Uncertain regression model with autoregressive time series errors

Uncertain regression model is a powerful analytical tool for exploring the relationship between explanatory variables and response variables. It is assumed that the errors of regression equations are independent. However, in many cases, the error terms are highly positively autocorrelated. Assuming that the errors have an autoregressive structure, this paper first proposes an uncertain regression model with autoregressive time series errors. Then, the principle of least squares is used to estimate the unknown parameters in the model. Besides, this new methodology is used to analyze and predict the cumulative number of confirmed COVID-19 cases in China. Finally, this paper gives a comparative analysis of uncertain regression model, difference plus uncertain autoregressive model, and uncertain regression model with autoregressive time series errors. From the comparison, it is concluded that the uncertain regression model with autoregressive time series errors can improve the accuracy of predictions compared with the uncertain regression model.