A Unified Grey Riccati Model

Abstract

The grey Riccati model (GRM) is a generalization of the grey Verhulst model (GVM). Both the GRM and GVM generally perform well in simulating and forecasting the raw sequences with a bell-shaped or single peak feature. Although there are several methods to solve the Riccati differential equation, the existing time response functions of the GRM are generally complicated. In order to reduce the computational complexity of the time response function, this study attempts to transform the Riccati equation into a Bernoulli equation with the help of a known particular solution. Then, a unified time response function of the GRM is obtained by the proposed methodology. The simulation results demonstrate that the proposed unified grey Riccati model performs the same as the grey generalized Verhulst model (a kind of grey Riccati model) and is better than the traditional grey Verhulst model. The fact also reveals that the newly developed grey Riccati model is reasonable and effective.