Affiliations: [a] Department of Mathematical Sciences, Tsinghua University, Beijing, China
| [b] School of Mathematical Sciences, Inner Mongolia University, Inner Mongolia, China
Correspondence:
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Corresponding author. Dalin, School of Mathematical Sciences, Inner Mongolia University, Inner Mongolia 010010, China. E-mail: [email protected].
Abstract: Uncertain time series analysis has been developed for studying the imprecise observations. In this paper, we propose a nonlinear model called uncertain max-autoregressive (UMAR) model. The unknown parameters in model are estimated by the least squares estimation. Then the residual analysis is presented. In many cases, there are some outliers in the time series due to short-term change in the underlying process. The UMAR model offers an alternative for detecting outliers in the imprecise observations. Based on the previous theoretical results, the UMAR model is used to forecast the future. Finally, an example suggests that the new proposed time series model works well compared to the uncertain autoregressive (UAR) model.
Keywords: Uncertain time series analysis, principle of least squares, residual analysis, outlier detection, confidence interval
