Mathematical modeling of the dynamics of the industry development

the purpose of the research is to develop models and methods for analyzing and forecasting the long-term dynamics of the development of industries. Methods: the methods used in the presented study are the methods of regression analysis of time series based on the decomposition of the observed processes into the rates of their development with the identification of trend and oscillatory components. Findings: the study presents an integro-differential model of production development and proposes its approximation based on the representation of development rates in the form of an oscillatory process against the background of a monotonically decreasing trend. An assessment of the noise level in the initial data caused by the influence of random unpredictable external factors, which fundamentally limits the accuracy of models and forecasting capabilities, is carried out. Algorithms for obtaining an analytical representation of the dynamics of production development are proposed. Conclusions: the analysis of actual data reveals the presence of almost periodic oscillatory processes of tempos, which can be represented by the sum of harmonic oscillations with different periods. Fluctuations in individual industries are not synchronous, respectively, crisis phenomena arise when extreme rates in different industries coincide, a kind of "parade of planets" and do not have a strict periodicity. In particular, the crisis of 2008 occurs at the level of a descending line of fluctuations in the growth rates of various industries, starting from 2005-2006, a similar picture is characteristic of the late 60s of the twentieth century. The accuracy of the forecast is fundamentally limited by the presence of an unpredictable noise component and the absence of strict almost periodic fluctuations, which inevitably leads to errors in the forecast both in the values of the predicted value and in the time of the occurrence of the corresponding events.

mathematical modeling, economic dynamics, time series, stochastic process, investments, economic cycles, lagging systems, trend, almost periodic fluctuations, noisy data