The Correlation Analysis Between The Price Of Gold And The US Dollar Index Based On Copulas

Among the methods of correlation analysis, the linear correlation coefficient and the granger causality analysis are the traditional ones. But these methods are only suitable for a linear relationship between variables, they are not fit to most of the financial variables, which are nonlinear, there is some misleading if we do it.Copula function is a flexible and robust tool in the analysis of correlations, the correlation measures derived from it can overcome the limitations of the use of linear correlation parameters. besides, it has many advantages in the description of the correlate structure between the financial variables.In this thesis, on the base of the introduction of the basic theoretical knowledge of time series and Copula function, a Copula model to describe the correlation between the price of gold and the dollar index is established. The sample is selected as the international price of gold and the dollar index from September2of2009to December16of2011.The model requires two steps:first, the determine of the marginal distribution, which describes the piece of gold and the dollar index distribution characteristics; second, select the appropriate Copula function, which describes the correlate structure between the two variables. The marginal distribution is established by time series model after being processed by the Eviews software, based on the data characteristics, the GARCH model is selected to describe the marginal distribution of the price of gold and the dollar index, and the quantile-quantile plots support the conclusion that the GARCH model can fit the marginal distribution perfectly. The Copula function is selected from five Copulas:binary normal Copula、binary t-Copula、Gumbel Copula、Clayton Copula and Frank Copula. After the estimation of the linear parameters、the calculation of the correlation measure the drawing of the distribution function and density function of the Copula have been done, the binary normal Copula、binary t-Copula、Frank Copula are selected to describe the correlation structure of the price of gold and the dollar index.Finally, through the introduction of the experience Copula function, the square Euclidean distance is obtained, it gives that the binary t-Copula is the best one to fit the model.So in this thesis,the t-Copula-GARCH model is made to describe the correlation between gold prices and the dollar index.It gives the practical significance of the correlation coefficient and the density function of the model.This provides good advices for inventors so that they can pay close attention to the dramatic changes in the moment of the dollar index when investing in gold.