The NLS-based Grey Bass Model for Simulating New Product Diffusion

Abstract

To solve the problems inherent in the existing Bass model, this paper develops a grey Bass model using a non-linear least squares method (NLS) and provides the whitenisation solution of differential equations. A Bass model exploits the specific advantage in simulating and predicting new product diffusion. Unfortunately, the existing Bass model has two problems: one lies in the conflict between the small sample support in new product diffusion and the large sample requirement in Bass model estimations; the other is over-reliance on the subjective experience in estimating potential market capacity. Although Wang et al. (2011) proposed the grey Bass model to solve the first problem, the second problem remains untouched. Based on this work by Wang and colleagues, the improved method described in this paper is not only suitable for the small sample situation, but also directly estimates potential market capacity. Using the WeChat case, the authors test the improved method's estimation and prediction effects. The results show that the estimations for internal coefficient, external coefficient and potential market capacity are all significant at the 1% level, and the prediction effect in grey theory critical level reaches level 1. Additionally, internal and external sample prediction are both consistent with the raw data and company report.