Детерминированный факторный анализ: методы интегро-дифференцирования нецелого порядка

Abstract

Objective: to summarize the methods of deterministic factor economic analysis, namely the differential calculus and the integral method. Methods: mathematical methods for integro-differentiation of non-integral order, the theory of derivatives and integrals of fractional (non-integral) order.Results: the basic concepts are formulated and the new methods are developed that take into account the memory and non-locality effects in the quantitative description of the influence of individual factors on the change in the effective economic indicator. Two methods are proposed for integro-differentiation of non-integral order for the deterministic factor analysis of economic processes with memory and non-locality. It is shown that the method of integro-differentiation of non-integral order can give more accurate results compared with standard methods (method of differentiation using the first order derivatives and the integral method using the integration of the first order) for a wide class of functions describing effective economic indicators.Scientific novelty: the new methods of deterministic factor analysis are proposed: the method of differential calculus of non-integral order and the integral method of non-integral order.Practical significance: the basic concepts and formulas of the article can be used in scientific and analytical activity for factor analysis of economic processes. The proposed method for integro-differentiation of non-integral order extends the capabilities of the determined factorial economic analysis. The new quantitative method of deterministic factor analysis may become the beginning of quantitative studies of economic agents behavior with memory, hereditarity and spatial non-locality. The proposed methods of deterministic factor analysis can be used in the study of economic processes which follow the exponential law, in which the indicators (endogenous variables) are power functions of the factors (exogenous variables), including the processes described by the Cobb - Douglas production function, since these methods allow to more accurately describe the total influence of the factors in comparison with the standard method. The proposed methods can be used in the study of economic processes described by equations with a power-law non-locality in factor space and in state space.