Long waiting lists are a symbol of inefficiencies of hospital services. The dynamics of waiting lists are complex, especially when trying to understand how the lists grow due to the demand of a particular treatment relative to a hospital's capacity. Understanding the uncertainty of forecasting growth/decline of waiting lists could help hospital managers with capacity planning. We address this uncertainty through the use of statistical tolerance intervals, which are intervals that contain a specified proportion of the sampled population at a given confidence level. Tolerance intervals are available for numerous settings, however, the approaches for autoregressive models are far more limited. This article fills that gap and establishes tolerance intervals for general AR(p) models, which may also have a mean or trend component present. A rigorous development of tolerance intervals in this setting is presented. Extensive simulation studies identify that good coverage properties are achieved when the AR process is stationary and the parameters of the AR model are well within the stationarity constraints. Otherwise, a bootstrap‐based correction can be applied to improve the coverage probabilities. Finally, the method is applied to the monthly number of patients on hospital waiting lists in England.

中文翻译：

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自回归模型的公差区间，并应用于医院候诊清单

漫长的等待名单是医院服务效率低下的象征。等待列表的动态非常复杂，尤其是在试图了解由于特定治疗需求（相对于医院容量）而导致列表如何增长时。了解预测候诊人数增长/下降的不确定性可以帮助医院管理人员进行容量规划。我们通过使用统计公差区间来解决这种不确定性，该区间是在给定的置信度下包含指定比例的抽样人群的区间。公差间隔可用于多种设置，但是，自回归模型的方法受到更多限制。本文填补了这一空白，并建立了一般AR（p）模型，也可能存在均值或趋势分量。提出了在这种情况下公差区间的严格发展。大量的仿真研究表明，当AR过程平稳且AR模型的参数处于平稳性约束范围内时，可以实现良好的覆盖范围。否则，可以应用基于引导的校正来提高覆盖率。最后，该方法适用于英格兰每月在医院候诊名单上的患者人数。