Hierarchical Bayes forecasts of multinomial Dirichlet data applied to coupon redemptions

This paper considers forecasting count data from a multinomial Dirichlet distribution. The forecasting procedure implements hierarchical Bayes methods in order to develop a prior distribution for a new series of data. The methodology is applied to the redemption of cents-off promotional coupons. In a forecasting experiment, early forecasts of new series are similar to those from pooling all redemptions from previous coupon promotions. However, the hierarchical Bayes model provides realistic estimates of forecasting errors, while those for the pooled forecasts are consistently optimistic. As the current series evolves, the hierarchical Bayes forecasts adapt more rapidly and are more accurate than pooled forecasts.