A general structural model for decomposing time series and its analysis as a generalized regression model

The model of Harrison and Stevens (1976) for decomposing economic time series is reformulated and, following Harvey (1984), the reformulation is proposed as a general structural model. The discussion of this general model shows that it contains many recently discussed time series models as special cases. For structural models, the Kalman filter technique is usually used to decompose economic data. An alternative for the unifying description is the well-known regression analysis, which has some desirable properties. It is whown that in a first step classical estimation procedure such as the ML method, and test procedures such as the likelihood ratio test can be applied in the generalized regression model without increasing the low computational complexity reached by the Kalman filter algorithm. In a second step, the unobserved components such as trend, cycle and season can be determined in a generalized regression form. This form can also be used in a descriptive exploratory procedure for decomposing time series.