Comparing seasonal components for structural time series models

This paper discusses several encompassing representations for linear seasonal models in the structural framework. Their time and frequency domain properties are ascertained in a unifying framework, casting particular attention on the notion of 'smoothness' of the seasonal component. The shape of the forecast function is compared with that arising from a number of exponential smoothing algorithms. Finally, we investigate whether the specification of the seasonal model is likely to affect the out-of-sample predictive performance of the basic structural model. We conclude that the latter depends upon the features of the time series under investigation, and in particular on the degree of smoothness of the seasonal pattern.