Generalized moment estimation for uncertain differential equations
Generalized moment estimation for uncertain differential equations
复制标题
不确定微分方程的广义矩估计
DOI：
10.1016/j.amc.2020.125724
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发表时间：
2021-03-01
影响因子：
4
通讯作者：
Liu, Z.
中科院分区：
文献类型：
--
作者：
Liu, Z.
参数估计是不确定微分方程充分发挥其潜力的关键问题。基于Liu过程的性质和不确定微分方程的差分形式，现有的矩量法虽然直观，但有时无解。因此，该方法是无效的，需要替代方法来估计不确定微分方程中的未知参数。受此启发，本文提出了广义矩估计，这是最小化问题的最优解。广义矩估计与存在矩估计时的矩估计等价，并且在矩估计无效时仍能很好地工作。对利率的数值算例和实证分析说明了广义矩估计的合理性和优越性。 (c) 2020 Elsevier Inc. 保留所有权利。
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. (c) 2020 Elsevier Inc. All rights reserved.