Abstract
Uncertain nonlinear time series analysis is a set of statistical techniques that use uncertainty theory to predict future values via nonlinear dynamics based on the previous observations. By assuming that the disturbance term is an uncertain variable, an uncertain nonlinear time series model is derived in this paper. In addition, this paper presents a method to estimate unknown parameters in an uncertain nonlinear time series model. Finally, some real examples (motion analysis and epidemic spreading) are provided to illustrate uncertain nonlinear time series analysis. As a result, it is shown that the uncertain nonlinear time series model may provide higher forecast accuracy than linear one.
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Chen, D., & Yang, X. (2021). Maximum likelihood estimation for uncertain autoregressive model with application to carbon dioxide emissions. Journal of Intelligent & Fuzzy Systems, 40(1), 1391–1399.
Jiang, B., & Ye, T. (2023). Uncertain panel regression analysis with application to the impact of urbanization on electricity intensity. Journal of Ambient Intelligence and Humanized Computing, 14(9), 13017–13029.
Lio, W., & Liu, B. (2018). Residual and confidence interval for uncertain regression model with imprecise observations. Journal of Intelligent & Fuzzy Systems, 35(2), 2573–2583.
Lio, W., & Liu, B. (2020). Uncertain maximum likelihood estimation with application to uncertain regression analysis. Soft Computing, 24(13), 9351–9360.
Liu, B. (2007). Uncertainty theory (2nd ed.). Springer.
Liu, B. (2009). Some research problems in uncertainty theory. Journal of Uncertain Systems, 3(1), 3–10.
Liu, B. (2010). Uncertainty theory: A branch of mathematics for modeling human uncertainty. Springer.
Liu, B. (2023). Uncertainty theory (5th ed.). https://cloud.tsinghua.edu.cn/d/df71e9ec330e49e59c9c/.
Liu, Y. (2022). Analysis of China’s population with uncertain statistics. Journal of Uncertain Systems, 15(4), 2243001.
Liu, Y., & Liu, B. (2022). Residual analysis and parameter estimation of uncertain differential equations. Fuzzy Optimization and Decision Making, 21(4), 513–530.
Liu, Y. (2023). Moment estimation for uncertain regression model with application to factors analysis of grain yield. Communications in Statistics-Simulation and Computation. https://doi.org/10.1080/03610918.2022.2160461
Liu, Y., & Liu, B. (2023a). A modified uncertain maximum likelihood estimation with applications in uncertain statistics. Communications in Statistics-Theory and Methods. https://doi.org/10.1080/03610926.2023.2248534
Liu, Y., & Liu, B. (2023b). Estimation of uncertainty distribution function by the principle of least squares. Communications in Statistics-Theory and Methods. https://doi.org/10.1080/03610926.2023.2269451
Liu, Z. (2021). Uncertain growth model for the cumulative number of COVID-19 infections in China. Fuzzy Optimization and Decision Making, 20(2), 229–242.
Yang, L., & Liu, Y. (2023). Solution method and parameter estimation of uncertain partial differential equation with application to China’s population. Fuzzy Optimization and Decision Making. https://doi.org/10.1007/s10700-023-09415-5
Yang, X., & Liu, B. (2019). Uncertain time series analysis with imprecise observations. Fuzzy Optimization and Decision Making, 18(3), 263–278.
Yang, X., & Ni, Y. (2021). Least squares estimation for uncertain moving average model. Communications in Statistics-Theory and Methods, 50(17), 4134–4143.
Yang, X., & Ke, H. (2023). Uncertain interest rate model for Shanghai interbank offered rate and pricing of American swaption. Fuzzy Optimization and Decision Making, 22(3), 447–462.
Ye, T., & Yang, X. (2021). Analysis and prediction of confirmed cases of COVID-19 in China by uncertain time series. Fuzzy Optimization and Decision Making, 20(2), 209–228.
Ye, T., & Liu, B. (2022). Uncertain hypothesis test with application to uncertain regression analysis. Fuzzy Optimization and Decision Making, 21(2), 157–174.
Ye, T., & Kang, R. (2022). Modeling grain yield in China with uncertain time series model. Journal of Uncertain Systems, 15(4), 2243003.
Ye, T., & Liu, B. (2023a). Uncertain hypothesis test for uncertain differential equations. Fuzzy Optimization and Decision Making, 22(2), 195–211.
Ye, T., & Liu, B. (2023b). Uncertain significance test for regression coefficients with application to regional economic analysis. Communications in Statistics-Theory and Methods, 52(20), 7271–7288.
Ye, T., & Zheng, H. (2023). Analysis of birth rates in China with uncertain statistics. Journal of Intelligent & Fuzzy Systems, 44(6), 10621–10632.
Ye, T. (2023). Analysis of labour income share in China with uncertain regression model. Technical Report.
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This work was supported by National Natural Science Foundation of China (Grant No.62203026) and the Funding of Science and Technology on Reliability and Environmental Engineering Laboratory, China (No.6142004220101).
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Xie, J., Lio, W. Uncertain nonlinear time series analysis with applications to motion analysis and epidemic spreading. Fuzzy Optim Decis Making 23, 279–294 (2024). https://doi.org/10.1007/s10700-024-09421-1
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DOI: https://doi.org/10.1007/s10700-024-09421-1