Volatility is integral for the financial market. As an emerging market, the Chinese stock market is acutely volatile. In this study, the data of the Shanghai Composite Index and Shenzhen Component Index returns were selected to conduct an empirical analysis based on the generalised autoregressive conditional heteroskedasticity (GARCH)-type model. We established the autoregressive moving average (ARMA)-GARCH model with t-distribution for the sample series to compare model effects under different distributions and orders. In contrast, we proposed threshold-GARCH (TGARCH) and exponential-GARCH (EGARCH) models to capture the features of the index. Additionally, the error degree and prediction results of different models were evaluated in terms of mean squared error (MSE), mean absolute error (MAE) and rootmean-squared error (RMSE). The results denote that the ARMA (4,4)-GARCH (1,1) model under Student's t-distribution outperforms other models when forecasting the Shanghai Composite Index return series. For the return series of the Shenzhen Component Index, ARMA(1,1)-TGARCH(1,1) display the best forecasting performance among all models. This study could provide an effective information reference for the macro decision-making of the government, the operation of listed companies and investors' investment decision-making.

With increasing extremal risk, VaR has been becoming a popular methodology because it is easy to interpret and calculate. For comparing the performance of extant VaR models, this paper makes an empirical analysis of five VaR models: simple VaR, VaR based on RiskMetrics, VaR based on different distributions of GARCH-N, GARCH-GED, and GARCH-t. We exploit the daily closing prices of the Shanghai Composite Index from January 4, 2010, to April 8, 2020, and divide the entire sample into two periods for empirical analysis. The rolling window is used to update the daily estimation of risk. Based on the failure rates under different significance levels, we test whether a specific VaR model passes the back-testing. The results indicate that all models, except the RiskMetrics model, pass the test at a 5% level. According to the ideal failure rate, only the GARCH-GED model can pass the test at a 1% level. For the Kupiec confidence interval, the GARCH-t model can also pass the back-testing at all aforementioned levels. Particularly, we find that the GARCH-GED model has the lowest forecasting failure rate in the class of GARCH models.