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Activity Number: 119 - SPEED: Bayesian Methods Student Awards
Type: Contributed
Date/Time: Monday, July 31, 2017 : 8:30 AM to 10:20 AM
Sponsor: Section on Bayesian Statistical Science
Abstract #322871 View Presentation
Title: A Nonparametric Bayesian Approach to Copula Estimation
Author(s): Shaoyang Ning* and Neil Shephard
Companies: and Professor and Chair, Harvard Statistics Department
Keywords: copula ; Polya tree ; nonparametric Bayes ; Gaussian copula mixture model ; kernel method
Abstract:

We propose a novel Dirichlet-based Polya tree (D-P tree) prior on the copula and a non- parametric Bayesian inference procedure based on the D-P tree. Through theoretical results and simulations, we are able to show that the flexibility of the D-P tree prior ensures its con- sistency in copula estimation, thus able to detect more subtle and complex copula structures than earlier non-parametric Bayesian models, such as a Gaussian copula mixture under model misspecification. 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 structure 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.


Authors who are presenting talks have a * after their name.

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