We introduce the graphical models to describe the changing dependency structure between multivariate time series and design the algorithm by the markov chain monte carlo method. The model is applied to the stock market of Shanghai in China to study the changing correlation of five segments of the market, empirical results show that there is stronger dependency structure in the bear market and weaker correlation in the bull market.

The graphical approach is applied to the autoregressive conditional heteroskedasticity time series models. After transformation, it is shown that the coefficients of GARCH model are the conditional correlation coefficients conditioned on the other components of the time series, then a new method is proposed to test the significance of the coefficients of GARCH model.