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Parameter estimation of uncertain differential equation by implementing an optimized artificial neural network

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  • Noorani, Idin
  • Mehrdoust, Farshid

Abstract

This study suggests a novel method for estimation of uncertain stock model parameters driven by Liu process. The proposed method decomposes the parameter estimation problem into two sub-problems: the first sub-problem implements an optimized artificial neural network based on the observed data, and the next sub-problem estimates the uncertain model parameters according to the optimized artificial neural network. We apply Nelder–Mead algorithm to optimize the artificial neural network and parameter estimation problem. The main supremacy of the presented method is that the estimation problem is independent of time intervals among observations and can be used to model future data. Providing a comparative method shows that the proposed approach can be effective for non-linear problems in which the artificial neural network structures perform well.

Suggested Citation

  • Noorani, Idin & Mehrdoust, Farshid, 2022. "Parameter estimation of uncertain differential equation by implementing an optimized artificial neural network," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    • Handle: RePEc:eee:chsofr:v:165:y:2022:i:p1:s0960077922009481
    DOI: 10.1016/j.chaos.2022.112769
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    References listed on IDEAS

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    1. Yang Liu & Baoding Liu, 2022. "Residual analysis and parameter estimation of uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 21(4), pages 513-530, December.
    2. Waichon Lio & Baoding Liu, 2021. "Initial value estimation of uncertain differential equations and zero-day of COVID-19 spread in China," Fuzzy Optimization and Decision Making, Springer, vol. 20(2), pages 177-188, June.
    3. Kai Yao & Baoding Liu, 2020. "Parameter estimation in uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 19(1), pages 1-12, March.
    4. Liu, Z., 2021. "Generalized moment estimation for uncertain differential equations," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    5. Yang, Xiangfeng & Liu, Yuhan & Park, Gyei-Kark, 2020. "Parameter estimation of uncertain differential equation with application to financial market," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    6. Tang, Han & Yang, Xiangfeng, 2021. "Uncertain chemical reaction equation," Applied Mathematics and Computation, Elsevier, vol. 411(C).
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