Abstract:
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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.
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