Bayesian Inferences Of GJR-GARCH Model Based On MCMC Algorithm

Leverage effect exist in financial market remarkably,that is,positive and negative impulse response have different impact on products yield,The GJR-GARCH model studied in this paper can describe this kind of error well.In terms of parameter estimation of the model,the classical statistical school usually adopts the maximum likelihood estimation method,but when the objective function has no maximum value,it is difficult for the method to achieve the numerical optimization of the objective function.Since there is no specific conditional posterior density in the model,we use Metropolis-Hastings sampling method to simulate the conditional posterior distribution of the model parameters,and then use the samples obtained from the simulation for Bayesian inference of model parameters.This method solves the problem of high-dimensional numerical integration in the parameter estimation.The simulation results show that the simulation result of GJR-GARCH-T model is better than the GJR-GARCH-N model in the description of Shanghai stock index and Shenzhen stock index series.This paper mainly studies the parameter estimation method of GJR-GARCH model,and compares the GJR-GARCH-N model with the GJR-GARCH-T model.The main contents are as follows:1.The research background,significance,research status,research content and arrangement of GJR-GARCH model are discussed,and the financial time series of China is analyzed.2.The parameter estimation method of GJR-GARCH model is introduced.In this paper,MCMC method is used to estimate the parameters of GJR-GARCH model,this method combines Bayes estimation method,and the random walk chain M-H algorithm is used in the sampling process.In Bayesian estimation,a theoretical formula for posterior distribution is derived from prior information.In random walk chain M-H algorithm,taking GJR-GARCH-T model as an example,we describe the sampling process of a random walk chain M-H algorithm completely.3.Bayesian analysis of GJR-GARCH-N model and GJR-GARCH-T model is carried out,and the expression of the likelihood function of the two models is deduced through theoretical hypothesis,which lays a theoretical foundation for parameter estimation of the following GJR-GARCH model.4.In the part of empirical analysis,we select the Shanghai stock index and Shenzhen stock index daily closing price,and calculate the logarithmic rate of return.Through the results of parameter estimation to compare the effect of estimation of GJR-GARCH-N model and GJR-GARCH-T model.