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Bayesian analysis of multivariate stable distributions using one-dimensional projections

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  • Tsionas, Mike G.

Abstract

In this paper we take up Bayesian inference in general multivariate stable distributions. We exploit the representation of Matsui and Takemura (2009) for univariate projections, and the representation of the distributions in terms of their spectral measure. We present efficient MCMC schemes to perform the computations when the spectral measure is approximated discretely or, as we propose, by a normal distribution. Appropriate latent variables are introduced to implement MCMC. In relation to the discrete approximation, we propose efficient computational schemes based on the characteristic function.

Suggested Citation

  • Tsionas, Mike G., 2016. "Bayesian analysis of multivariate stable distributions using one-dimensional projections," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 185-193.
    • Handle: RePEc:eee:jmvana:v:143:y:2016:i:c:p:185-193
    DOI: 10.1016/j.jmva.2015.09.005
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    References listed on IDEAS

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    1. Marc Hallin & Yves-Caoimhin Swan & Thomas Verdebout & David Veredas, 2013. "R-estimation in linear models with stable errors," ULB Institutional Repository 2013/136281, ULB -- Universite Libre de Bruxelles.
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    4. Matsui, Muneya & Takemura, Akimichi, 2009. "Integral representations of one-dimensional projections for multivariate stable densities," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 334-344, March.
    5. Hallin, Marc & Swan, Yvik & Verdebout, Thomas & Veredas, David, 2013. "One-step R-estimation in linear models with stable errors," Journal of Econometrics, Elsevier, vol. 172(2), pages 195-204.
    6. Lombardi, Marco J. & Veredas, David, 2009. "Indirect estimation of elliptical stable distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2309-2324, April.
    7. Broda, Simon A. & Haas, Markus & Krause, Jochen & Paolella, Marc S. & Steude, Sven C., 2013. "Stable mixture GARCH models," Journal of Econometrics, Elsevier, vol. 172(2), pages 292-306.
    8. Ogata, Hiroaki, 2013. "Estimation for multivariate stable distributions with generalized empirical likelihood," Journal of Econometrics, Elsevier, vol. 172(2), pages 248-254.
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    10. Ravishanker, Nalini & Qiou, Zuqiang, 1999. "Monte Carlo EM estimation for multivariate stable distributions," Statistics & Probability Letters, Elsevier, vol. 45(4), pages 335-340, December.
    11. repec:ulb:ulbeco:2013/136280 is not listed on IDEAS
    12. Dominicy, Yves & Veredas, David, 2013. "The method of simulated quantiles," Journal of Econometrics, Elsevier, vol. 172(2), pages 235-247.
    13. J. Huston McCulloch, 2000. "Estimation of the Bivariate Stable Spectral Representation by the Projection Method," Computational Economics, Springer;Society for Computational Economics, vol. 16(1/2), pages 47-62, October.
    14. Abdul-Hamid, Husein & Nolan, John P., 1998. "Multivariate Stable Densities as Functions of One Dimensional Projections," Journal of Multivariate Analysis, Elsevier, vol. 67(1), pages 80-89, October.
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    Cited by:

    1. Karling, Maicon J. & Lopes, Sílvia R.C. & de Souza, Roberto M., 2023. "Multivariate α-stable distributions: VAR(1) processes, measures of dependence and their estimations," Journal of Multivariate Analysis, Elsevier, vol. 195(C).
    2. Mike G. Tsionas & Nicholas Apergis, 2023. "Another look at contagion across United States and European financial markets: Evidence from the credit default swaps markets," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 28(1), pages 1137-1155, January.

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