The objective of time series analysis is to study the relationship between the data over time and to predict future values. Traditionally, statisticians assume that the observation data are precise, and we can get some exact values. However, in many cases, the imprecise observation data are available. We assume that these data are uncertain variables in the sense of uncertainty theory. In this paper, the ridge method is used to compute the unknown parameters in the uncertain autoregressive model. First, the ridge estimation of the parameters is given. The shrinkage parameter in the ridge estimation is obtained by ridge trace analysis. Based on the fitted autoregressive model, the forecast value and confidence interval of the future data are derived. Then two numerical examples are presented to verify the feasibility of this approach. Finally, the effectiveness of our model in reducing the influence of the outliers is shown by the comparative analysis.

中文翻译：

---

具有不精确观测值的不确定自回归模型的岭估计

时间序列分析的目的是研究数据随时间变化的关系并预测未来值。传统上，统计学家假设观察数据是精确的，我们可以得到一些精确的值。但是，在许多情况下，可以获得不精确的观测数据。我们假设这些数据是不确定性理论意义上的不确定变量。本文采用岭法计算不确定自回归模型中的未知参数。首先，给出了参数的岭估计。脊估计中的收缩参数是通过脊迹分析获得的。基于拟合的自回归模型，推导出未来数据的预测值和置信区间。然后给出了两个数值例子来验证该方法的可行性。最后，