Typical Algorithms for Estimating Hurst Exponent of Time Sequence: A Data Analyst’s Perspective

The Hurst exponent is a significant metric for characterizing time sequences with long-term memory property and it arises in many fields such as physics, engineering, mathematics, statistics, economics, psychology, and so on. The available methods for estimating the Hurst exponent can be categorized into time-domain and spectrum-domain methods based on the representation of the time sequence, and into linear regression and Bayesian method based on parameter estimation techniques. Although there are various estimation methods for the Hurst exponent, there are still some disadvantages that should be overcome: firstly, the estimation methods are mathematics-oriented instead of engineering-oriented; secondly, the accuracy and effectiveness of the estimation algorithms are inadequately assessed; thirdly, the framework of classification for the estimation methods are insufficient; and lastly there is a lack of clear guidance for selecting proper estimation in practical problems involved in data analysis. The contributions of this paper lie in four aspects: 1) the optimal sequence partition method is proposed for designing the estimation algorithms for Hurst exponent; 2) the algorithmic pseudo-codes are adopted to describe the estimation algorithms, which improves the understandability and usability of the estimation methods and also reduces the difficulty of implementation with computer programming languages; 3) the performance assessment is carried for the typical estimation algorithms via the ideal time sequence with given Hurst exponent and the practical time sequence captured in applications; 4) the guidance for selecting proper algorithms for estimating the Hurst exponent is presented and discussed. It is expected that the systematic survey of available estimation algorithms could help the users to understand the principles and the assessment of the various estimation methods could help the users to select, implement and apply the estimation algorithms of interest in practical situations in an easy way.