Forecasting the Diffusion of Innovation: A Stochastic Bass Model With Log-Normal and Mean-Reverting Error Process

Abstract

Forecasting the diffusion of innovations plays a major role in managing technology development and in engineering management overall. In this paper, we extend the conventional Bass model stochastically by specifying the error process of sales as log-normal and mean-reverting. Our model satisfies the following reasonable properties, which are generally ignored in the existing literature: sales cannot be negative, the error process can have a memory, and sales fluctuate more when they are high and less when they are low. The conventional and widely used model that assumes normally distributed error term does not have these properties. We address how to forecast properly under the log-normal and mean-reverting error process, and show analytically and numerically that in our extended model sales forecasts can substantially alter conventional Bass forecasts. We also analyze the model empirically, showing that our extension can improve the accuracy of future sales forecasts.