The parameter estimations for uncertain regression model with autoregressive time series errors

Abstract

Uncertain regression model with autoregressive time series errors studies the relations between response variables and explanatory variables when the errors are dependence. The estimations of the unknown parameters are worth exploring in further research. The least square (LS) estimations were proposed to estimate the unknown parameters. However, when the outliers appear, we find that the LS is not effective. So, in this article, the least absolute deviations (LAD) and the maximum likelihood estimations (MLE) are proposed to estimate the unknown parameters. Moreover, some examples are given to verify the applicability and practicability of these two methods. The comparative analysis is given to verify that the proposed methods are more advantageous and effective than the least square method when the observed data are affected by outliers. Finally, the example of exploring the relationships between GDP and related influencing factors for China, from 2004 to 2020, is given to testify the practicability of the methods.

KEYWORDS:

• Uncertainty theory
• the least deviation estimation
• the maximum likelihood estimation
• GDP
• prediction

Conflict of interest

All the authors declare no conflicts of interest in this article.

Additional information

Funding

This work was funded by the National Natural Science Foundation of China (Grant Nos. 12061072 and 62162059) and the Xinjiang Key Laboratory of Applied Mathematics (Grant No. XJDX1401).