Generalized moment estimation for uncertain differential equations

Parameter estimation is a critical problem for the uncertain differential equation to achieve its full potential. Based on the Liu process's properties and the difference form of the uncertain differential equation, the existing method of moments is intuitive but sometimes has no solution. As a result, this method is invalid and alternative ways are needed to estimate unknown parameters in the uncertain differential equation. Motivated by this, this paper proposes the generalized moment estimation which is the optimal solution of a minimization problem. Generalized moment estimation is equivalent to moment estimation when moment estimation exists, and still works well when moment estimation is invalid. Numerical examples and an empirical analysis on the interest rate illustrate the rationality and superiority of the generalized moment estimation. © 2020 Elsevier Inc.