A Comparison of Some Standard Seasonal Forecasting Systems

Many seasonal forecasting systems employ exponentially weighted moving averages usually in the estimation of a trend which consists of sums of products of polynomials and sinusoids. The difference equation structure of such trends is exploited to obtain adaptive predictors. Brown's General Exponential Smoothing, i.e. discounted least squares, the Holt-Winters seasonal form and Harrison's Seatrend and Doubts are shown to be optimal in a minimum mean square error sense for a particular family of stochastic processes, and comparisons are made between them and the Box-Jenkins systems for these processes. One criterion for choosing between the standard systems is considered, viz. stationarity of the forecast errors, and the effect on this choice of invertibility of the forecasting system noted. Some recommendations regarding application are made.