Calculation of the Exact Value of the Fractal Dimension in the Time Series for the Box-Counting Method

Abstract

In this paper, the problem of precise determination of the size of the fractal dimension of the time series is considered. The bottom line is that the classical box method equally takes into account both filled and not filled boxes of the superimposed grid. In the proposed method, the size of the boxes is tied to the scale of the values of the time series levels. As a result, there is a minimum coverage of the graph, which provides the exact value of the fractal dimension. The comparison of estimates of fractal dimension calculated by classical and proposed methods is given.