The Research Of GARCH-NN Hybrid Volatility Model Base On Stylized Fact In China’s Stock Markets

As is known to all, it is crucial and difficulty to accurately describe dynamic feature and estimate the level of financial asset volatility for financial asset pricing and risk measurement and management. And the describing and prediction of volatility dynamic feature has a great influence on interpreting and prediction ability of financial theory to the actual problems. If the predicting to volatility is failing, the decisions made by management on the basis of these predicting will be deviation from the actual situation, and measures taken by management will be invalid, and huge losses will be suffered, and risk management well be failure, even the financial crisis will be happened. Therefore, estimation and forecast to volatility is not only the central to the test of financial asset pricing theory and hedging strategy design of financial derivatives, but also needed to be solved in practice for investor and economic management department.In recent years, however, the explosion of the stylized facts in the financial markets will make the dynamic characters description of the volatility become more complicated and difficult. And Cont, Famous scholar, pointed out that if we want to make related the research conclusion valuable and significant, the stylized fact features must be incorporated into the financial theoretical analysis and empirical research. Even, with the rapid development of computer storage capacity and simulation technology, more and more stylized fact features will be captured, and it will inevitably cause "dimension disaster" problem, and make it extremely difficult to describe dynamic feature and estimate the level of the volatility.Although many scholars have research and analyze financial asset volatility under the restriction of the stylized facts, the GARCH family models, which strictly limit distributions and is unable to mining hidden pattern of data, are used to do it.Although some scholars use Neural Network Model, which abandon distribution limitation and add other fluctuation influence factors, to analyze financial asset volatility, it can’t capture the stylized facts. Although others researcher constructed hybrid models, combined GARCH model with artificial neural network model, to capture the stylized facts and mining hidden pattern of data, there is still a "black box" problem, that is to say, it can’t explain economic meanings of its parameters. What’s more, the related researches also lack of scientifically rigorous test of volatility models, especially hybrid volatility models.Therefore, the primary of this paper is to find out the stylized fact features of the China Securities Index 300 and Shanghai Stock Exchange Composite index in China’s stock market. According to the descriptive statistics analysis, BDS and detrended fluctuation analysis, we found that there are leverage effect and long memory in China’s stock market, and leverage coefficient of Shanghai Stock Exchange Composite index is significantly and negative. It indicates that the influence of positive or negative losses on the stock market are asymmetric, and the influence of the negative influence is greater than the positive, that is to say, there are "Buying the winners" in the Shanghai Stock Exchange Composite index. And if we want to accurately describe dynamic feature and estimate the level of China’s stock market volatility, the stylized fact features must be incorporated into the empirical research.Otherwise, research results will be deviated, and the conclusion is questionable.Secondly, how to construct the volatility models to accurately carve asymmetric leverage effects and long memory characteristic in China’s stock market. In view of research results have been shortcomings, GARCH-NN hybrid models combined artificial neural network model and GARCH family in this paper are constructed. Not only can it capture the stylized fact like GARCH family models, but also it can mine internal implicit patterns of data, and its economic meaning can be interpreted by its parameter. In addition, the GARCH-NN hybrid model can accurately estimate the volatility.Thirdly, how to scientifically test the constructed volatility model? To begin with,we test log-return of the China Securities Index 300 and Shanghai Stock Exchange Composite index to verify that it does exist leverage effect and long memory in the Chinese stock market. Then, the results of significance level of the parameter estimation and residual descriptive statistics after filtering indirectly indicate that GARCH-NN hybrid model can accurately carve the stylized fact in China’s stock market. After that, we use the sign and size bias test to check the performance captured the leverage effect, and use the detrended fluctuation analysis test the performance captured the long memory. At last, loss function, MSE, is used to test estimated and prediction accuracy of GARCH-NN hybrid model. The results show that GARCH, GJR, FIGARCH, GARCHNN, GJRNN and FIGARCH accurately depict asymmetric leverage effects and long memory characteristic in China’s stockmarket without exception, but the performance of the GARCH-NN hybrid model is superior to the GARCH family models in terms of prediction accuracy and descriptive ability. So, volatility models constructed in this paper can be used to describe dynamic feature and estimate the level of the volatility in other makets, and the research ideas of this paper also can be used to other volatility models, and the conclusion in this paper can also be get used to other financial theory research.Finally, according to the empirical results and the research conclusion of this paper, the following suggestions are put forward:(1) Keeping a close eye on the stylized fact features and their impacts in the financial market. Since China’s stock market has many stylized facts, the stylized fact must be incorporated into the empirical research analysis.(2) To strengthen the construction of financial market system, and to guide investors to make rational investment. From the empirical results,there may be many investment behavior like “buying the winners" in China’s stock market, so the government shoulde take measures to strengthening shareholder investment theory knowledge education.(3) The conclusion in this paper can be used to improve accuracy of the financial asset pricing, raise the level of risk management of economic management department. Certainly, financial theory researchers can also employ the established model and the research train of thought to promote other financial theory research.