Hybrid Instrumental Means of Predictive Analysis of the Dynamics of Natural and Economic Processes

Abstract

The purpose of the presented research is the development and adaptation of mathematical and instrumental methods of analysis and risk management through the forecasting of both economic and natural time series with memory based on the application of new mathematical methods of investigation. The paper poses the problem of developing a constructive method for predictive analysis of time series in the framework of the currently emerging trend of using so-called “graphical tests” in the process of time series’ modeling using nonlinear dynamics methods. The main purpose of using graphical tests is to identify both stable and unstable quasiperiodic cycles (quasi-cycles), the whole set of which includes a strange attractor (if one exists). New computer technologies that made it possible to study complex phenomena and processes “on a display screen” were used as instrumentation for the implementation of methods of non-linear dynamics. The proposed approach differs from classical methods of forecasting by new implementation of accounting trends (the evolution of centers and sizes of dimensional rectangles), and appears to be a new tool for identifying cyclic components of the time series in question. As a result, the person, that is making decision has more detailed information, which is impossible to obtain by the methods of classical statistics. The work was supported by Russian Foundation for Basic Research (Grants № 17-06-00354 A).