Empirical estimates for heteroscedastic hierarchical dynamic normal models

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.