A Copula Based GARCH Dependence Model of Shanghai and Shenzhen Stock Markets

Copula is a function which can link two or more marginal distributions together to form a joint distribution. This paper aims to analyze the dependence between Shanghai and Shenzhen stock markets using copula theory based on GARCH. We use the synchronous 100 times daily returns data and copula based GARCH to model the joint distribution of stock index returns because copula based GARCH can fit the properties of stock market returns: dynamic and non-normal. Univariate AR(1)-GARCH(1, 1) model is used to study the marginal distribution of each index return, while copula is used to analyze the dependence between the two marginal distributions. Copula families offer various alternatives to the common assumption of normal dependence, including constant and time-varying. After fitting the marginal distributions into the constant and time-varying copula, we find constant t-copula and time-varying normal copula can explain the dependence between Shanghai and Shenzhen stock markets better. We also find evidence that there is obvious conditional dependence between the two stock markets.