The propagation and identification of ARMA demand under simple exponential smoothing: forecasting expertise and information sharing

It is common for firms to forecast stationary demand using simple exponential smoothing (SES) due to the ease of computation and understanding of the methodology. We consider a retailer who observes autoregressive moving average (ARMA) demand but for the sake of convenience, uses the widely available SES method to forecast its demand. This creates a potential disconnect between the true mechanism generating demand and the forecasting methodology. We show that the supplier, given a sufficiently long history of the retailer's orders, is always able to recover the retailer's true shocks, and in addition is able to infer the true ARMA model generating the retailer's demand process if the retailer shares its exponential smoothing parameter. We further prove that under these assumptions, the supplier is then able to infer the retailer's demand as well. Thus, the supplier is in possession of expertise that would benefit the retailer. However, as a result of the supplier sharing its forecasting expertise, we demonstrate that the demand the supplier will face can have a smaller or larger mean squared forecast error than when the retailer uses the suboptimal SES forecast. In addition, we show that if the supplier provides its forecasting expertise to the retailer, there may be value in the retailer sharing its demand with the supplier. We also perform a simulation study for a special case of an AR(1) demand process and demonstrate that as the sample size of data increases, the difference of mean squared errors between the supplier's estimations of the retailer's demand shocks and the retailer's true demand shocks converges to zero.