Copula Method Based On Bayesian Estimation And Its Applications In The Financial Analysis

With the foreign trade opening, introduction and improvement of the financialderivatives, the financial market is becoming complex and diverse. In the age offinancial crisis happen frequently, it’s very important to use the reasonable methods tomeasure the risk of the financial market.Copula theory can measure the non-linear relationship between variables. AsCopula can separate marginal distribution from joint distribution, it becomes a swordto solve the financial risk problem. It’s very important to choose a suitable marginaldistribution to build Copula model. Many empirical shows that GARCH-t coulddescribe the High Kurtosis and Fat Tail feature of the financial time series. Thetraditional method of parameter estimate to GARCH is Maximum likelihood estimate,which is hard to achieve numerical optimization for the objective function when theobjective function has no maximum value.Bayesian estimation based on Bayesian theory regards parameter as variable andcombines the prior to the data to get the posterior and further statistical inference.Comparing with the traditional method, Bayesian estimator has smaller square errorand more accurate prediction. The confidence interval of Bayesian high posteriordensity is shorter than the traditional method considering no prior. It can solve theproblem appearing in the traditional estimate to use the Bayesian method to GARCH,and the series of constraint condition in GARCH is suitable for Bayesian method.This article introduce the Copula theory and Bayesian theory at first, then applyBayesian method to building time varying Copula-GARCH, at last we chooseagriculture, manufacture, transportation, property and culture as research object toobserve the static relationship and time varying relationship and Based on Z test,investigate the variable structure. The result shows that the structure between propertyand manufacture, agriculture has been broken as to the effect of nation policy,increasing inventory and lack of crash.