AbstractsBusiness Management & Administration

Big data applications increasingly involve high-dimensional and sophisticated dependence structures in complex data. Modelling high-dimensional dependence, that is, the dependence between a set of high-dimensional variables, is a critical but challenging issue in many applications including social media analysis and financial markets. A typical example concerns the interplay of financial variables involved in driving complex market movements. A particular problem is understanding the dependence between high-dimensional variables with tail dependence and asymmetric characteristics which appear widely in financial markets. Typically, existing methods, such as the Bayesian logic program, relational dependency networks and relational Markov networks, build a graph to represent the conditional dependence structure between random variables. These models aim at high-dimensional domains, and have the advantage of learning latent relationships from data. However, they tend to force the local quantitative part of the model to take a simple form such as the discretized form of the data when multivariate Gaussian or its mixtures cannot capture the data in the real world. The complex dependencies between high-dimensional variables are difficult to capture. In statistics and finance, the copula has been shown to be a powerful tool for modelling high-dimensional dependencies. The copula splits the multivariate marginal distributions from dependence structures, so that the specification of dependence structures can be investigated independently of the marginal distributions. It can provide a flexible mechanism for modelling real world distributions that cannot be handled well by graphical models. Thus, researchers have tried to combine copula and probability graphical models, such as the tree-structured copula model and copula Bayesian networks. These copula-based models aim to resolve the limitations of discretizing data, but they impose assumptions and restrictions on the dependence structure. These assumptions and restrictions are not appropriate for dependence modelling among financial variables. In order to address these research limitations and challenges, this thesis proposes the use of the truncated partial correlation-based canonical vine copula, partial correlation-based regular vine copula and truncated partial correlation-based regular vine copula to model the dependence of high-dimensional variables. Chapter 3 introduces a new partial correlation-based canonical vine to identify the asymmetric and non-linear dependence structures of asset returns without any prior dependence assumptions. To simplify the model while maintaining its merit, a partial correlation-based truncation method is proposed to truncate the canonical vine. The truncated partial correlation-based canonical vine copula is then applied to construct and analyse the dependence structures of European stocks as a case study. Chapter 4 introduces the truncated partial correlation-based regular vine copula to explore the relations in multiple variables.…