Seasonal Adjustment and Forecasting in the Presence of Trend

Abstract

A general linear statistical model for simultaneous seasonal adjustment and trend estimation is considered for one and two term deterministic trend functions. Explicit estimates of the parameters and variances are derived in a convenient computational form from which the properties of these estimates become apparent. In connection with possible uses of the model for forecasting, the Smallest Neighbourhood (SN) is introduced, within which the trend is assumed to be either linear or representable by a single term. Examples are given to show that simple techniques in certain situations may yield accurate forecasts in return for a comparatively modest amount of computational effort. A procedure season is given which calculates, for any general one term trend function, estimates of seasonal and trend constants together with standard errors and provides predictions, also with standard errors, for any required period.