Parameters Estimation and Stability Analysis of Nonlinear Fractional-Order Economic System Based on Empirical Data

Abstract

This paper is devoted to propose a novel method for studying the macroeconomic system with fractional derivative, which can depict the memory property of actual data of economic variables. First of all, we construct a constrained optimal problem to evaluate the coefficients of nonlinear fractional financial system based on empirical data and design the corresponding genetic algorithm. Then, based on the stability criteria of fractional dynamical systems, the methodology of stability analysis is proposed to investigate the stability of the estimated nonlinear fractional dynamic system. Finally, our method is applied to discuss the macroeconomic system of the US, Australia, and UK to demonstrate its effectiveness and applicability.