An Efficient And Fast MCMC Method Based On SV Model

Stochastic volatility(SV)model is an important model in the field of financial time series.Because of the complexity of the likelihood function of the SV model,the MCMC method,which is based on the bayesian framework,is usually used to study the model.MCMC method has good advantage such as accuracy in parameter estimation,but MCMC method is based on the property of smooth convergence of markov chain,which requires a large amount of time to be consumed in the sampling of latent variables,so the current MCMC method has the problem of slow sampling speed and low estimate efficiency.In order to improve the speed of MCMC method based on SV model,we try to improve the parameter estimation of the model according to the SV model and the characteristics of MCMC method.By combining Gaussian linear state space theory,MMP algorithm and multi-Gaussian M-H sampling algorithm,the sampling problem of target parameters is solved,so a fast MCMC algorithm(FMCMC algorithm)based on SV model is proposed.Furthermore,for improving the estimation efficiency of the model,basing on FMCMC algorithm,two FMCMC algorithms of central parameterized SVC model and non-central parameterized SVNC model were used to perform interleaving sampling with the interleaving strategy(ASIS),so an efficient and fast fma-2 algorithm is proposed in the paper.In the numerical simulation,the results show that FMCMC algorithm can complete the parameter estimation of SV model accurately and quickly.Furthermore,the efficient and fast FMA-2 algorithm proposed by combining FMCMC algorithm with ASIS strategy has higher estimation efficiency than FMCMC algorithm.In this paper,compared with other MCMC algorithms,FMA-2 algorithm is found to have higher sampling efficiency and faster sampling speed,which proves that FMA-2 algorithm is more efficient and fast.Finally in the empirical study,the time series data of Shanghai Stock Index and Shenzhen Stock index are studied by FMA-2 algorithm,the study found that both the Shanghai composite index and the shenzhen composite index not only had a small average volatility trend,but also had volatility aggregation and high persistence phenomena,which are consistent with the objective law ofvolatility in China’s financial market.This also verifies the efficiency and rapidity of the FMA-2 algorithm in practical application.