Comparison of classical and modified methods for calculating the fractal dimension of time series using the Hurst exponent

A complete formal formulation of the classical method for determining the fractal dimension of time series using the Hurst exponent (R/S analysis) is given. A modified (simplified) method for calculating the Hurst index is proposed. Software has been developed for calculating the fractal dimension of series, the Mandelbrot dimension, and the correlation ratio. Practical testing of the software package is carried out and a comparative analysis of the two calculation methods under study is given.