The Estimation Of Multivariate Time Series Model And Financial Applications

The characteristics of fat tail, strong autocorrelation, cumulative variance rate effect and smile effect make the data of the financial market quite different from other time series data. Many economists keep on working hard, making a great effort to try to find a time series model which can capture most of these characteristics of financial data. That's the motivation which has been driving time series models changing from fixed-variance ones to vary-variance ones. The more complexity the model becomes, maybe the closer it gets to the real data.GARCH models are thought to be better models in capturing financial time series. And Copula, which is a newly developed theory, has a very good performance in analyzing multivariate distributions. It is natural for us to build up a model with these two theories to analyze multivariate time series. To make the model closer to reality, which means the return should be related directly to the risk, the volatility is brought to the mean equation. Based on this thought, we get GARCH-M model. Further, ARMA-GJR-M model is obtained to reflect leverage effect of good and bad news on the volatility. We try the Bayesian method through Gibbs sampling, instead of the classical maximum likelihood method. The structure of this paper is as follows.Firstly, in Chapter 2, we give a brief description of the definition of Copula and its related characteristics. Two types of statistics are used to describe the relationship between variables. We classify common copulas into two main groups, and introduce some copulas and their characteristics under this classification. The third chapter analyzes GARCH models and GARCH-M models, in which we point out the necessity of GARCH-M models, on the basis of which, we develop another model ARMA-GJR-M models and MCMC method is our suggestion to estimate the parameters, for it is with less limitations and more stable. After that, the thesis introduces the sampling methods of each parameter in detail. The fourth chapter gives the estimation of parameters of ARMA-GJR-M models.At last we confirm the Bayesian estimation is appropriate by simulating. Then we use this method to analyze the Chinese financial market and find out that it is more appropriate to fit the stock return of Shanghai and Shenzhen using ARMA-GJR-M models than ordinary GARCH models and a multivariate model is constructed for the Shanghai Stock Index and Shenzhen Component Index together.