The available heteroscedastic hierarchical models perform well for a wide range of real-world data, but for data sets that exhibit a dynamic structure they seem fit poorly. In this work, we develop a two-level dynamic heteroscedastic hierarchical model and suggest some empirical estimators for the association hyper-parameters. Moreover, we derive the risk properties of the estimators. Our proposed model has the feature that the dependence structure among observations is produced from the hidden variables in the second level and not through the observations themselves. The comparison between various empirical estimators is illustrated through a simulation study. Finally, we apply our methods to a baseball data.

可用的异方差分层模型在各种现实数据中表现良好，但对于显示动态结构的数据集，它们的拟合度似乎很差。在这项工作中，我们建立了一个两级动态异方差分层模型，并为关联超参数提出了一些经验估计。此外，我们得出估计量的风险属性。我们提出的模型具有以下特征：观测值之间的依存关系是由第二级隐藏变量产生的，而不是通过观测值本身产生的。通过仿真研究说明了各种经验估计量之间的比较。最后，我们将方法应用于棒球数据。