China’s Stock Markets’ Volatility Forecast Based On MCMC Method

With the development of scientific and technological innovation and the profound impact of economic globalization, new financial products have emerged, financial markets have grown more complex, and financial risks are also rising. Financial markets play an important role in economic development, as well as an important object in academic study and financial regulators. Once there is a significant risk in financial markets, it would have significant impact on the economy, and even may cause the global economic crisis. The financial crisis has a close and complex relationship with the strong fluctuation in the price of financial products. Therefore, this paper will establish volatility models to analysis and predict the volatility of financial product price, to deal with financial risk.In financial markets, stocks are a platform for capital accumulation, transferring capital. And stocks is a kind of strong participation, high mobility and high risk financial product. It not only can reflect the volatility in the stock market, but also can reflect a country’s or region’s economic development to some extent. China’s stock markets set up a short time, lack of financial risk of mature experience, there are many defects in risk control and prevention; Meanwhile, with close links with overseas financial markets, stocks under the influence of foreign financial market is also growing in China, and thus face the risk of more severe challenges. Therefore, taking the stock market as the object of study, the study of risk characteristics are representative of the entire financial market.Many empirical studies have shown that the return of financial asset often have these characteristics, such as volatility clustering, leptokurtic and fat tailed, structural change. And traditional statistical methods were unable to describe these typical characteristics in financial assets. The GARCH models, including ARCH model, GARCH model, EGARCH model and GJR-GARCH model, can depict these features very well. But GARCH models do not take into account the financial time series by structural change. In order to solve this problem, researchers combined with structural change, and proposed the Markov state transition models to analysis financial time series, such as MRS-ARCH model and MRS-GARCH model. And the residual series have extended from the normal distribution to a student’s t distribution and generalized error distribution skewed distribution.Plenty of scholars used the MLE to estimate the parameters of MRS-GARCH model, but this method is limited by parameters’ constraints, and exists the path dependence problems. So the estimated results will appear deviation with MLE. Based on Bayesian statistical theory of Markov Chain Monte Carlo(MCMC) which through fractional sampling, continuous iteration until parameter convergence can solve the problem, and MCMC methods can be able to quickly and effectively address the issue of high-dimensional data, fitting of parameters more accurately. Depending on the different of sampling method and the transfers of nuclear, MCMC methods can be classified into various categories, such as Metropolis method, Metropolis-Hastings method, Gibbs sampling method and grid methods such as Gibbs sampling method.Based on above analysis, this paper analyses the volatility of SSEI. Through analysing the volatility of SSEI, we find that the return of SSEI have these features, including heavy-tailed, serial correlation, heteroskedasticity effect and structural characteristics. Taking into account the return’s residual series may follow skewed distribution, this paper leads normal distribution and student’s t distribution in GARCH model and MRS-GARCH model, to depict and forecast the volatility of SSEI. And this paper uses MCMC method to estimate the models’ parameters. Then, based on MCMC framework, this paper uses the fitting models to simulate and forecast the volatility of SSEI in each Gibbs iterative, and uses loss of functions and SR indicator to evaluate the results. The research results show that the MRS-GARCH models are better than the single mechanism of GARCH models in fitting the data. And the distributions of residual series have effect on the fitting result of the models, there the models’ residual series with student’s t distribution are better than the normal distribution. Therefore, the MRS-GARCH-t model can accurately depict the volatilities’ features in SSEI. It’s worth noting that the MRS-GARCH-t model have the lowest loss functions and highest SR indicators. So, the MRS-GARCH-t model have better capacity in forecasting the volatility of the Shanghai composite index.