Simplified Pair Copula-GARCH Models Base on Regular Vines in High Dimensions
|Course||Probability Theory and Mathematical Statistics|
|Keywords||Copula function GARCH family models Pair Copula decompo-sition Simplified regular vines Maximum spanning tree Vuong test|
In recent years, it is very popular to use a series of Pair Copula building blocks to construct joint distribution of the portfolio by the logical structure of regular vine and copula theory. This is due to their high flexibility, which makes them able to model a wide range of complex dependency structure in the high-dimensional portfolio. N-evertheless, these structures have some shortcomings in the practical application and operation. First of all, the number of Pair Copulas are quadratic of the dimension and increases rapidly as the dimension becomes larger. As a result, it will be to bring great inconvenience for the select of pair copulas type. Secondly, The number of estimated parameters grows exponentially with the dimension, the computational effort is very enormous and burdensome. In the end, it is also horrendous and burdensome to cal-culate the VaR or CVaR of the portfolio by means of the Monte Carlo simulation after we workout the joint distribution function of all the assets. In order to find the prop-er fitting one under limited time and computational resources, the paper introduces the Simplified Pair Copula-GARCH Models base on a more general regular vines in high dimensions, while most of the literatures proposed the simplified canonical vine copula using a multivariate copula. The main construction methods of this model are as follows. First of all, we will build a proper easy to simplify the structure of R-vine by the measures of dependence between variables and the maximum spanning tree algorithm in graph theory. Second, we try to determine the effective simplified level k of the structure of R-vine by means of AIC/BIC test or Vuong test. Then we choose different Pair Copulas to fit the structure of R-vine before the k trees and Gauss copulas to fit the rest trees of the structure of R-vine. At the end of the paper, we use them to investigate a16-dimensional financial data set to testify and prove the feasibility and effectiveness in practical application.