This paper presents uncertain nonlinear time series analysis, a statistical method using uncertainty theory to predict future values based on previous observations. The paper introduces an uncertain nonlinear time series model, assuming the disturbance term is an uncertain variable. It also proposes a method to estimate unknown parameters in such models. Real-world applications in motion analysis and epidemic spreading are used to demonstrate the effectiveness of this approach. The results show that the uncertain nonlinear time series model can provide higher forecast accuracy than linear models. Uncertainty theory, developed by Liu, is used as a mathematical framework for analyzing uncertain phenomena. Uncertain statistics, a branch of uncertainty theory, has been successfully applied in various fields, including economics, epidemic spread, and currency exchange rates. Uncertain time series analysis, an important part of uncertain statistics, uses uncertainty theory to predict future values based on past observations. While previous studies have focused on linear models, this paper introduces uncertain nonlinear time series analysis to account for nonlinear features in real-world dynamics. The paper is organized into nine sections. Section 2 introduces the uncertain nonlinear time series model. Section 3 presents a minimization problem to estimate unknown parameters using the principle of least squares. Section 4 discusses residual analysis. Section 5 uses uncertain hypothesis testing to assess model fit. Sections 6 and 7 introduce forecast values and confidence intervals. Section 8 applies the method to model motion and epidemic spread. Section 9 concludes the paper. The study demonstrates that uncertain nonlinear time series analysis can provide more accurate predictions than linear models in real-world scenarios.This paper presents uncertain nonlinear time series analysis, a statistical method using uncertainty theory to predict future values based on previous observations. The paper introduces an uncertain nonlinear time series model, assuming the disturbance term is an uncertain variable. It also proposes a method to estimate unknown parameters in such models. Real-world applications in motion analysis and epidemic spreading are used to demonstrate the effectiveness of this approach. The results show that the uncertain nonlinear time series model can provide higher forecast accuracy than linear models. Uncertainty theory, developed by Liu, is used as a mathematical framework for analyzing uncertain phenomena. Uncertain statistics, a branch of uncertainty theory, has been successfully applied in various fields, including economics, epidemic spread, and currency exchange rates. Uncertain time series analysis, an important part of uncertain statistics, uses uncertainty theory to predict future values based on past observations. While previous studies have focused on linear models, this paper introduces uncertain nonlinear time series analysis to account for nonlinear features in real-world dynamics. The paper is organized into nine sections. Section 2 introduces the uncertain nonlinear time series model. Section 3 presents a minimization problem to estimate unknown parameters using the principle of least squares. Section 4 discusses residual analysis. Section 5 uses uncertain hypothesis testing to assess model fit. Sections 6 and 7 introduce forecast values and confidence intervals. Section 8 applies the method to model motion and epidemic spread. Section 9 concludes the paper. The study demonstrates that uncertain nonlinear time series analysis can provide more accurate predictions than linear models in real-world scenarios.