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When developing his model, Alan was careful to include alleged sales as a predictor, thus reducing error autocorrelation. This additional predictor implies a carryover effect of price and promotion on sales. What type of carryover effect should we expect? If shoppers react to promotions by stocking up (i.e., forward-buying), the carryover in the weeks following a promotion should be negative. On the other hand, if promotions have a lasting positive impact on demand, one should expect a positive estimate. Looking at the posterior means for the hyper-distribution of the 's'', five brands had estimates greater than two standard errors, and all five were positive, thus implying some long-term positive effect. While this effect was relatively small for most of these five brands, the estimate was reasonably large (0.35) for one of the brands (Citrus Hill 96 oz.), implying about 54% additional long-term 4% cumulative promotion effects, relative to the immediate effects.
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