Detection Of Structural Change-points In Multivariate Models And Research Of Bayesian Graphical Modelling

In this paper, we focus on the study of Graphical Modelling, that is the study of conditional relativity of two variables given the rest variables in the multivariate models. In practice, such conditional relativities are usually time-varying. Sometimes, conditional independent variables may become conditional dependent, while sometimes the inverse process happens. So, in order to find out the conditional relativities of variables correctly, we need to detect the probable change points first. After obtaining the estimations of the change points, we are able to study the conditional relativities of variables within a time block which contain no structural change.We first consider an approach of detecting the volatility change points in multivariate models. Via performing transformation to sample series, we change the single problem of detecting the volatility change points in multivariate models into several problems of detecting the mean shifts in univariate models. Then we address the problems by a wavelet method. Simulation results show that the approach behaves well when the sample size is large, but its performance under small sample size is not satisfying. So we improve a modified approach for small-sample case. When some assumption of the distribution of the error vector in the multivariate model is given, we may show the critical values from the small-sample distributions of statistics via Monte Carlo.Next, by simplifying Makram Talih's model in 2003, we introduce a Bayesian approach of detecting the structures of graphs. When previous and professional message are absent, the approach of detecting the structures of graphs, based on hypothesis test, usually behaves poorly, since it is hard to choose the null hypothesis correctly. So in such case, the Bayesian approach is a better choice.At last, we study the stock market of China, specially the conditional relativities of six segments of the market, via our models. The research results show that there are 12 volatility change points between 1995 and 2004. The position of the last change point before 2004 is June 2003, so we may study the condition relativities of the six segments by performing the Bayesian approach to the samples from July 2003 to the end of 2004.