Research On Correlations Based On ARCH-Copula Models

According to the advantages in modelling and potential applications in practical fields such as Potfolio, Asset Pricing and Risk Management, the Copula function has became a key research field on the researches of correlation analysis.The main content of this dissertation is on the research of correlations analysis with the tool of ARCH based Copula models. On analysis of ARCH models, methods are explored for jointly modelling of the two models. In which, we take the ARCH models for marginal distribution models, and the Copula function for discribing the correlation structure between varibles. On the base of this idea and the research fruits of former authors, our researchs concerntrate on these aspects as follows:To the disadvantages of classic ARCH models for manually set the specific distribution of standard errors and normality assumption for parameters estimation, we propose a new method for Copula modelling which takes a semiparametric GARCH model for marginal modelling, and then tests its fitting cability through simulation application.On the aspects of model object, developping idea, model presentation and estimation methods, we discover the nature coincidence between the multivariate GARCH models and dynamic Copulas.We take a research on two kinds of dynamic Copulas. For one kind which has consitent structure but time varying parameters, in analysing the exchange data, we develop a new parameter evolving functions, and empirical result shows that our developped model can fit the correlation of datas better. Experiment shows that structure switching feature exists between the correlation process between Shanghai and Shenzhen Stock markets, after break point detection with Artificial Neuro-Networks, a subsection modelling method is used to model the dynamic correlation between the Shanghai and Shenzhen Stock markets.Static multivariate Copula modelling based on vine structrues is studied. Further, dynamic idea is imported to combine the multivariate and dynamic Copulas, and then a multivariate dynamic Copula based on vine structures is proposed, empirical analysis is carried out as well.