The Total Triangles Area (TTA) algorithm was introduced as a good alternative for the estimation of the Hurst exponent in Lotfalinezhad and Maleki (2020). However, a theoretical framework for the validity of the TTA algorithm was missing. The main goal of this paper is to provide such a theoretical framework. A slightly different approach to the TTA algorithm is also presented, which leads to the introduction of the Triangle Area (TA) algorithm. A comparison of the accuracy of these algorithms (also with respect to the GHE one) is also carried out with fractional Brownian motions, in order to provide some light about when it is better to apply each of the algorithms.

在 Lotfalinezhad 和 Maleki（2020）中引入了总三角形面积 (TTA) 算法作为估计 Hurst 指数的一个很好的替代方法。但是，缺少 TTA 算法有效性的理论框架。本文的主要目标是提供这样一个理论框架。还介绍了一种与 TTA 算法略有不同的方法，这导致了三角形区域 (TA) 算法的引入。还使用分数布朗运动对这些算法（也相对于 GHE 算法）的准确性进行了比较，以便提供一些关于何时更好地应用每种算法的信息。