. We focus on the minimum number of data points required to use VG and on two key descriptors: the degree distribution P(k), which often follows a power law P(k) ~ k^-gamma, and the Hurst exponent H, which identifies persistent and antipersistent time series. While the VG method has attracted growing attention in recent years, its ability to consistently characterize time series from diverse dynamical systems remains unclear. Our analysis shows that the reliable application of the VG method requires a minimum of 1000 data points. Furthermore, we find that for time series with a Hurst exponent H <= 0.5, the corresponding critical exponent satisfies gamma >= 2. These results clarify the sensitivity of the VG method and provide practical guidelines for its application in the analysis of stochastic and chaotic time series.