| In order to reflect the characteristics of volatility clustering on financial data accurately,the GARCH model with Markov Regime Switching is introduced to the return of assets,and divides the asset volatility into high and low states.In the meanwhile,due to the high-frequency characteristics of financial data,such as peak,thick tail and the truncated characteristics of the return on assets,we use truncated stable distribution to fit the residual series of the mean equation on the GARCH model.In this paper,we study the GARCH model with Markov Regime Switching,and assume that the residuals obey the truncated stable distribution.In the theoretical research,firstly,we study the relationship between parameters and the higher-order moments,and the moment estimation method with the second-order moment and the fourth-order moment to estimate the characteristic parameters of truncated stable distribution is proposed.The kurtosis expression of truncated stable distribution is given by deducing the relationship between parameters and higher-order moments.It shows that the kurtosis decreases with characteristic parameter a increases when 1<α<2.Secondly,the maximum likelihood estimation and MCMC algorithm are used to estimate the parameters of the volatility model.The result shows that there is no path dependence issue with MCMC method,and the results are more reliable than the maximum likelihood estimation method.In the empirical study,this paper takes the daily return data of PingAn stock and silver futures of China as samples.ADF test,nonlinear test and ARCH test are carried out on the data.we calculate the state transition probability at first,and then the smooth probability plot of high fluctuation state is drawn.It shows that the Markov Regime Switching model can distinguish the high and low fluctuation states.The plot shows that the VaR value based on the stable distribution model is larger in the high volatility state and smaller in the low volatility state by the VaR back testing analysis of PingAn stock data,which fits better on the data of peak and thick tail.Finally,compared with the GARCH model based on normal distribution and t-distribution,the prediction error of the model based on truncated stable distribution is smaller. |
