A nonparametric Bayesian approach to copula estimation. (English) Zbl 07192593
Summary: 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.
MSC:
| 62G99 | Nonparametric inference |
| 62G07 | Density estimation |
| 62H20 | Measures of association (correlation, canonical correlation, etc.) |
| 62H99 | Multivariate analysis |
| 62P05 | Applications of statistics to actuarial sciences and financial mathematics |
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