Quantile Forecasts of Product Life Cycles Using Exponential Smoothing

by Xiaojia Guo, Kenneth C. Lichtendahl Jr., and Yael Grushka-Cockayne

Overview — Many important business decisions rely on a manager’s forecast of a product or service’s life cycle. One of the most widely used forecasting techniques is exponential smoothing models. This paper introduces a model suitable for large-scale forecasting environments where key operational decisions depend on quantile forecasts.

Author Abstract

We introduce an exponential smoothing model that a manager can use to forecast the demand of a new product or service. The model has five features that make it suitable for accurately forecasting product life cycles at scale. First, the trend in our model follows the density of a new distribution called the tilted-Gompertz distribution. This model can capture the wide range of skewed diffusions commonly found in practice—diffusions of innovations described as having “extra-Bass” skew. Second, its parameters can be updated via exponential smoothing; therefore, the model can react to local changes in the environment. This model is the first exponential smoothing model to incorporate a life-cycle trend. Third, the model relies on multiplicative errors, instead of the additive errors primarily used in existing models. Multiplicative errors ensure that all quantile forecasts are strictly positive. Fourth, the model includes prior distributions on its parameters. These prior distributions become regularization terms in the model and allow the manager to make accurate forecasts from the beginning of a life cycle, which is notoriously difficult. The model's skewed shape, time-varying, regularized parameters, and multiplicative errors can make its quantile forecasts more accurate than leading diffusion models, such as the Bass, gamma/shifted-Gompertz, and trapezoid models. Fifth, the model's estimation procedure is based on an efficient optimization routine, which can be used to forecast product life cycles at scale. In two empirical studies, one of search interest in social networks and the other of new computer sales, we demonstrate that our model outperforms leading diffusion models in out-of-sample forecasting. Our model's point and other quantile forecasts are more accurate. Accurate quantile forecasts at different horizons are critical to many operational decisions, such as capacity and inventory management.

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