On the development of innovation diffusion model using stochastic differential equation incorporating change in the adoption rate

Bass innovation and diffusion model and many of its extended forms have been reported in marketing literature and applied successfully for depicting and predicting adoption curve for products from different sectors of economy, segments of markets and strata of society. All these models assume the adoption process as a discrete counting process. However, if the potential adopter population is large and product is in the market with greater life cycle length, it is quite likely that adoption process is a stochastic process with continuous state space. In this paper, we propose a new innovation and diffusion model based on type of stochastic differential equation (SDE). It also incorporates the change-point concept, where the rate of product adoption per remaining potential adopter might change due shift in marketing/promotional strategy, entry/exit of some of the competitors in the market. The applicability and accuracy of the proposed model are illustrated using new product sales data. Predictive validity and mean squared error have been used to check the validity of the model. It has been shown that SDE-based model with change point performs comparatively better than Bass innovation and diffusion model.