The Copula-AR-GARCH Model Based On Bayesian And Maximum Likelihood Estimation

In order to study the dependence of random variables,in the Chapter1 we first describe the background of Copula.In the Chapter2 we introduce the applicable to macroeconomic time series model in the field of AR-GARCH function,and analyzes its advantages.In the Chapter3,we introduce the Copula function and the dependent structure.Firstly,the definition and properties of Copula function are explained.Secondly,several kinds of common Copula functions are constructed,and the specific calculation process is written.After that,we introduce several common dependent measures,and revalidate the limit relationship between Spearman and Kendell coefficient in the parameter family of Gumbel Copula,and extend it to the general parameter family.Then,by using the distribution function,gradient and direction function diagram of two kinds of parameters,the tail dependence is described,and the theory and analysis are combined to prove the authenticity of the image.Subsequently,we propose to interpret the parameters as quantiles and explain them with the price fluctuations of rice and grain.Finally,through the example of Shanghai index and Shenzhen index,the dependence measure is applied to the actual financial market,and the dependence measure and influence between them are explained.In the Chapter4,we introduce the parameter estimation and testing methods of AR-GARCH model,and mainly reviews the maximum likelihood estimation and the Bayes estimation theory.Then introduces MCMC algorithm in two of the most famous algorithm(Gibbs algorithm and M-H respectively).After that,the specific steps of the parameters in the estimation model are described in detail,and the parameters of the AR-GARCH function and Copula function are applied to the parameter estimation and model verification.The Chapter5,we carry on the empirical research for the Copula-AR-GARCH model.We analyze that historical interest rate and exchange rate data have obvious cluster effect after difference.So we need to extract the level of information and volatility related information for time series modeling.And then by using the maximum likelihood method and Bayes method respectively we estimate the parameters of AR-GARCH function and four kinds of Copula functions.So that we can get joint distribution of the exchange rate and interest rate.The four kinds of Copula functions are the Gumbel Copula function,the Clayton Copula function,the Frank Copula function,and the Joe Copula function.Subsequently,the most useful information criterion AIC and SBC are used to compare the advantages and disadvantages of the model,and it is found that the AR-GARCH-Joe Copula function is most suitable for establishing the correlation model between the exchange rate and the interest rate.Finally,we summarize the points that need to be improved and still be explored.