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UBC Theses and Dissertations

Structured factor copulas and tail inference Krupskii, Pavel


In this dissertation we propose factor copula models where dependence is modeled via one or several common factors. These are general conditional independence models for $d$ observed variables, in terms of $p$ latent variables and the classical multivariate normal model with a correlation matrix having a factor structure is a special case. We also propose and investigate dependence properties of the extended models that we call structured factor copula models. The extended models are suitable for modeling large data sets when variables can be split into non-overlapping groups such that there is homogeneous dependence within each group. The models allow for different types of dependence structure including tail dependence and asymmetry. With appropriate numerical methods, efficient estimation of dependence parameters is possible for data sets with over 100 variables. The choice of copula is essential in the models to get correct inferences in the tails. We propose lower and upper tail-weighted bivariate measures of dependence as additional scalar measures to distinguish bivariate copulas with roughly the same overall monotone dependence. These measures allow the efficient estimation of strength of dependence in the joint tails and can be used as a guide for selection of bivariate linking copulas in factor copula models as well as for assessing the adequacy of fit of multivariate copula models. We apply the structured factor copula models to analyze financial data sets, and compare with other copula models for tail inference. Using model-based interval estimates, we find that some commonly used risk measures may not be well discriminated by copula models, but tail-weighted dependence measures can discriminate copula models with different dependence and tail properties.

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