The Modelling and Seasonal Adjustment of Weekly Observations - (Now published in 'Journal of Business and Economic Statistics', 15 (1997), pp.354-368.)
Andrew C Harvey, Siem Jan Koopman and Marco Riani
A number of important economic time series are recorded on a particular day every week. Seasonal adjustment of such series is difficult because the number of weeks varies between 52 and 53 and the position of the recording day changes from year to year. In addtion certain festivals, most notably Easter, take place at different times according to the year. This paper presents a general solution to problems of this kind by setting up a structural time series model which allows the seasonal pattern to evolve over time and enables trend extraction and seasonal adjustment to be carried out by means of state space filtering and smoothing algorithms. The method is illustrated with a Bank of England series on the money supply.