Title: A nonparametric Bayesian approach to copula estimation
Authors: Shaoyang Shaoyang Ning - Harvard University (United States) [presenting]
Neil Shephard - Harvard University (United States)
Abstract: A novel Dirichlet-based Polya tree (D-P tree) prior on the copula is proposed, and based on the D-P tree prior, a nonparametric Bayesian inference procedure is developed. Through theoretical analysis and simulations, we are able to show that the flexibility of the D-P tree prior ensures its consistency in copula estimation, thus able to detect more subtle and complex copula structures than earlier nonparametric Bayesian models, such as a Gaussian copula mixture. Further, the continuity of the imposed D-P tree prior leads to a more favorable smoothing effect in copula estimation over classic frequentist methods, especially with small sets of observations. We also apply our method to the copula prediction between the S\&P 500 index and the IBM stock prices during the 2007-08 financial crisis, finding that D-P tree-based methods enjoy strong robustness and flexibility over classic methods under such irregular market behaviors.