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Uncertain hypothesis test for uncertain differential equations

Author

Listed:
  • Tingqing Ye

    (Beihang University)

  • Baoding Liu

    (Tsinghua University)

Abstract

Uncertain hypothesis test is a statistical tool that uses uncertainty theory to determine whether some hypotheses are correct or not based on observed data. As an application of uncertain hypothesis test, this paper proposes a method to test whether an uncertain differential equation fits the observed data or not. In order to demonstrate the test method, some numerical examples are provided. Finally, both uncertain currency model and stochastic currency model are used to model US Dollar to Chinese Yuan (USD–CNY) exchange rates. As a result, it is shown that the uncertain currency model fits the exchange rates well, but the stochastic currency model does not.

Suggested Citation

  • Tingqing Ye & Baoding Liu, 2023. "Uncertain hypothesis test for uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 22(2), pages 195-211, June.
    • Handle: RePEc:spr:fuzodm:v:22:y:2023:i:2:d:10.1007_s10700-022-09389-w
    DOI: 10.1007/s10700-022-09389-w
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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. Tingqing Ye & Baoding Liu, 2022. "Uncertain hypothesis test with application to uncertain regression analysis," Fuzzy Optimization and Decision Making, Springer, vol. 21(2), pages 157-174, June.
    3. Tingqing Ye & Xiangfeng Yang, 2021. "Analysis and prediction of confirmed COVID-19 cases in China with uncertain time series," Fuzzy Optimization and Decision Making, Springer, vol. 20(2), pages 209-228, June.
    4. 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.
    5. Kai Yao & Baoding Liu, 2020. "Parameter estimation in uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 19(1), pages 1-12, March.
    6. Xiangfeng Yang & Baoding Liu, 2019. "Uncertain time series analysis with imprecise observations," Fuzzy Optimization and Decision Making, Springer, vol. 18(3), pages 263-278, September.
    7. Liu, Z. & Yang, Y., 2021. "Uncertain pharmacokinetic model based on uncertain differential equation," Applied Mathematics and Computation, Elsevier, vol. 404(C).
    8. 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).
    9. Liu, Z. & Yang, Y., 2021. "Pharmacokinetic model based on multifactor uncertain differential equation," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    10. Tang, Han & Yang, Xiangfeng, 2021. "Uncertain chemical reaction equation," Applied Mathematics and Computation, Elsevier, vol. 411(C).
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    Cited by:

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    2. Meiling Jin & Fengming Liu & Yufu Ning & Yichang Gao & Dongmei Li, 2024. "A Mathematical Optimization Model Designed to Determine the Optimal Timing of Online Rumor Intervention Based on Uncertainty Theory," Mathematics, MDPI, vol. 12(16), pages 1-21, August.
    3. Zhe Liu & Yanbin Li, 2024. "Pricing and valuation of carbon swap in uncertain finance market," Fuzzy Optimization and Decision Making, Springer, vol. 23(3), pages 319-336, September.
    4. Haoxuan Li & Xiangfeng Yang & Yaodong Ni, 2024. "Pricing of shout option in uncertain financial market," Fuzzy Optimization and Decision Making, Springer, vol. 23(3), pages 449-467, September.
    5. Zhiwei Wang & Yuanguo Zhu, 2024. "LQ optimal control of uncertain fractional differential systems," Fuzzy Optimization and Decision Making, Springer, vol. 23(4), pages 577-597, December.
    6. He, Liu & Zhu, Yuanguo, 2024. "Nonparametric estimation for uncertain fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    7. Jinran Chen, 2024. "Prediction of global trade network evolution with uncertain multi-step time series forecasting method," Fuzzy Optimization and Decision Making, Springer, vol. 23(3), pages 387-414, September.
    8. Liu, Zhe & Wang, Shihai & Liu, Bin & Kang, Rui, 2023. "Change point software belief reliability growth model considering epistemic uncertainties," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    9. Yang Liu & Zhongfeng Qin & Xiang Li, 2024. "Are the queueing systems in practice random or uncertain? Evidence from online car-hailing data in Beijing," Fuzzy Optimization and Decision Making, Springer, vol. 23(4), pages 497-511, December.

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