Risk management has become one of crucial parts of the daily operation in the financial industry. After the risk has been successfully quantified, the study of risk and related statistical techniques is rapidly developed. A statistically developed measure introduced by JP Morgan in 1995, called Value at Risk (VaR), is the most popular and simplest measure of risk by now. In recent years, a lot of work has been done to provide more accurate models and more rigorous backtesting methods for VaR studies. Nevertheless, the multi-dimensional studies are relatively behind the trend of the development in the other disciplines of VaR. In this thesis, a rolling analysis implementing multivariate GARCH model and copula is presented. Corresponding backtesting results are examined. With the development in the statistical programming areas, a lot more can be achieved for better predictions on VaR of portfolios with multiple assets included.