On weighted threshold moment estimation of uncertain differential equations with applications in interbank rates analysis

Abstract

Uncertainty theory is a branch of mathematics for modeling belief degrees. Within the framework of uncertainty theory, uncertain variable is used to represent quantities with uncertainty, and uncertain process is used to model the evolution of uncertain quantities. Uncertain differential equation is a type of differential equation involving uncertain processes, which has been successfully applied in many disciplines such as finance, optimal control, differential game, epidemic spread and so on. Uncertain differential equation has become the main tool to deal with dynamic uncertain systems. One of the key issues within the research of uncertain differential equations is the estimation of parameters involved based on the observed data. However, it is relatively difficult to solve this issue when the structures of the corresponding terms in the equations are not known in advance. To address this problem, one nonparametric estimation technique called weighted threshold moment estimation for homogeneous uncertain differential equations is proposed in this paper when no prior information about the terms is obtained. Numerical examples are presented to demonstrate the feasibility and efficiency of our method, highlighted by an empirical study of the Shanghai Interbank Offered Rate in China. The paper concludes with final remarks and recommendations for future research.