Difference Equations in Forecasting Formulas

The deviation of actual sales (or other time-dependent statistics) from a model of sales will give rise to forecasting errors that are enhanced, damped out, or shifted in phase, depending on the particular formulas that are used for forecasting. Following R. G. Brown, P. Winters, and Theil, Nerlove, and Wage, we start from a general set of forecasting formulas, but make fewer assumptions than those authors about deviations from the model, and obtain a more extensive collection of results. In particular, we show how to treat errors not serially uncorrelated, and how to investigate forecasting formulas of order higher than second.