基于Pair Copula和GARCH(1,1)模型的股市研究

Research of Stock Market Based on Pair Copula and GARCH(1,1) Model

摘要: 本文在GARCH(1,1)模型的基础上，运用Pair Copula降维法探究非线性结构的股票市场间相关性。我们基于4种不同的残差分布来构建GARCH(1,1)模型，对比发现只有残差服从广义误差分布时，模型通过显著性检验，从而找到相对好的金融资产序列的边缘分布拟合模型。我们使用Pair Copula降维方法，依据AIC/BIC准则(赤池信息准则/贝叶斯信息准则)，发现D-Vine结构比C-Vine结构更适合描述股票市场间相关关系，于是最终选用D-vine结构来构建市场间相关结构的Pair Copula函数。

Abstract: In this paper, based on the GARCH(1,1)-model, we use the Pair Copula dimension reduction method to explore the correlation between the stock markets with nonlinear structure. We construct the GARCH(1,1)-models basing on four different forms of residual error distributions. We check the significance test of GARCH(1,1) with these four kinds of residual error distributions, and find out only when the residual error follows the generalized error distribution, the model passes the significance test. Therefore, we get a better choice for the edge distribution for financial asset series. With the help of Pair Copula reduction method and AIC/BIC criterion (Akaike Information Criterion/Bayesian Information Criterion), we find out that D-Vine structure is more suitable than C-Vine structure to describe the correlation between the stock markets. Finally we construct the correlation function between the stock markets basing on the D-Vine structure Pair Copula function.