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Residual analysis and parameter estimation of uncertain differential equations

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Abstract

All existing methods to estimate unknown parameters in uncertain differential equations are based on difference scheme, and do not work when the time intervals between observations are not short enough. In order to overcome this shortage, this paper presents a concept of residual. Afterwards, an algorithm is designed for calculating residuals of uncertain differential equation corresponding to observed data. In addition, this paper presents a method of moments based on residuals to estimate the unknown parameters in uncertain differential equations. Finally, some examples (including Alibaba stock price) are provided to illustrate the parameter estimation method.

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Notes

  1. MATLAB R2021a, 9.10.0.1602886, maci64, Optimization Toolbox, “fsolve” function.

  2. MATLAB R2021a, 9.10.0.1602886, maci64, Optimization Toolbox, “fminsearch” function.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China Grant Nos.61873329 and 12026225.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China

    Yang Liu & Baoding Liu

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  1. Yang Liu
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  2. Baoding Liu
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Correspondence to Baoding Liu.

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Liu, Y., Liu, B. Residual analysis and parameter estimation of uncertain differential equations. Fuzzy Optim Decis Making 21, 513–530 (2022). https://doi.org/10.1007/s10700-021-09379-4

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  • DOI: https://doi.org/10.1007/s10700-021-09379-4

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