Comparison of GARCH Models based on Different Distributions

Since ARCH and GARCH models are presented, more and more authors are interested in the study of volatilities in financial markets with GARCH models. Method for estimating the coefficients of GARCH models is mainly the maximum likelihood estimation. Now we consider another method—MCMC method to substitute for maximum likelihood estimation method. Then we compare three GARCH models based on it. MCMC method developed based on Markov chain, which is one kind of straggling time and state random process with no offspring imitates. It attracts extensive attention because of its applications in many fields. In this article, we will compare GARCH models based on different distributions with MCMC method. At last we have the conclusion that both in uni-variable case and binary variable case, GED-GARCH is the best model to describe the volatility compared to other two models, and we will provide the application of binary GED-GARCH models in forecasting the volatility in China’s stock markets.