  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.
