A discrete bass model and its parameter estimation

Abstract

A discrete Bass model, which is a discrete analog of the Bass model, is proposed. This discrete Bass model is defined as a difference equation that has an exact solution. The difference equation and the solution respectively tend to the differential equation which the Bass model is defined as and the solution when the time interval tends to zero. The discrete Bass model conserves the characteristics of the Bass model because the difference equation has an exact solution. Therefore, the discrete Bass model enables us to forecast the innovation diffusion of products and services without a continuous-time Bass model. The parameter estimations of the discrete Bass model are very simple and precise. The difference equation itself can be used for the ordinary least squares procedure. Parameter estimation using the ordinary least squares procedure is equal to that using the nonlinear least squares procedure in the discrete Bass model. The ordinary least squares procedures in the discrete Bass model overcome the three shortcomings of the ordinary least squares procedure in the continuous Bass model: the time-interval bias, standard error, and multicollinearity.