Utilizing the GARCH Model for Analysis and Prediction of Stock Market Trends

Abstract

This study utilizes the Generalized Auto-regressive Conditional Heteroskedasticity (GARCH) model to analyze the Shanghai Stock Exchange Composite Index and the Shenzhen Composite Index. It computes the returns and logarithmic returns, fits the GARCH model with a student-t distribution, and calculates the standardized residuals of the stock. Tests for normality and heteroskedasticity of residuals are conducted, follows by the creation of auto-correlation and partial auto-correlation plots to aid in volatility forecasting. The findings indicate that both returns of stock distributions exhibit multiple peaks and significant fluctuations, revealing that there exists pronounced volatility clustering and strong abrupt changes. Historical fluctuations significantly affect current fluctuations, showing a clustering effect. Volatility in returns has been very persistent, reflecting strong speculation and elevated overall risk. Histograms and skewness assessments show a left-skewed distribution for both indices, with a kurtosis greater than three, indicating a "fat-tailed" distribution. The positive mean values imply that China's economy is growing constantly, while the low standard deviation implies the immaturity of China's stock market. These insights highlight the dynamic behaviors and risk profiles in Chinas major stock indices, offering a deeper understanding of their speculative nature and economic implications. The Advantages and disadvantages of GARCH models and limitations of a single model are acknowledged in the report.