The paper provides an assessment of the state of economic theory and the possibility of its use in the mathematical description of macroeconomic processes in order to analyze and synthesize the management system of economic objects that are quasi-static in nature with a difficult to formalize pattern of slowly changing economic indicators, which was used as GDP. An analysis is given of the reasons that cause difficulties in identifying this indicator in a long period of time due to random internal and external influences on the object under study. The article describes a methodology and a computational experiment associated with modeling GDP statistics in the range from 1998 to 2020 in the classes of functions: exponential, logarithmic, exponential, and polynomial. The results are obtained in the form of aperiodic trends that do not reflect changes in GDP indicators during the crisis and economic recession. The study of the possibility of using the GDP model in the procedure for extrapolating (forecasting) analytical results until 2023 also led to a negative result. The conducted studies have shown an urgent need to create dynamic models with functional and statistical links, which make it possible to identify the influence of external and internal influences on an economic object.