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.

中文翻译：

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时间序列赫斯特指数估计方法综述

赫斯特指数是表征时间序列自相似性和长期记忆特性的重要指标。它在物理、技术、工程、数学、统计学、经济学、心理学等领域有着广泛的应用。目前，可用的时间序列Hurst指数估计方法可分为不同类别：基于时间序列表示的时域方法和谱域方法，基于参数估计方法的线性回归方法和贝叶斯方法。尽管文献中讨论了各种方法，但仍然存在一些不足：估计算法的描述只是数学导向的，缺乏伪代码；估计算法的有效性和准确性尚不清楚；没有考虑估算方法的分类，缺乏对估算方法选择的指导。在这项工作中，重点放在估计赫斯特指数的十三种主要方法上。为了降低用计算机程序实现估计方法的难度，简要讨论了数学原理，并给出了算法的伪代码和必要的细节。预计该调查可以帮助研究人员在实际情况中以简单的方式选择、实现和应用感兴趣的估计算法。