Uncertain time series analysis aims to explore how the current observation is affected by the disturbance terms and past imprecise observations characterized as uncertain variables. For the case that the current observation is affected by a single past disturbance term, the 1-order uncertain moving average (UMA) model has been tentatively explored. While for the situation that the current observation is affected by multiple past disturbance terms, this paper initiates a high-order UMA model to more accurately describe this relationship. By transforming the high-order UMA model into an uncertain autoregressive model via a backward shift operator, the unknown parameters are calculated through the least squares method. Then, a tth residual is defined to describe the properties of disturbance terms. Furthermore, the forecast value and the confidence interval are derived from the fitted model. Finally, two examples are presented to demonstrate the effectiveness of this method.

不确定时间序列分析旨在探索当前观测如何受到干扰项和过去不精确观测的影响，这些观测被表征为不确定变量。对于当前观测受单个过去扰动项影响的情况，已初步探索了 1 阶不确定移动平均 (UMA) 模型。而对于当前观测受多个过去干扰项影响的情况，本文提出了一个高阶UMA模型来更准确地描述这种关系。通过后移算子将高阶UMA模型转化为不确定的自回归模型，通过最小二乘法计算未知参数。然后，一个t定义残差来描述扰动项的性质。此外，预测值和置信区间来自拟合模型。最后，给出了两个例子来证明该方法的有效性。