The LAD estimation of UMAR model with imprecise observations

Article type: Research Article

Authors: Wu, Jing | Shi, Yuxin | Sheng, Yuhong^{; *}

Affiliations: College of Mathematics and Systems Science, Xinjiang University, Urumqi, China

Correspondence: [*] Corresponding author. Yuhong Sheng, College of Mathematics and Systems Science, Xinjiang University, Urumqi, 830046, China. E-mail: shengyh@xju.edu.cn.

Abstract: Uncertain time series analysis is a method of predicting future values by analyzing imprecise observations. In this paper, the least absolute deviation (LAD) method is applied to solve for the unknown parameters of the uncertain max-autoregressive (UMAR) model. The predicted value and confidence interval of the future data are calculated using the fitted UMAR model. Moreover, the relative change rate of parameter is proposed to test the robustness of different estimation methods. Then, two comparative analyses demonstrate the LAD estimation can handle outliers better than the least squares (LS) estimation and the necessity of introducing the UMAR model. Finally, a numerical example displays the LAD estimation in detail to verify the effectiveness of the method. The LAD estimation is also applied to a collection of actual data with cereal yield.

Keywords: Uncertain time series, uncertain max-autoregressive model, least absolute deviation estimation, relative change rate

DOI: 10.3233/JIFS-232789

Journal: Journal of Intelligent & Fuzzy Systems, vol. 45, no. 5, pp. 7797-7809, 2023