Residual analysis and parameter estimation of uncertain differential equations

Yang Liu () and Baoding Liu ()
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Yang Liu: Tsinghua University
Baoding Liu: Tsinghua University

Fuzzy Optimization and Decision Making, 2022, vol. 21, issue 4, No 1, 513-530

Abstract: 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.

Keywords: Uncertainty theory; Uncertain differential equation; Residual analysis; Parameter estimation (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (17)

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DOI: 10.1007/s10700-021-09379-4

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