Application Of Grey System Study Stock Index Variation

In recent years, after the rapid development of China economy, people's living standards improve year by year, household income has increased, people also have the more spare cash to invest in the stock market, and the enthusiasm to investment is very high. According to statistics, by the end of 2014, China's stock account has reached 120 million households. The price trend of stock market is vital for social and economic stability and the majority of people's life. Therefore, how to accurately forecast the price of stock or stock index trend for guiding investment decisions of investors is very important. Eugene Fama professor in 1970 put forward the famous "efficient market hypothesis", which laid the theoretical development finance. With the rise of nonlinear economics, this doctrine waning. Based on the nonlinear theory, fractals theory and the chaos phenomenon also subsequently been widely applied to financial market research. With the continuous development of mathematical statistics, operations research, management science and computer technology, the prediction and analysis method of the stock market is no longer stay in the traditional method of fundamental analysis, more and more scholars began to study volatility of stock market, if they can accurately the prediction of stock price and stock index volatility trend, for investors and market economy, it would be an innovation. The current stock price prediction methods are: nonlinear dynamic, vector machine, time series analysis method, neural network model, the method of fuzzy mathematics and grey systems theory. In these methods, the Grey System proposed by Professor Deng Julong of Huazhong University in 1982 for the first time belongs to the emerging theory, in recent years, and some scholars have adopted the theory, and achieved certain results. The advantage of this method is that the original data distribution requirements is not high, few data, a small amount of information is not a problem, as long as the original data of not less than 4, can carry on the forecast to the future development of data, has the good forecast effect in the short term prediction of social and economic activities. CSI 300 index was formally promulgated in 2005, which covers Shanghai and Shenzhen stock market capitalization of about 60%, and contains a number of industries, a good representation of the market trend. This paper mainly study and discuss the grey prediction method and its application in financial market, the basic principle and method of using grey prediction, respectively on the CSI 300 index of long-term and short-term predictions and one-day GM(1,1) model predictions. This paper collected 5 years'( from 2010 to 2014) CSI 300 index week closing index, with the first three years of data as the original data, the establishment of grey system waveform forecasting model, predict 2013 to 2014 two years week closing trend. The result of the average relative error is 9.77%, according to test the accuracy of the standard model, the predicted results of inspection, can be used as a reference for investors' long-term investment. Then select the September 30, 2014 to January 16, 2015 in CSI 300 index closing data as raw data, on which September 30, 2014 to December 31,2014 is established the model and predict the index from January 5, 2015 to January 16, 2015 data, getting the average relative error is 2.36% and the correlation coefficient is 0.642, which more than 0.6, according to the testing standards, the model accuracy is better for short-term forecasts, investors can choose to buy or sale at the right time according to this result, it is valuable for judging the trend in short time. The average relative error for daily GM(1,1) model was 1.22%, which is the lowest. This paper has described the application of grey prediction method in the prediction of stock index, hoping it can provide method for investors.