Studies On Bayesian Algorithm Of Wishart Autoregressive Models

With the development of the financial market integration, the investor should not only study the single asset returns and market volatility, but also consider the influence between the asset and market in the process of controlling and managing risk by financial instruments, so as to defense, disperse and dissolve financial market risk effectively, thus optimize assets investment combination. Under the assumption of the covariance of multivariate time series follows the Wishart autoregressive process, the Wishart regression is a extension on multivariate stochastic volatility model. The assumption reflects the volatility spillover effect between variables in the wave equation rather than the mean equation, so that we can estimate and predict the volatility and co-volatility of multivariate financial time series. Fatherly, we can master the fluctuations of various markets and assets, and then we can exam their mechanism in the transmission of volatility process. However, latent variables was contained in the models, what leads to high-dimensional integration, so we can not obtain closed form expressions of the likelihood function of Wishart regression model, thus many general parameter estimation methods result in failure. At the same time, taking account of that Markov chain Monte Carlo sampling algorithm is good at dealing with high-dimensional parameter estimation problem, we try to design the Bayesian Markov chain Monte Carlo algorithm for Wishart autoregressive models for the purpose of estimating models’ parameters, time-varying volatility and co-volatility, and thus we can depict the time-varying correlation coefficient among variables. Furthermore, a simulation with the stock market and the precious metal futures market data is done.This paper designs the Markov chain Monte Carlo sampling algorithm for Wishart autoregressive models. Firstly, basing on the analysis of the statistical structure and Bayes’ theorem, the posterior distribution of parameters is inferred. Next, MCMC algorithm is applied for posterior simulation, so as to achieve the distribution characteristics and parameter estimation. Then, a simulation experiment is done, and the result demonstrates the effectiveness of the algorithm. Finally, Bayesian Wishart Autoregressive model is applied for depicting the time-varying correlation coefficient and discussing the volatility spillover effects between the stock market and the precious metal futures market. The results showed that the volatility spillover effects between the silver future market and stock market is weak, and the gold future is the same as silver future market, while the gold future market and the silver future market have strong volatility spillover effect.