A seasonal index for business

This paper explores the problem of obtaining a multiplicative seasonal index for forecasting sales from a small set of historical data (as is common in business applications) and in the presence of a trend. It is shown that the standard method for generating a seasonal index (from a centered moving average) contains a systematic error. This error is transmitted through to forecasts that use the seasonal index and causes higher than necessary safety stocks and other consequences. The paper presents two alternative consistent methods for estimating the seasonal index in the presence of a trend, one for a multiplicative (nonlinear) trend and one for an additive (linear) trend. These methods may be run easily on a spreadsheet program or on statistical software. The nonlinear method is suggested as a convenient alternative to the standard method in many circumstances.