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Bivariate Student t distributions with variable marginal degrees of freedom and independence

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  • Shaw, W.T.
  • Lee, K.T.A.

Abstract

We propose a class of bivariate Student t distributions generalizing the standard density. Our generalization allows for differing marginal degrees of freedom and independent marginals. There are several approaches to constructing such distributions, but in the special case of the Student-normal distribution we show that there is a common canonical limit. Our distributions arise from the techniques used in t-copula simulation, rather than the traditional elliptical methodology.

Suggested Citation

  • Shaw, W.T. & Lee, K.T.A., 2008. "Bivariate Student t distributions with variable marginal degrees of freedom and independence," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1276-1287, July.
    • Handle: RePEc:eee:jmvana:v:99:y:2008:i:6:p:1276-1287
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    References listed on IDEAS

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    1. Kotz,Samuel & Nadarajah,Saralees, 2004. "Multivariate T-Distributions and Their Applications," Cambridge Books, Cambridge University Press, number 9780521826549.
    2. Jones, M. C., 2002. "A dependent bivariate t distribution with marginals on different degrees of freedom," Statistics & Probability Letters, Elsevier, vol. 56(2), pages 163-170, January.
    3. 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.
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    Cited by:

    1. William T. Shaw, 2011. "Risk, VaR, CVaR and their associated Portfolio Optimizations when Asset Returns have a Multivariate Student T Distribution," Papers 1102.5665, arXiv.org.
    2. Ebrahimi, Nader & Hamedani, G.G. & Soofi, Ehsan S. & Volkmer, Hans, 2010. "A class of models for uncorrelated random variables," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1859-1871, September.
    3. Paolella, Marc S. & Polak, Paweł, 2015. "ALRIGHT: Asymmetric LaRge-scale (I)GARCH with Hetero-Tails," International Review of Economics & Finance, Elsevier, vol. 40(C), pages 282-297.
    4. S.T. Boris Choy & Cathy W.S. Chen & Edward M.H. Lin, 2014. "Bivariate asymmetric GARCH models with heavy tails and dynamic conditional correlations," Quantitative Finance, Taylor & Francis Journals, vol. 14(7), pages 1297-1313, July.

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