A nonparametric Bayesian approach to copula estimation. Issue 6 (13th April 2018)

• Record Type: Journal Article
• Authors: Ning, Shaoyang; Shephard, Neil
• Is Part Of: Journal of statistical computation and simulation. Volume 88:Issue 6(2018)
• Page Start: 1081
• Page End: 1105
• Publication Date: 2018-04-13
• Subjects: Copula -- Pólya tree -- nonparametric Bayes -- Gaussian copula mixture model -- kernel method; 62G99 -- 62G07 -- 62H20 -- 62H99 -- 62P05; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5028505
• DOI: 10.1080/00949655.2017.1421194
• Languages: English
• ISSNs: 0094-9655

Abstract

ABSTRACT: We propose a novel Dirichlet-based Pólya tree (D-P tree) prior on the copula and based on the D-P tree prior, a nonparametric Bayesian inference procedure. 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. Furthermore, the continuity of the imposed D-P tree prior leads to a more favourable 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 behaviours.