Statistical Inference And Application Of Copula-Based Multivariate Volatility Models

In recent years,the application of Copula theory in multivariate time series is gradually mature with the great development of Copula theory.The Copula theory combined with GARCH model can reflect many properties of the multivariate financial time series,such as the time-varying volatility,volatility cluster,skewness,kurtosis and thick tail and so on.Meanwhile,the Copula theory makes it easier to study the dynamic correlation of multivariate financial series.Firstly,this paper introduces the basic theory of Copula and common form of the Copula-GARCH model.At the same time,we introduce same nonparametric Copula-NGARCH.Secondly,this paper introduces the time-varying Copula-GARCH,Where the marginal time series follows standard univariate GARCH model.and the time-varying Copula correlation coefficient follows certain evolution equation depending on their previous values and the historical data,Bayesian inference is developed where the whole set of model parameters are estimated simultaneously.It can be verified that Bayes estimation is superior than the maximum likelihood estimation under the condi-tion that the correct prior distribution is selected or the sample size is small.Parametric time-varying Copula-GARCH model is in common use but it is sensitive to model mis-specification.We propose a semi-parametric time-varying Copula-NGARCH model to deal with the problem.The marginal time series follow univariate nonparamet-ric GARCH model rather than standard GARCH model.We estimate the form of NGARCH by nonparametric weighted regression.We estimate also correlation coeffi-cient as an unknown function of time by the local likelihood method.Finally,we verify the proposed estimation methodology by analysing the dynamic linkages between the Shanghai stock market and international crude oil prices.The result shows that our model performs well in describing the correlation in time series.