  A finite trigonometric series model for seasonal time series is considered in
this paper. This component model is shown to be useful, in particular, for the
modeling of time series with two types of seasonality, a long-period and a
short period. This component model is also shown to be effective in the case of
ordinary seasonal time series with only one seasonal component, if the seasonal
pattern is simple and can be well represented by a small number of
trigonometric components. As examples, electricity demand data, bi-hourly
temperature data, CO2 data, and two economic time series are considered. The
last section summarizes the findings from the emperical studies.
