An Exponential Smoothing Model with a Life Cycle Trend

Abstract

We study the problem of forecasting a time series that evolves according to a dynamically changing, skewed life cycle. For instance, firms often need accurate distributional forecasts of product life cycles to make operational decisions about capacity and inventory management. These forecasts often need to be made prior to launch, updated frequently thereafter, and generated at scale. Exponential smoothing models are commonly used in practice to make time series forecasts because they are tractable, accurate, and easy to interpret. This work is the first to develop an exponential smoothing model with a life-cycle trend. The life-cycle trend in the model follows the density of a new distribution called the tilted-Gompertz distribution. 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 a notoriously difficult problem. We provide closed-form quantile forecasts from our model and demonstrate that the model can capture a wide range of skewed diffusions. In two empirical studies, our model outperforms leading diffusion models in out-of-sample point forecasting and quantile forecasting. The model's accuracy appears to be due to its flexible shape and regularized and time-varying parameters.

Keywords: demand forecasting; capacity planning; inventory management; new product adoption; skewed diffusions; quantile forecasts