Sequential-BEKK Multivariate GARCH Model And Its Application In The Stock Market

Understanding and predicting volatilities of asset returns has been the object of much attention, as it can be used in asset pricing, asset allocation and risk management. Although researchers have built many models such as VEC, BEKK, OGARH, CCC and DCC models, we still face the problems of curse of dimension due to the number of parameters and the restrictions on the parameters to ensure the positive definiteness of the variance-covariance matrix. We follow the idea of sequential estimation method of Palandri (2007) but simplify the specification to estimate the correlations with BEKK specification proposing the Sequential-BEKK model using multistep Maximum likelihood estimation procedures to estimate. And in the paper we provide the sufficient conditions to ensure the consistency and asymptotic normality of the estimators. By using data simulated by BEKK model, we found that our model performs moderately for both in-sample forecast and out-of-sample forecast. Even though it can not beat the all the other models, it at least is comparable to the best models. With the model we further explore linkage between the Chinese stock market and global capital markets by observing the time-varying correlations between the Chinese stock market and global capital markets. We found the interaction between A share and B share markets are tighter especially after the B share markets started to open to mainland Chinese citizens. Even though the correlations between the Chinese B share and global equity markets are higher than that between the Chinese A share and global equity markets, we did not see the correlations go up across time. Furthermore, the correlations between A share markets and global market is very weak, so Chinese stock market is an ideal place for institutions to diversity their risk. In addition, we found after the Asian Crisis, correlations between Korea stock market and the global markets are higher than that before Asian Crisis.