Fractals and Forecasting of Economic Cycles

Abstract

For many centuries, scientists have used classical methods of calculation in the process of exploring and modeling the universe. And such functions that did not carry the proper smoothness or regularity were often considered as pathologies and were not given much attention. The fractal geometry of Benoit Mandelbrot deals with the study of such irregular sets. The basic concept of fractal geometry is a fractal, the origin of which is associated with computer modeling. With the help of fractals, it was possible to describe the glow of the sky during a thunderstorm, the dynamics of the growth of tree branches, the fractal structure of the internal organs of a person, the psyche and organizational systems, etc. Recently, fractals have been widely used to study economic cycles. In particular, such a characteristic of a time series as fractal dimension makes it possible to determine the moment when the system becomes unstable and is ready to move to a new state. Modern science widely uses the theory of fractals to study time series in order to increase the reliability of forecasting economic dynamics. The main feature of a fractal is the infinite repetition of a self-similar structure in different scales. Analogous nature characterizes economic cycles. Samuelson and Hicks created an appropriate mathematical model for modeling economic cycles, later this approach was developed in the works of Goodwin. Recently, fractals have been widely used to study economic processes. To date, there are many different mathematical models of fractals, each of which differs from the others in a certain recursive function. With the help of methods of fractal analysis and their modifications, it is possible to determine moments of qualitative change in the behavior of the system and, accordingly, to predict their subsequent behavior in a relatively long-term perspective. The most urgent task, solved by the methods developed within this approach, is the identification of the moment of the onset of major economic crises, that is, forecasting them in the near future. Keywords: Fractals. Economic cycles. Prognosis.