Research on Stock Price Volatility Based on GARCH-type Models

Abstract

This study performs an empirical investigation into the price volatility characteristics of China’s stock market utilizing GARCH-family methodologies. Daily data of the Shanghai Composite Index from 2010 to 2024 are employed, and an ARMA-GARCH-type framework is constructed to capture the volatility structure of the return series. The analysis begins with stationarity and ARCH effect tests on the original series. The results indicate significant volatility clustering and conditional heteroskedasticity, justifying the application of GARCH modeling. Subsequently, alternative specifications are estimated, incorporating diverse distributional assumptions for the residuals, to assess their comparative goodness-of-fit. The results show that the EGARCH(1,1) model under the skewed t-distribution provides the best fit, effectively capturing both the asymmetric and heavy-tailed features of the return volatility. Ljung-Box and ARCH-LM tests on the standardized residuals confirm the adequacy of the model fit. The empirical findings suggest that volatility in China’s stock market returns exhibits strong persistence and heightened sensitivity to negative shocks. These results offer quantitative insights for investor risk management and regulatory market surveillance, and also provide a methodological foundation for future research on multivariate volatility modelling.