This paper investigates the impact of mis-specifying the market demand process on a serially linked two-level supply chain. Box-Jenkins models are used to represent both the true and a mis-specified market demand processes. It is shown that the impact of mis-specification on cost is minor if the supply chain tries to minimise the market demand forecast errors. Furthermore, our analysis suggests that mis-specification does not always result in additional costs. A managerial insight is revealed; poor forecast accuracy is not always bad for the total supply chain costs. In other words, employing more accurate forecasting methods may actually result in higher total supply chain costs.