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Bayesian Nonparametric Inference for a Multivariate Copula Function

Author

Listed:
  • Juan Wu

    (Huazhong University of Science and Technology)

  • Xue Wang

    (University of Kent at Canterbury)

  • Stephen G. Walker

    (University of Kent at Canterbury)

Abstract

The paper presents a general Bayesian nonparametric approach for estimating a high dimensional copula. We first introduce the skew–normal copula, which we then extend to an infinite mixture model. The skew–normal copula fixes some limitations in the Gaussian copula. An MCMC algorithm is developed to draw samples from the correct posterior distribution and the model is investigated using both simulated and real applications.

Suggested Citation

  • Juan Wu & Xue Wang & Stephen G. Walker, 2014. "Bayesian Nonparametric Inference for a Multivariate Copula Function," Methodology and Computing in Applied Probability, Springer, vol. 16(3), pages 747-763, September.
    • Handle: RePEc:spr:metcap:v:16:y:2014:i:3:d:10.1007_s11009-013-9348-5
    DOI: 10.1007/s11009-013-9348-5
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    References listed on IDEAS

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    1. Genest, Christian & Rémillard, Bruno & Beaudoin, David, 2009. "Goodness-of-fit tests for copulas: A review and a power study," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 199-213, April.
    2. Diers, Dorothea & Eling, Martin & Marek, Sebastian D., 2012. "Dependence modeling in non-life insurance using the Bernstein copula," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 430-436.
    3. Michael Pitt & David Chan & Robert Kohn, 2006. "Efficient Bayesian inference for Gaussian copula regression models," Biometrika, Biometrika Trust, vol. 93(3), pages 537-554, September.
    4. Michael S. Smith & Mohamad A. Khaled, 2012. "Estimation of Copula Models With Discrete Margins via Bayesian Data Augmentation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 290-303, March.
    5. Luciana Dalla Valle, 2009. "Bayesian Copulae Distributions, with Application to Operational Risk Management," Methodology and Computing in Applied Probability, Springer, vol. 11(1), pages 95-115, March.
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    Cited by:

    1. Sabyasachi Guharay & KC Chang & Jie Xu, 2017. "Robust Estimation of Value-at-Risk through Distribution-Free and Parametric Approaches Using the Joint Severity and Frequency Model: Applications in Financial, Actuarial, and Natural Calamities Domain," Risks, MDPI, vol. 5(3), pages 1-30, July.
    2. Zhu, Bo & Lin, Renda & Deng, Yuanyue & Chen, Pingshe & Chevallier, Julien, 2021. "Intersectoral systemic risk spillovers between energy and agriculture under the financial and COVID-19 crises," Economic Modelling, Elsevier, vol. 105(C).
    3. Levi, Evgeny & Craiu, Radu V., 2018. "Bayesian inference for conditional copulas using Gaussian Process single index models," Computational Statistics & Data Analysis, Elsevier, vol. 122(C), pages 115-134.

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