Structure learning for hierarchical Archimedean copulas

• Main Authors: Yen-Hsun Chen, 陳彥勳
• Other Authors: Huei-Wen Teng
• Format: Others
• Language: en_US
• Published: 2013
• Online Access: http://ndltd.ncl.edu.tw/handle/m9am8z

碩士 === 國立中央大學 === 統計研究所 === 101 === Copulas decompose a joint distribution into a dependence structure and its marginal distri¬butions, and thus provide a great deal of flexibility in modelling multivariate distributions. Elliptical and exchangeable Archimedean copulas have constrained dependence structure, which however can not capture most dependence behaviour in reality. Therefore, we study the hierarchical Archimedean copula (HAC), an extension to the exchangeable Archimedean copulas, that allows more flexibility for modeling non-symmetric dependence among different variables. In contrast to a structure learning method by Okhrin and Ristig (2012) and Okhrin et al. (2013a), we propose an alternative method to construct the dependence structure of the HAC based on a fact that the structure of the copula can be uniquely recovered from all bivariate margins. In simulation studies, we show that our method produces higher correct¬ness rate to recover the correct dependence structure for an HAC compared with Okhrin and Ristig (2012). In an empirical analysis, we consider exchange rates of seven countries with a study period from 2010/1/1 to 2013/3/29, and construct a multivariate time series models.