基于分层阿基米德Copula的金融时间序列的相关性分析

与阿基米德copula相比,分层阿基米德copula(HAC)的结构更具一般性,而相比于椭圆型copula它的待估参数个数更少。用两阶段极大似然法来估计HAC函数,主要的步骤是先估计出每个分量的边际分布,以此为基础再估计copula函数。实证分析中,采取Clayton和Gumbel型的HAC分析四只股票价格序列之间的相关性。在得出HAC的结构和估计其参数之前,运用ARMA-GARCH过程消除了序列的自相关性和条件异方差。通过比较赤迟信息准则,认为完全嵌套的Gumbel型HAC能更好地刻画这种相关性。

Dependence Analysis of Financial Time Series Based on Hierarchical Archimedean Copula

In this paper, we introduce the hierarchical Archimedean Copula （HAC） which is more flexible compared with the simple Archimedean Copula, and require a smaller number of parameters compared to elliptical copula. The 2--step maximum likelihood method is discussed which estimates the marginal distribution functions and Copula function, separately. For empirical study, we apply HAC with Clayton and Gumbel generators for modelling the dependence of four stocks, respectively. The ARMA-- GARCH process is used to model the series correlation and the conditional heteroscadesticity in each financial time series. The best structure and the estimation of the parameters of HAC are also received. In summary, based on Akaike information criterion, we conclude that the fully nested HAC with Gumbel generator exhibits better performance in this case.