Dynamic C-vine Copula and its Application

We tackled the challenge of modelling dependence amongst high-dimensional time series. We first studied a type of bivariate stochastic autoregresive copula and used pair-copula construction technique to build high-dimensional copula models which serve to capture time-varying dependence. We showed that the maximum likelihood estimation of this high-dimensional model can be decomposed into sequential estimations of bivariate models. We applied the dynamic copula models to study the dependence amongst four major Western Stock market indices and showed the advantages of the proposed model in-sample. We then used the estimated model to construct risk-managed portfolios to showed the usefulness of this model in portfolio management based on density forecasting. Finally, we proposed a method to obtain probability integral transformation (PIT) of high-dimensional copula models and showed that the high-dimensional time series can be studied block by block with the use of this technique. To illustrate the use thereof, we applied it to the major stock market indices of the Western and Eastern markets and studied the holistic dependence between the West and the East.