Weights and robustness of model-based seasonal adjustment

Model-based seasonal adjustment implicitly defines a set of weights at the ends of series as well as in the middle. Until now, with the exception of very simple models, the weights have been obtained numerically. In this paper we give the analytical expressions for the weights for both the structural and the ARIMA framework for a model which contains trend, seasonal and irregular component. In the final part of the paper we address the question of robustness of model-based seasonal adjustment. We analyse practically, using real time series, and theoretically, through the analysis of the shape of the weights, how the fitting of different specifications for the non-seasonal part affects the extraction of the seasonal component.