UDC 330.4                                           

DOI: http://doi.org/10.15350/2409-7616.2022.4.41

Boronnikova L.A.¹ (Perm, Russian Federation) – boronnikova00@inbox.ru, Vladimirova D.B.¹ (Perm, Russian Federation) – da0807@mail.ru

¹Perm National Research Polytechnic University

Abstract. The article investigates time financial series and methods of their analysis by methods of fractal analysis. The possibility of applying the theory and methods of fractal analysis to the analysis of real data – time series describing financial indices of several leading countries of the world is shown. These are the Russian MICEX stock price index, the American S&P 500, and the Chinese index of the Shanghai Stock Exchange SZSE. It is shown that there is a fractal component in all data series, which allows for further clarifying analysis. In order to give estimated characteristics to measures of randomness and ordering of data, a number of additional values and indicators are calculated, which include correlation dimension, phase space dimension, fractal dimension and Hurst index. Also, all data series were checked for the presence of multifractality, for this purpose, the output series were split and the analysis was repeated on each of the obtained parts. Additionally, in order to characterize the dynamical systems generating the time series under study, attractors of all data series are constructed. The analytical (fractal) and graphical (attractor) types of analysis made it possible to show which of the studied dynamic systems are multifractal, which of them are affected by hidden internal forces. For each case, the number of parameters that are necessary to describe the dynamics of the system is calculated. The finiteness of the correlation dimension is shown in each of the cases. The calculation of the correlation entropy, carried out simultaneously with the calculations of the Hurst index, allowed us to identify which of the series are most suitable for forecasting and have greater stability.

Keywords: fractal, fractal dimension, correlation dimension, entropy, financial time series, trend, forecast, digital analysis, Hurst index, multifractality, financial analysis, fractal analysis, dynamic systems.

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For citation:

Boronnikova L.A., Vladimirova D.B. On the application of fractal analysis methods for the study of financial time series. CITISE, 2022, no. 4, pp. 450-459. DOI: http://doi.org/10.15350/2409-7616.2022.4.41