DOI: 10.25136/2409-8647.2021.1.27680

Abstract: The subject of this research is the processes of price formation for raw materials depending on the demand for end consumer products. The article reviews a mathematical model that is based on the principle of maximum utility. The proposed model is founded on the stage-by-stage determination of the production output and consumption of end products, as well as corresponding prices depending on the prices of used raw materials and semi-finished products. The prices for intermediate products and raw materials are formed depending on the need for end products output with their optimization by demand. The article provides the basic mathematical ration with regards to using principle of maximum utility applicable to the demand-supply model and its implementation in multi-stage production. The acquired results indicate weak dependence of production output and prices for end products on the cost of raw material in terms of advanced refining. With limited production capacity of raw materials, the dynamics of prices is well predicted. The results of modeling, compared to the available statistical data, indicate the adequacy of the proposed model to the unfolding economic processes. It is determined that the accuracy of price prediction for raw products with a significant volume of its subsequent processing is limited.

DOI: 10.25136/2409-8647.2020.1.29404

Abstract: The subject of this research is the model of business development that describes the dependence of ongoing volume of production from previous investments and intensity of wear of production capacities. The investment process is characterized by a delay between the moment of investment, actual return and its continuation, gradual decrease in the level of return, and discreetness of investments. In the process of modeling, discrete investment were replaced by an integral, which leads to integral-differential equation, and in terms of facile assumption to the linear standard differential equation of second order or their system, solved by the disharmonious fluctuations on the background of an aperiodic trend. As the method of analysis of correspondence of the model data with the actual dynamics of business development, the research utilizes computational solution of the emerging differential equations. Comparison of the model data with the known statistics reveals their adequacy to the current economic processes. Statistical data contains noise component, which consists of various economic and political factors and principally limits the precision of forecasting. Differences in the length of fluctuation periods by industries impedes analysis of the economic behavior as a whole. At the same time, forecast of crisis phenomena that emerge in superposition of the phases of industry fluctuations can be executed with sufficient level of precision.

DOI: 10.25136/2644-5522.2018.6.27069

Abstract: The subject of research is the method of estimating the noise component in the time series and its removal, the selection of the trend and fluctuations with different periods, the concept of T-ε and T-h-ε almost periods for the final series is introduced. The analysis is based on the requirement of smoothness of a function representing the original data and having derivatives up to the fourth order inclusive and the allocation of almost periods based on functions of the Alter-Johnson type. Separately, the trend of the length of the periods identified in the data of a number of fluctuations. The algorithm for solving the problem is based on minimizing the deviations of the calculated values from the smooth function, provided that the deviations from the source data correspond to the noise level. To identify the oscillatory component and the trend of almost periods, the modified Alter-Johnson function is used. The proposed methodology and algorithms for estimating and eliminating noise in the data allow us to reasonably determine the noise level in the data, remove the noise component from the data, identify almost the periods in the data in the sense of the definitions introduced in the article, highlight the trend and oscillation components in the data, identify, if necessary, the trend of changes almost periods.