Exponential Smoothing and Short-Term Sales Forecasting

Non-seasonal forecasting methods are examined by considering demand generating processes which are reasonable and general descriptions of customer demand and for which the popular predictors are shown to be optimal. Tests of the adequacy of the generating processes are described. The way in which the forecasting errors vary with the forecasting period is examined, and it is shown that this is dependent not only on the length of the period but also on the values of the forecasting parameters. The sensitivity of the predictors to departures from the optimal parameters is investigated, and the long debated comparison of Holt's linear growth predictor (1957) and Brown's linear growth predictor (1959) is examined. It is shown for the assumed generating model and for forecasting parameters lying within the usual limits, that even if there is an infinite amount of data available to establish the optimum forecasting parameters, the standard error of the one step ahead predictor exceeds that of the Holt predictor by no more than 1.6 percent. The generalized polynomial generating process is shown to have as its optimal least squares predictor the corresponding Box-Jenkins polynomial predictor (1962).