A theoretical framework for the TTA algorithm

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.