Analysis of instrumental methods for modeling stochastic processes in the economy

Abstract

In this paper, the authors conduct a comparative analysis of instrumental methods used in modeling stochastic processes, namely, component analysis of time series, fractal modeling and modeling using p-adic mathematics. As an object of study, the authors chose the dynamics of the MICEX index. At the first step of the work, the authors carry out a detailed component analysis of the time series, which made it possible to identify the main development trend in the form of a quadratic function; periodic fluctuations with a period of six levels and a cyclical component describing fluctuations in the world economy with a period of fifty-five levels. At the second step of the work, the authors simulate the dynamics of the MICEX index using a fractal theory based on the self-similarity of the development of the economic process, which showed the ergodicity of the series under study with a stable influence of only the last twenty-four levels. The third step of the work was the p-adic modeling of the patterns existing in the series under study, which allowed the authors to reduce the model error to 6.8%. As a result of the work, a forecast of the dynamics of the MICEX exchange rate at four levels is presented, presented in three scenarios: optimistic, realistic and pessimistic. As conclusions of the work, an analysis was made of the possibility of using the considered methods for multiple, medium and long-term forecasts; the complexity of the methods and the need to use special software products are evaluated.