The Forecast Model Selection Of Shanghai Composite Index By GARCH Models

The research on financial volatility is the basis of analyzing the capital asset pricing, financial risk prevention and so on. The premise of the financial market quantitative research is that we should describe the volatility of financial market accurately and GARCH models are the regression model that specially made for financial data, especially, for the analysis and forecast of the volatility. But, until now GARCH models have existed more than30kinds. So which one or several models are more suitable for China’s stock market? For this, we select6GARCH models as an object of study in this paper, and select Shanghai composite index over the period9May2005to22November2010as empirical investigation. The main work and conclusions are as follows:First, we process the sample data and analyze the basic statistical characteristics, such as descriptive statistical characteristics, excess kurtosis and fat tail. The result is that the returns of Shanghai composite index has pronounced excess kurtosis and fat tail. And the sample data isn’t normal.Second, we test the ARCH effect before modeling. In this paper, we use LM test, and the result is that TR2=17.251>x0.052(1)=3.84and the returns of Shanghai composite index is presented high level ARCH test.Third, we use the maximum likelihood estimate method and estimating function method respectively to estimate the returns of Shanghai composite index adjusted for6GARCH models and then forecast them.Fourth, we use loss function values and SPA test values to evaluate the6models’forecast performance after having forecasted values. The results are as follows:for the6GARCH models in this paper, the best predict model is EGARCH model, and TSGARCH model is the better one, and GARCH model is the worst one. It is worth noting that the predict performance by estimating function method is better than the performance by the maximum likelihood estimate method for EGARCH model.