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In modern society, economy, stock plays an increasingly important role, who can grasp the development trend of the stock, who can make the right decisions in the shortest possible time, who will be able to gain a great deal on the stock market wins persons. Price index as a measure of an important indicator of the stock trends, become the focus of many stock analysts and investors, and the gray system theory and neural network technology used in the stock price index forecast, construction gray neural network model can achieve on stock prices better the prediction accuracy of the index, while the model with a small sample size, faster training, high prediction accuracy, provides a new way for the stock price index forecast. This paper first describes neural network technology and gray system theory; basis of in-depth study of two single prediction model - BP neural network model and the gray GM (1,1) model. On the one hand, the introduction of the learning algorithm of BP neural network model and analysis of the deficiencies of BP neural network algorithm, then these deficiencies improved method and design the BP neural network model. On the other hand, the GM (1,1) model as the core of one of the forecasting model of gray theory, and now has a more mature learning algorithm, but its scope has not proved theory, the paper by exploring GM (1 , 1) the application of the model and development coefficient-a relationship, draw the relevant conclusions of the scope of application of GM (1,1) model. Gray uncertainty for stock index prediction problem, this paper established a prediction model to solve the problem, including: BP neural network model, GM (1,1) model, GM (1, N) model, GNNM (1,1) model GNNM (1, N) model. Were introduced five models the process of building and learning algorithm, a single prediction model in five models, of which the first three models, the use of neural network theory and gray theory to solve the prediction problem; behind the two models establish combined gray neural network model, in which the fourth model is the model for the one-dimensional gray, the fifth model is the model for the multi-dimensional gray. In this paper, the Shanghai Index daily closing price for the study, the use of gray relational analysis analysis of 11 stocks of the public commonly used technical indicators and the date of the closing price of the relationship, screening the Gray Neural Network Model and the date of the relationship between the closing price of the most closely the indicators as input variables , from the perspective of large sample sets and small sample set, the design of three predictive model analysis shows that the predicted effect of the combined gray neural network model, three prediction model of BP neural network model, GM (1,1) model and GNNM (1, N) model. Simulation results show that, the use GNNM (1, N) model can achieve better prediction accuracy than the BP neural network model and GM (1,1) model. Finally developed a stock index prediction program to based on the Visual Basic6.0 and MATLAB7.0 The program includes three forecast models are available for the user to choose to use the BP neural network model GM (1,1) model, GNNM (1, N) model is applied to the prediction of the actual Shanghai Composite Index.
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