COMPUTER MODELING OF ECONOMIC PROCESSES USING FRACTAL ANALYSIS METHODS

Abstract

The development of modern information and analytical technologies opens up new opportunities for economic analysis and forecasting of market situations. Many technologies of modern financial analysis are based on the efficient market hypothesis, according to which price changes in the securities market in logarithmic coordinates represent a random (Gauss) process. However, studies of the last 30 years show that this is not the case and the usual statistical model is not suitable for analyzing most economic indicators. The effective roar hypothesis is replaced by the fractal theory and the fractal market hypothesis based on the concept of self-similarity in different time scales. The article is devoted to the mathematical and statistical analysis of the dynamics of economic indicators based on the theory of fractals. The results of the fractal analysis of the time series of the dynamics of the EUR/RUB exchange rate for the period 2013-2022 by the method of the normalized Hearst swing are presented. The result of the study was the identification of the fractal properties of the specified time series, the proof of its nonlinearity and the presence of the effect of long-term memory in the dynamics. The results obtained prove the necessity of using specialized fractal methods for further research and forecasting the dynamics of time series with a self-similar statistical structure. Purpose of the work is to analyze economic processes based on the tools of fractal mathematics. The method or methodology of work: in the course of the research, general methodological principles of scientific cognition were used: comparative, analytical, abstract-logical analyses, economic-mathematical, economic-statistical models and modeling using modern software. The calculations were carried out using the application programs Microsoft Excel, Statistica, R, Matrixer. Results: we have identified fractal properties of the financial time series, justified the need to use new methods of forecasting economic indicators. Scope of the results: it is advisable to apply the obtained results to economists, traders and business analysts studying the dynamics of economic and financial indicators.

Keywords

• computer modeling
• fractal
• hurst index
• nonparametric analysis
• fractal series
• persistence
• trend tolerance
• model
• dynamics
• cyclicity