Bayesian Ensembles of Exponentially Smoothed Life-Cycle Forecasts

We study the problem of forecasting an entire demand distribution for a new product before and after its launch. Firms need accurate distributional forecasts of demand to make operational decisions about capacity, inventory and marketing expenditures. We introduce a unified, robust, and interpretable approach to producing these pre- and post-launch distributional forecasts. Our approach is inspired by Bayesian model averaging. Each candidate model in our ensemble is a life-cycle model fitted to the completed life cycle of a comparable product. A pre-launch forecast is an ensemble with equal weights on the candidate models’ forecasts, while a post-launch forecast is an ensemble with weights that evolve according to Bayesian updating. Our approach is part frequentist and part Bayesian, resulting in a novel form of regularization tailored to the demand forecasting challenge. We also introduce a new type of life-cycle or product diffusion model with states that can be updated using exponential smoothing. The trend in this model follows the density of an exponentially tilted Gompertz random variable. For post-launch forecasting, this model is attractive because it can adapt itself to the most recent changes in a product’s life cycle. We provide closed-form distributional forecasts from our model. In two empirical studies, we show that when the ensemble’s candidate models are all in our new type of exponential smoothing model, this version of the ensemble outperforms several leading approaches in both point and quantile forecasting. In a data-driven operations environment, our model can produce accurate fore- casts frequently and at scale. When quantile forecasts are needed, our model has the potential to provide meaningful economic benefits. In addition, our model’s interpretability should be attractive to managers who already use exponential smoothing and ensemble methods for other forecasting purposes