On the Bass diffusion theory, empirical models and out-of-sample forecasting

The Bass (1969) diffusion theory often guides the construction of forecasting models for new product diffusion. To match the model with data, one needs to put forward a statistical model. This paper compares four empirical versions of the model, where two of these explicitly incorporate autoregressive dynamics. Next, it is shown that some of the regression models imply multi-step ahead forecasts that are biased. Therefore, one better relies on the simulation methods, which are put forward in this paper. An empirical analysis of twelve series (Van den Bulte and Lilien 1997) indicates that one-step ahead forecasts substantially improve by including autoregressive terms and that simulated two-step ahead forecasts are quite accurate.