Grey Time-delayed Verhulst Model for Forecasting the Market Diffusion of New Products

Abstract

Abstract Taking account of the time-delayed phenomenon in diffusion of new products, we propose the timedelayed Verhulst model and then establish grey time-delayed Verhulst model using the method of greying differential equations. The related parameter packets of the novel model is obtained under the rule of OLS. The results show that traditional grey Verhulst model is a special example of grey timedelayed Verhulst model which can reflect the time-delayed information effectively. An actual example of market diffusion shows the modeling accuracy is remarkably improved by using grey time-delayed Verhulst model.