Forecast error is not only caused by the randomness of the data‐generating process but also by the uncertainty due to estimated model parameters. We investigate these different sources of forecast error for a popular type of count process, the Poisson first‐order integer‐valued autoregressive (INAR(1)) process. However, many of our analytical derivations also hold for the more general family of conditional linear AR(1) (CLAR(1)) processes. In addition, results from a simulation study are presented, to verify and complement our asymptotic approximations.

中文翻译：

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估计不确定性下的CLAR（1）点预测

预测误差不仅由数据生成过程的随机性引起，而且还由估计模型参数导致的不确定性引起。我们针对流行的计数过程（泊松一阶整数值自回归（INAR（1））过程）调查了这些不同的预测误差源。但是，我们的许多分析推导也适用于条件线性AR（1）（CLAR（1））过程的更一般的系列。此外，还提供了仿真研究的结果，以验证和补充我们的渐近近似。