The Hurst exponent is a significant indicator for characterizing the self-similarity and long-term memory properties of time sequences. It has wide applications in physics, technologies, engineering, mathematics, statistics, economics, psychology and so on. Currently, available methods for estimating the Hurst exponent of time sequences can be divided into different categories: time-domain methods and spectrum-domain methods based on the representation of time sequence, linear regression methods and Bayesian methods based on parameter estimation methods. Although various methods are discussed in literature, there are still some deficiencies: the descriptions of the estimation algorithms are just mathematics-oriented and the pseudo-codes are missing; the effectiveness and accuracy of the estimation algorithms are not clear; the classification of estimation methods is not considered and there is a lack of guidance for selecting the estimation methods. In this work, the emphasis is put on thirteen dominant methods for estimating the Hurst exponent. For the purpose of decreasing the difficulty of implementing the estimation methods with computer programs, the mathematical principles are discussed briefly and the pseudo-codes of algorithms are presented with necessary details. It is expected that the survey could help the researchers to select, implement and apply the estimation algorithms of interest in practical situations in an easy way.

翻译：赫斯特指数是表征时间序列自相似性与长记忆特性的重要指标，在物理学、技术科学、工程学、数学、统计学、经济学、心理学等领域具有广泛应用。当前，时间序列赫斯特指数的估计方法可按不同标准分类：基于时间序列表示形式的时域方法和频域方法，基于参数估计方法的线性回归方法和贝叶斯方法。尽管文献中已探讨多种方法，但仍存在若干不足：估计算法的描述仅侧重于数学推导而缺乏伪代码；估计算法的有效性和精确性尚不明确；缺乏对估计方法的分类研究，且缺少选择估计方法的指导。本文重点研究十三种主流赫斯特指数估计方法。为降低估计算法计算机程序实现的难度，本文简要阐述数学原理，并提供包含必要细节的算法伪代码。本综述有望帮助研究人员在实际应用场景中便捷地选择、实现和应用感兴趣的估计算法。