Spline-modeling and analysis of interactions in the economy with the possible presence of switching points of regression

In the study of relationships, it is often necessary to take into account the instability of the form of communication, changes in the number of factors and the degree of their mutual influence. Thus, some models of relationships in the economy can be considered systems with variable structure. In a situation where it is impossible to formulate hypotheses about the position of points of structural changes a priori, it is important to avoid smoothing modeling methods that worsen the initial economic signal. The work offers methods of a new science, the «new econometrics» for simulation of variable-structure systems using analysis of interrelations of processes. Possible switching points of regression in studying relationships complicate the use of classical methods of econometrics. The goal of the study was to investigate whether spline modeling can adequately assess the evolution of the relationship between processes, which remains unnoticed in simple regression models. Approximation of the dynamics of splines allows to accurately preserve the initial economic signal. Then it becomes possible to compare the real mutual effects of processes continuously. Fixation of «special points», points, switching regression, «return points», points breaking or tearing of the trends at the interface of different structural conglomerates gains particular complexity and importance in such systems. Fixation is possible only through the first derivative of the economic signal, which must be present in the «new econometric» model analytically, graphically and numerically. Violations of the well-known negative correlation between the dollar and oil prices have been found in some time intervals. Effective instruments for implementing the proposed method for investigating the interconnections with a «patch» structure can be considered as an approximation of the dynamics by splines, the transition from comparison of discrete states of processes in key points to comparison of segments. The constructed phase trajectory of the relationship between the dollar and oil prices has confirmed that the proposed method for analyzing the temporal features of the relationship has advantages over the simplified regression of the least squares method. As an instrumental base of the study, we propose a spline approximation with analytical modeling and visualization of processes in the Maple computer mathematics system.