This paper discusses several encompassing representations for linear season
al models in the structural framework. Their time and frequency domain prop
erties are ascertained in a unifying framework, casting particular attentio
n on the notion of 'smoothness' of the seasonal component. The shape of the
forecast function is compared with that arising from a number of exponenti
al smoothing algorithms. Finally, we investigate whether the specification
of the seasonal model is likely to affect the out-of-sample predictive perf
ormance 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. (C) 2000 Elsevier Sci
ence B.V. All rights reserved.