Some recent developments in the analysis of component models for economic time series

Abstract

Three approaches to the ‘classical’ problem of decomposing an economic time series into several components are presented. The first one is a certain generalization of known methods for the construction of moving averages to smooth a time series. It takes into account not only the trend-cyclical component—by polynomials—, but at the same time the seasonal component. Furthermore, due to a unified approach, one gets “best” weighting systems not only for the central parts but also for the tails of the time series. Very often the selection and the comparison of smoothing and seasonal adjustment procedures is made with respect to the properties of the frequency response function of the corresponding filters. Therefore it seems justified that the construction itself of appropriate filters is oriented at these properties. An approach which proceeds from this principle is proposed in the second section. Here one can rely on techniques developed in electrical engeneering. There the design of filters with desirable transfer properties is a well known problem. Two main types of filters, nonrecursive and recursive ones, are at the designers disposal. The application of recursive filters to component models for economic time series is relatively new. The application of spline functions seems to suggest itself as a possible alternative to established smoothing filters. We discuss this in the third section. One possible application consists in the use of spline functions as regressors for the smooth component in a regression model. Besides this splines are used when the smoothest curve through a point cloud is to be found. A discrete alternative to this approach which allows for seasonal variations is presented at the end of the paper.