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A Generalized Asymmetric Student-T Distribution With Application To Financial Econometrics

  • John Galbraith

    ()

  • Dongming Zhu

    ()

This paper proposes a new class of asymmetric Student-t (AST) distributions, and investigates its properties, gives procedures for estimation, and indicates applications in financial econometrics. We derive analytical expressions for the cdf, quantile function, moments, and quantities useful in financial econometric applications such as the expected shortfall. A stochastic representation of the distribution is also given. Although the AST density does not satisfy the usual regularity conditions for maximum likelihood estimation, we establish consistency, asymptotic normality and efficiency of ML estimators and derive an explicit analytical expression for the asymptotic covariance matrix. A Monte Carlo study indicates generally good finite-sample conformity with these asymptotic properties.

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File URL: http://www.mcgill.ca/files/economics/asymmetric_t.pdf
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Paper provided by McGill University, Department of Economics in its series Departmental Working Papers with number 2009-02.

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Length: 37 pages
Date of creation: Apr 2009
Date of revision:
Handle: RePEc:mcl:mclwop:2009-02
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  1. Philip Hans Franses & Marco van der Leij & Richard Paap, 2008. "A Simple Test for GARCH Against a Stochastic Volatility Model," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 6(3), pages 291-306, Summer.
  2. Mittnik, Stefan & Paolella, Marc S., 2003. "Prediction of Financial Downside-Risk with Heavy-Tailed Conditional Distributions," CFS Working Paper Series 2003/04, Center for Financial Studies (CFS).
  3. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-30, August.
  4. Luc Bauwens & Sébastien Laurent, 2002. "A New Class of Multivariate skew Densities, with Application to GARCH Models," Computing in Economics and Finance 2002 5, Society for Computational Economics.
  5. John Galbraith & Dongming Zhu, 2009. "Forecasting Expected Shortfall With A Generalized Asymmetric Student-T Distribution," Departmental Working Papers 2009-01, McGill University, Department of Economics.
  6. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew "t"-distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389.
  7. Dima Alberg & Haim Shalit & Rami Yosef, 2008. "Estimating stock market volatility using asymmetric GARCH models," Applied Financial Economics, Taylor & Francis Journals, vol. 18(15), pages 1201-1208.
  8. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-47, August.
  9. Panayiotis Theodossiou, 1998. "Financial Data and the Skewed Generalized T Distribution," Management Science, INFORMS, vol. 44(12-Part-1), pages 1650-1661, December.
  10. Kjersti Aas & Ingrid Hobaek Haff, 2006. "The Generalized Hyperbolic Skew Student's t-Distribution," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(2), pages 275-309.
  11. Branco, Márcia D. & Dey, Dipak K., 2001. "A General Class of Multivariate Skew-Elliptical Distributions," Journal of Multivariate Analysis, Elsevier, vol. 79(1), pages 99-113, October.
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