Modeling multivariate nonstationary time series of economic dynamics based on Fokker-Planck equation

Oleksandr Isaenko; Vyacheslav Glushchevsky; Oleksandr Isaenko

Oleksandr Isaenko Zaporozhye state engineering academy
Vyacheslav Glushchevsky Zaporozhye state engineering academy
Oleksandr Isaenko Zaporozhye state engineering academy

Keywords: multivariate time series, Fokker-Planck equation, forecasting, stock exchange

Abstract

Purpose and subject of researchThe actual problem of modeling of the multivariate nonstationary time series of economic dynamics is being researched for the purpose of analysis, forecasting and decision-making in financial markets.Research methodologyThe proposed approach to the modeling of time series is based on the methodology of multivariate analysis and continuity equation, which relates the probability density function of the state variables of the system with their speeds.Value resultsEquation of motion of a point in a multidimensional phase space of state variables derived under the assumption that the evolution of the economic system based on the interaction of two factors - the growth and dissipation. It is assumed that the growth rate has a deterministic function, which means that there is a causal link between variables, and the diffusion component of the velocity is proportional to the gradient of the state probabilities in a local point of phase space. In this case the state of the system is determined by multivariate Fokker-Planck equation. On the basis of two-dimensional Fokker-Planck equations is constructed model of the real economic process - trading on the stock exchange. The structure of the model equations of nonlinear responsible paradigm of financial markets and agreed with the results of empirical research. We derive differential equations for the evolution of one-dimensional distributions of prices, trading volume, and spread their moments that are needed to complete the system for the unknown probability density functions.ConclusionsThe evolution equations are based on sample data and agreed with the two-dimensional Fokker- Planck equation. Modeling the dynamics and forecasting of trades carried out by numerical integration of the equations of evolution in a sliding window of the sample. The proposed approach to modeling allows the best use of the information contained in the multivariate time series and to obtain high prediction accuracy. Verification of the model performed on the rows indices trading on the Ukrainian stock market.Key words: multivariate time series, Fokker-Planck equation, forecasting, stock exchange.

Author Biographies

Oleksandr Isaenko, Zaporozhye state engineering academy

Isaenko Oleksandr Oleksandrovychpostgraduate, department of software and automated systems, Zaporozhye state engineering academy(Zaporozhye,Ukraine)

Vyacheslav Glushchevsky, Zaporozhye state engineering academy

Glushchevsky Vyacheslav Valentinovichcandidate of economic sciences, associate professor, faculty of economics and management, Zaporozhye state engineering academy(Zaporozhye, Ukraine)

Oleksandr Isaenko, Zaporozhye state engineering academy

Isaenko Oleksandr Mykolayovychcandidate of technical sciences, associate professor, economic cybernetics department, Zaporozhye state engineering academy(Zaporozhye, Ukraine)

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