The advantages and disadvantages of BP neural network and grey Verhulst model for time series prediction are analyzed respectively, this article proposes a new time series forecasting model for the time series growth in S-type or growth being saturated. From the data fitting's viewpoint, the new model named grey Verhulst neural network is established based on grey Verhulst model and BP neural network. Firstly, the Verhulst model is mapped to a BP neural network, the corresponding relationships between grey Verhulst model parameters and BP network weights is established. Then, the BP neural network is trained by means of BP algorithm, when the BP network convergences, the optimized weights can be extracted, and the optimized grey Verhulst neural network model can be obtained. The experiment results show that the new model is effective with the advantages of high precision, less samples required and simple calculation, which makes full use of the similarities and complementarities between grey system model and BP neural network to settle the disadvantage of applying grey model and neural network separately. It is concluded that grey Verhulst neural network is a feasible and effective modeling method for the time series increasing in the curve with S-type.

In grey theory, GM(1,1) model is widely discussed and studied. The purpose of GM(1,1) model is to work on system forecasting with poor, incomplete or uncertain messages. The parameters estimation is an important factor for the GM(1,1) model, thus improving estimation method to enhance the model forecasting accuracy becomes a hot topic of researchers. This study proposes an optimization method for GM(1,1) model based on BP neural network. The GM(1,1) model is mapped to a BP neural network, the corresponding relation between GM(1,1) model parameters and BP network weights is established, the GM(1,1) model parameters estimation problem is transformed into an optimization problem for the weights of neural network. The BP neural network is trained by use of BP algorithm, when the BP network convergence, optimization model parameters can be extracted, and the optimization modeling for GM(1,1) Model based on BP algorithm can be also realized. The experiment results show that the method is feasible and effective, the precision is higher than the traditional method and other optimization modeling methods.