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Bayesian Approach for Mixture Copula Model

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Part of the book series: Studies in Computational Intelligence ((SCI,volume 809))

Abstract

This paper aims to use the Bayesian estimation as an alternative method for formulating and estimating mixed copula models. This method has claimed to be more efficient than the conventional maximum likelihood estimator as it can deal with the high dimension copula and large parameter estimates under limited sample. In this study, we present various mixed copula functions constructed from both Elliptical and Archimedean copulas. We employ a simulation study to investigate the performance of this estimator for comparison with the maximum likelihood estimator. The results show that the Bayesian estimation is considerably more accurate than maximum likelihood estimator in various scenarios. Finally, we extend the Bayesian mixed copula to the real data and show that our approach perform well in this real data analysis.

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References

  1. Ardia, D.: bayesGARCH: Bayesian Estimation of the GARCH (1, 1) Model with Student-t Innovations in R (2007). http://CRAN.R-project.org/package=bayesGARCH

  2. Besag, J., Green, P., Higdon, D., Mengersen, K.: Bayesian computation and stochastic systems. Stat. Sci. 10, 3–41 (1995)

    Article  MathSciNet  Google Scholar 

  3. Brooks, C., Burke, P., Heravi, S., Persand, G.: Autoregressive conditional kurtosis. J. Financ. Econ. 3(3), 399–421 (2005)

    Google Scholar 

  4. Chib, S., Jeliazkov, I.: Marginal likelihood from the Metropolis-Hastings output. J. Am. Stat. Assoc. 96(453), 270–281 (2001)

    Article  MathSciNet  Google Scholar 

  5. Czado, C., Kastenmeier, R., Brechmann, E.C., Min, A.: A mixed copula model for insurance claims and claim sizes. Scand. Actuar. J. 2012(4), 278–305 (2012)

    Article  MathSciNet  Google Scholar 

  6. Danaher, P.J., Smith, M.S.: Modeling multivariate distributions using copulas: applications in marketing. Mark. Sci. 30(1), 4–21 (2011)

    Article  Google Scholar 

  7. Hastings, W.K.: Monte Carlo sampling methods using Markov chains and their applications (1970)

    Article  MathSciNet  Google Scholar 

  8. Hu, L.: Dependence patterns across financial markets: a mixed copula approach. Appl. Financ. Econ. 16(10), 717–729 (2006)

    Article  Google Scholar 

  9. Huard, D., Évin, G., Favre, A.C.: Bayesian copula selection. Comput. Stat. Data Anal. 51(2), 809–822 (2006)

    Article  MathSciNet  Google Scholar 

  10. Joe, H., Xu, J.J.: The estimation method of inference functions for margins for multivariate models (1996)

    Google Scholar 

  11. Jondeau, E., Rockinger, M.: Conditional volatility, skewness and kurtosis: existence, persistence, and comovements. J. Econ. Dyn. Control 27(10), 1699–1737 (2003)

    Article  MathSciNet  Google Scholar 

  12. Maneejuk, P., Yamaka, W., Sriboonchitta, S.: Mixed-copulas approach in examining the relationship between oil prices and ASEAN’s stock markets. In: International Econometric Conference of Vietnam, pp. 531–541. Springer, Cham, January 2018

    Google Scholar 

  13. Min, A., Czado, C.: Bayesian inference for multivariate copulas using pair-copula constructions. J. Financ. Econ. 8(4), 511–546 (2010)

    Google Scholar 

  14. Nelsen, R.B.: An Introduction to Copulas (Springer Series in Statistics), p. 3. Springer New York Inc., Secaucus (2006)

    Google Scholar 

  15. Nguyen, C., Bhatti, M.I., Komorníková, M., Komorník, J.: Gold price and stock markets nexus under mixed-copulas. Econ. Model. 58, 283–292 (2016)

    Article  Google Scholar 

  16. Patton, A.J.: Modelling asymmetric exchange rate dependence. Int. Econ. Rev. 47(2), 527–556 (2006)

    Article  MathSciNet  Google Scholar 

  17. Sklar, M.: Fonctions de repartition an dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris 8, 229–231 (1959)

    MathSciNet  MATH  Google Scholar 

  18. Smith, M.S., Gan, Q., Kohn, R.J.: Modelling dependence using skew t copulas: Bayesian inference and applications. J. Appl. Econ. 27(3), 500–522 (2012)

    Article  MathSciNet  Google Scholar 

  19. Tansuchat, R., Maneejuk, P.: Modeling dependence with copulas: are real estates and tourism associated? In: International Symposium on Integrated Uncertainty in Knowledge Modelling and Decision Making, pp. 302–311. Springer, Cham, March 2018

    Google Scholar 

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Acknowledgements

The authors are grateful to Puay Ungphakorn Centre of Excellence in Econometrics, Faculty of Economics, Chiang Mai University for the financial support.

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Correspondence to Sukrit Thongkairat .

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Thongkairat, S., Yamaka, W., Sriboonchitta, S. (2019). Bayesian Approach for Mixture Copula Model. In: Kreinovich, V., Thach, N., Trung, N., Van Thanh, D. (eds) Beyond Traditional Probabilistic Methods in Economics. ECONVN 2019. Studies in Computational Intelligence, vol 809. Springer, Cham. https://doi.org/10.1007/978-3-030-04200-4_58

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