Parameters estimation of uncertain autoregressive model based on modified maximum likelihood approach

Uncertain time series analysis occupies an indispensable position in the field of statistics, and it uses time series models to conduct in-depth mining of time series data under uncertain environments, aiming at forecasting the future development trend of variables. However, once the data set is disturbed by outliers, the existing research methods will be ineffective. In order to reduce the influence of outliers on the fit degree and prediction accuracy of the uncertain autoregressive model, this paper uses the modified uncertain maximum likelihood idea to re-estimate the unknown parameters and disturbance term in the uncertain autoregressive model and provides a numerical algorithm to solve these estimators. Subsequently, we also illustrate the modified uncertain maximum likelihood approach proposed in this paper by two numerical examples and compare it with the existing uncertain maximum likelihood method. Finally, we applied this new approach to forecast the air temperatures of Beijing Capital Airport and further verified its effectiveness by comparing it with the existing statistical inference methods.