Seasonal Adjustment Based on a Mixed Additive--Multiplicative Model

Abstract

Seasonal-adjustment procedures based on regression methods applied to a mixed additive-multiplicative model are described. The procedures are based on the traditional model of trend, seasonal and irregular components but instead of assuming that the seasonal is purely additive or purely multiplicative as in the usual methods of seasonal adjustment they permit the use of a mixture of additive and multiplicative components. Tests are developed which are intended to investigate whether a purely additive, a purely multiplicative or a mixed additive-multiplicative model is required by the data. For the general case where both additive and multiplicative components are required, the seasonal component is assumed to consist of a seasonal pattern and a seasonal amplitude which are estimated separately. The trend is estimated using moving-average filters and the seasonal component is fitted by means of a stepwise regression method applied to additive and multiplicative Fourier components. Two main computer programs have been developed, the first of which tests whether a purely additive, a purely multiplicative or a mixed additive-multiplicative seasonal model is required; the second estimates the seasonal component and produces a seasonally adjusted series. The methods are applied to a number of unemployment series for several countries.