Uncertain time-varying autoregressive model with imprecise observations and its applications

In real life, the uncertainty of data will lead to two situations: the situation of residual non white noise and the situation of inaccurate data. Uncertainty theory provides a theoretical basis for solving the above problems. In this paper, a new uncertain time-varying autoregressive model is proposed in the branch of uncertain time series. Considering the complexity of data fluctuation, time-varying coefficients are included in the uncertain autoregressive model, and the dynamic changes of data are captured by introducing time-varying coefficients to cope with the complexity of data fluctuation. In order to verify the effectiveness of the new model, two empirical analyses are carried out for the above two situations: first, the model is applied to the prediction of total energy consumption. Compared with the traditional time series model, the new model can effectively deal with the problem of non white noise residuals, and shows its advantages in comparison with the existing uncertain time series model; Secondly, the model has been applied to the empirical analysis of China's methane emissions, effectively handling imprecise data, and showing higher accuracy and effectiveness in capturing the dynamic changes of data compared with existing models. These results show that the uncertain time-varying autoregressive model can improve the prediction accuracy, effectively capture data changes, and can be used to analyze and predict data series with inaccurate observations and residual non white noise.