Modeling Trigonometric Seasonal Components for Monthly Economic Time Series

The basic structural time series model has been designed for the modelling and forecasting of seasonal economic time series. In this paper we explore a generalisation of the basic structural time series model in which the time-varying trigonometric terms associated with different seasonal frequencies have different variances for their disturbances. The contribution of the paper is two-fold. The first aim is to investigate the dynamic properties of this frequency specific basic structural model. The second aim is to relate the model to a comparable generalised version of the Airline model developed at the U.S. Census Bureau. By adopting a quadratic distance metric based on the restricted reduced form moving-average representation of the models, we conclude that the generalised models have properties that are close to each other compared to their default counterparts. In some settings, the distance between the models is almost zero so that the models can be regarded as observationally equivalent. An extensive empirical study on disaggregated monthly shipment and foreign trade series illustrates the improvements of the frequency-specific extension and investigates the relations between the two classes of models.