Affiliations: [a] Department of Mathematical Sciences, Tsinghua University, Beijing, China
| [b] School of Information Technology and Management, University of InternationalBusiness and Economics, Beijing, China
Correspondence:
[*]
Corresponding author. Xiangfeng Yang, School of Information Technology and Management, University of International Business and Economics, Beijing 100029, China. E-mail: yangxf@uibe.edu.cn.
Abstract: The objective of uncertain time series analysis is to explore the relationship between the imprecise observation data over time and to predict future values, where these data are uncertain variables in the sense of uncertainty theory. In this paper, the method of maximum likelihood is used to estimate the unknown parameters in the uncertain autoregressive model, and the unknown parameters of uncertainty distributions of the disturbance terms are simultaneously obtained. Based on the fitted autoregressive model, the forecast value and confidence interval of the future data are derived. Besides, the mean squared error is proposed to measure the goodness of fit among different estimation methods, and an algorithm is introduced. Finally, the comparative analysis of the least squares, least absolute deviations, and maximum likelihood estimations are given, and two examples are presented to verify the feasibility of this approach.
Keywords: Uncertain variable, autoregressive model, maximum likelihood estimation, mean squared error
