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16

Section: Economic and Mathematical Modeling
UDC 330.46
Isaienko O. O.
Modelling Non-stationary Time Series of Economic Dynamics on the Basis of Fokker – Planck Equations (p. 99 - 105)
The article studies the topical issue of modelling non-stationary time series of economic dynamics. The proposed approach to modelling time series is based on the methodology of multidimensional analysis and continuity equation, which combines the system state variables probability density function with their rates. Equation of point motion in the multi-dimensional phase space of state variables is drawn in an assumption that interaction of two factors – growth and dissipation – lies in the basis of economic system evolution. The article assumes that the rate of growth is a deterministic function, which means availability of cause-effect relation between variables, and the diffusion component of the rate is proportional to the gradient of probability of states in a local point of the phase space. In this case the system state is determined by the Fokker – Plank multidimensional equation. One-dimensional time series is considered together with series of its derivatives as a multidimensional non-stationary process, which is modelled by the two-dimensional Fokker – Planck equation by coordinates and increments. Model equations are based on an assumption about linearity of series of finite differences and are co-ordinated with the results of empirical phase analysis. The article builds an adaptive model with the non-stationary time series memory. The adaptation mechanism is realised through the system of equations of evolution of selected numerical characteristics of the series and its differences. Time series memory is taken into account through the system of equations of evolution of the coordinate moment functions. Forecast of the series is carried out through numeric integration of the obtained evolution and Fokker – Planck equations. Results of modelling show practical suitability of the models for forecasting price indicators of the financial market for a middle-term period.
Keywords: state function, state variables, Fokker – Planck equation, model, forecast, economic time series
Fig.: 2. Formulae: 18. Bibl.: 12.

Isaienko Oleksandr O. – Postgraduate Student, Department of software for automated systems, Zaporizhzhia State Engineering Academy (226 Sobornyi Ave., Zaporizhzhia, 69006, Ukraine)
Email: [email protected]

Reference to this article:
Isaienko, Oleksandr O. (2014) “Modelling Non-stationary Time Series of Economic Dynamics on the Basis of Fokker – Planck Equations.” Business Inform 4:99–105.

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