Spline Analysis of Flow Correlation in Economic Systems

The effectiveness of process control in complex socio-economic systems requires a significant increase in accuracy in mathematical modeling of the dynamics of the studied indicators. When searching for interconnections between processes, there often arises the problem of comparability of data representing the static and dynamic components in economic systems (stocks and flows). If in a discrete representation, data transformation is possible by calculating chain gains, then it is necessary to differentiate the stock function in systems with continuous time. Thus, by analogy with physical movement, the first derivative or rate of change of stocks becomes a stream. Given the functional relationship between the dynamics of stocks and their flows, it is essential to maintain accuracy when modeling the dynamics of stocks and their subsequent transformation into flows. The proposed methodology for the spline approximation of economic dynamics with absolute coincidence at the nodal points of empirical and model equivalents allows us to preserve the accuracy of the data. The differentiability of the splines solves the problem of data conversion. The paper investigates the efficiency of the apparatus of spline functions in modeling the dynamics of different “quantities” in the economy by the example of an analysis of the relationship between the flow of oil exports and money supply in the Russian economy. The proposed methodology of analytical data transformation with the search for the relationship between continuous paths of acceleration and deceleration of processes determines the scientific novelty of the study. The study results can be useful in solving the problems of managing stocks and flows in the economy, when searching for the relationship between flows, and studying the seasonality and cyclical nature of flows.