IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v14y2012i4d10.1007_s11009-011-9220-4.html
   My bibliography  Save this article

Bayesian Model Choice of Grouped t-Copula

Author

Listed:
  • Xiaolin Luo

    (CSIRO Mathematics, Informatics and Statistics)

  • Pavel V. Shevchenko

    (CSIRO Mathematics, Informatics and Statistics)

Abstract

One of the most popular copulas for modeling dependence structures is t-copula. Recently the grouped t-copula was generalized to allow each group to have one member only, so that a priori grouping is not required and the dependence modeling is more flexible. This paper describes a Markov chain Monte Carlo (MCMC) method under the Bayesian inference framework for estimating and choosing t-copula models. Using historical data of foreign exchange (FX) rates as a case study, we found that Bayesian model choice criteria overwhelmingly favor the generalized t-copula. In addition, all the criteria also agree on the second most likely model and these inferences are all consistent with classical likelihood ratio tests. Finally, we demonstrate the impact of model choice on the conditional Value-at-Risk for portfolios of six major FX rates.

Suggested Citation

  • Xiaolin Luo & Pavel V. Shevchenko, 2012. "Bayesian Model Choice of Grouped t-Copula," Methodology and Computing in Applied Probability, Springer, vol. 14(4), pages 1097-1119, December.
    • Handle: RePEc:spr:metcap:v:14:y:2012:i:4:d:10.1007_s11009-011-9220-4
    DOI: 10.1007/s11009-011-9220-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-011-9220-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-011-9220-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Peters, Gareth W. & Wüthrich, Mario V. & Shevchenko, Pavel V., 2010. "Chain ladder method: Bayesian bootstrap versus classical bootstrap," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 36-51, August.
    2. Peters, Gareth W. & Shevchenko, Pavel V. & Wüthrich, Mario V., 2009. "Model Uncertainty in Claims Reserving within Tweedie's Compound Poisson Models," ASTIN Bulletin, Cambridge University Press, vol. 39(1), pages 1-33, May.
    3. W. Breymann & A. Dias & P. Embrechts, 2003. "Dependence structures for multivariate high-frequency data in finance," Quantitative Finance, Taylor & Francis Journals, vol. 3(1), pages 1-14.
    4. Cairns, Andrew J. G., 2000. "A discussion of parameter and model uncertainty in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 27(3), pages 313-330, December.
    5. Fang, Hong-Bin & Fang, Kai-Tai & Kotz, Samuel, 2002. "The Meta-elliptical Distributions with Given Marginals," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 1-16, July.
    6. Gareth W. Peters & Pavel V. Shevchenko & Mario V. Wuthrich, 2009. "Model uncertainty in claims reserving within Tweedie's compound Poisson models," Papers 0904.1483, arXiv.org.
    7. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    8. Pavel V. Shevchenko, 2010. "Implementing loss distribution approach for operational risk," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 26(3), pages 277-307, May.
    9. Gareth W. Peters & Mario V. Wuthrich & Pavel V. Shevchenko, 2010. "Chain ladder method: Bayesian bootstrap versus classical bootstrap," Papers 1004.2548, arXiv.org.
    10. Sylvia Fruhwirth-Schnatter, 2004. "Estimating marginal likelihoods for mixture and Markov switching models using bridge sampling techniques," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 143-167, June.
    11. Tatiana Miazhynskaia & Georg Dorffner, 2006. "A comparison of Bayesian model selection based on MCMC with an application to GARCH-type models," Statistical Papers, Springer, vol. 47(4), pages 525-549, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Man Chung Fung & Gareth W. Peters & Pavel V. Shevchenko, 2016. "A unified approach to mortality modelling using state-space framework: characterisation, identification, estimation and forecasting," Papers 1605.09484, arXiv.org.
    2. Alice X. D. Dong & Jennifer S. K. Chan & Gareth W. Peters, 2014. "Risk Margin Quantile Function Via Parametric and Non-Parametric Bayesian Quantile Regression," Papers 1402.2492, arXiv.org.
    3. Avanzi, Benjamin & Taylor, Greg & Vu, Phuong Anh & Wong, Bernard, 2020. "A multivariate evolutionary generalised linear model framework with adaptive estimation for claims reserving," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 50-71.
    4. Agbeyegbe, Terence D., 2015. "An inverted U-shaped crude oil price return-implied volatility relationship," Review of Financial Economics, Elsevier, vol. 27(C), pages 28-45.
    5. Peters, Gareth W. & Shevchenko, Pavel V. & Young, Mark & Yip, Wendy, 2011. "Analytic loss distributional approach models for operational risk from the α-stable doubly stochastic compound processes and implications for capital allocation," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 565-579.
    6. Gian Paolo Clemente & Nino Savelli & Diego Zappa, 2019. "Modelling Outstanding Claims with Mixed Compound Processes in Insurance," International Business Research, Canadian Center of Science and Education, vol. 12(3), pages 123-138, March.
    7. Pierre-Olivier Goffard & Patrick Laub, 2021. "Approximate Bayesian Computations to fit and compare insurance loss models," Working Papers hal-02891046, HAL.
    8. Heberle, Jochen & Thomas, Anne, 2014. "Combining chain-ladder claims reserving with fuzzy numbers," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 96-104.
    9. 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.
    10. Avanzi, Benjamin & Taylor, Greg & Vu, Phuong Anh & Wong, Bernard, 2016. "Stochastic loss reserving with dependence: A flexible multivariate Tweedie approach," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 63-78.
    11. Pavel V. Shevchenko, 2010. "Implementing loss distribution approach for operational risk," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 26(3), pages 277-307, May.
    12. Woźniak, Tomasz, 2015. "Testing causality between two vectors in multivariate GARCH models," International Journal of Forecasting, Elsevier, vol. 31(3), pages 876-894.
    13. Radu Tunaru, 2015. "Model Risk in Financial Markets:From Financial Engineering to Risk Management," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 9524, January.
    14. Denuit, Michel & Trufin, Julien, 2016. "Beyond the Tweedie Reserving Model: The Collective Approach to Loss Development," LIDAM Discussion Papers ISBA 2016030, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    15. Thomas A. Dean & Sumeetpal S. Singh & Ajay Jasra & Gareth W. Peters, 2014. "Parameter Estimation for Hidden Markov Models with Intractable Likelihoods," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 970-987, December.
    16. Taylor, Greg, 2019. "A Cape Cod model for the exponential dispersion family," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 126-137.
    17. Karthik Sriram & Peng Shi, 2021. "Stochastic loss reserving: A new perspective from a Dirichlet model," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 88(1), pages 195-230, March.
    18. Kylie-Anne Richards & Gareth W. Peters & William Dunsmuir, 2012. "Heavy-Tailed Features and Empirical Analysis of the Limit Order Book Volume Profiles in Futures Markets," Papers 1210.7215, arXiv.org, revised Apr 2015.
    19. Gareth W. Peters & Wilson Ye Chen & Richard H. Gerlach, 2016. "Estimating Quantile Families of Loss Distributions for Non-Life Insurance Modelling via L-Moments," Risks, MDPI, vol. 4(2), pages 1-41, May.
    20. Nicolas Chopin & Christian P. Robert, 2010. "Properties of nested sampling," Biometrika, Biometrika Trust, vol. 97(3), pages 741-755.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metcap:v:14:y:2012:i:4:d:10.1007_s11009-011-9220-4. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.