On the use of ‘reaction-diffusion’ model in the business cycle analysis

Introduction The goal of this work is to find a practical method of market condition analysis. Numerous researches are subjugated to this topical subject, although it would be premature to speak about their classical condition in this course. A methodological problem faced by the market analysis is well-known and comes to the global equilibrium problem. The market is a peculiar mathematical modeling object in terms of the fact that its equilibrium conditions can be multiple. For example, a number of equilibrium conditions for a standard Arrow—Debreu model comes to be infinite, and not only is it infinite but also forming a continual set. Practically, it means that a condition of price development process about a local equilibrium poorly depends on the prehistory of such a process. Therefore, an import of the forecasting methodology from physical system analysis, where dependence of the current condition of the process on its prehistory is significant, to market condition analysis, occurs to be useless. Particularly, considering a character of differences between the business cycle and the cycle of lunisolar eclipses, the classical methods, excellent for analyzing the celestial mechanics cycles, do not allow us to achieve even imperfect results in the market analysis. This research leans upon the only assumption that a mechanism to be designated as a strongly dissipative system produces the market condition data. Finally, we will get all results of our research in the form of a regression on the assumption, and all our solutions will result from the analysis of the market condition data. We will use Dow-Jones Industrial Average (DJIA) time series, which are accessible data of the market condition and can be easily found on the Internet.