State space time series

Structural time series models are a powerful technique for variance reduction in the framework of small area estimation (SAE) based on repeatedly conducted surveys. Such models, however, contain unknown hyperparameters that have to be estimated before the Kalman filter can be launched to estimate state variables of the model.
This paper describes a simulation aimed at studying the properties of the model hyperparameters. Simulating hyperparameter distributions under different model specifications complements standard model diagnostics for state space models. Uncertainty around the model hyperparameters is another major issue. To account for hyperparameter uncertainty in the MSE estimates of the Dutch Labour Force survey (DLFS), several estimation approaches known in the literature are considered. Apart from the MSE bias comparison, this paper also provides insight into the variances and MSEs of the MSE estimators considered. The results based on the DLFS suggest that the best performing approach we reviewed may correct for a 2-percent negative relative bias in the signal MSE produced by the Kalman filter, by offering a positive bias of 2 percent.