A Generalized Asymmetric Student-T Distribution With Application To Financial Econometrics
AbstractThis 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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Bibliographic InfoPaper provided by McGill University, Department of Economics in its series Departmental Working Papers with number 2009-02.
Length: 37 pages
Date of creation: Apr 2009
Date of revision:
Other versions of this item:
- Zhu, Dongming & Galbraith, John W., 2010. "A generalized asymmetric Student-t distribution with application to financial econometrics," Journal of Econometrics, Elsevier, vol. 157(2), pages 297-305, August.
- Dongming Zhu & John Galbraith, 2009. "A Generalized Asymmetric Student-t Distribution with Application to Financial Econometrics," CIRANO Working Papers 2009s-13, CIRANO.
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
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- 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).
- 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.
- Panayiotis Theodossiou, 1998. "Financial Data and the Skewed Generalized T Distribution," Management Science, INFORMS, vol. 44(12-Part-1), pages 1650-1661, December.
- BAUWENS, Luc & LAURENT, Sébastien, 2002.
"A new class of multivariate skew densities, with application to GARCH models,"
CORE Discussion Papers
2002020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- 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.
- Dongming Zhu & John Galbraith, 2009.
"Forecasting Expected Shortfall with a Generalized Asymmetric Student-t Distribution,"
CIRANO Working Papers
- 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.
- 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.
- 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.
- Hansen, B.E., 1992.
"Autoregressive Conditional Density Estimation,"
RCER Working Papers
322, University of Rochester - Center for Economic Research (RCER).
- 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.
- 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.
- Fernández, C. & Steel, M.F.J., 1996. "On Bayesian Modelling of Fat Tails and Skewness," Discussion Paper 1996-58, Tilburg University, Center for Economic Research.
- 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.
- Alexander, Carol & Cordeiro, Gauss M. & Ortega, Edwin M.M. & Sarabia, José María, 2012.
"Generalized beta-generated distributions,"
Computational Statistics & Data Analysis,
Elsevier, vol. 56(6), pages 1880-1897.
- Carol Alexander & Gauss M. Cordeiro & Edwin M. M. Ortega & José María Sarabia, 2011. "Generalized Beta-Generated Distributions," ICMA Centre Discussion Papers in Finance icma-dp2011-05, Henley Business School, Reading University.
- Carol Alexander & Jose Maria Sarabia, 2010. "Generalized Beta-Generated Distributions," ICMA Centre Discussion Papers in Finance icma-dp2010-09, Henley Business School, Reading University.
- Daniel T. Cassidy & Michael J. Hamp & Rachid Ouyed, 2010. "Student's t-Distribution Based Option Sensitivities: Greeks for the Gosset Formulae," Papers 1003.1344, arXiv.org, revised Jul 2010.
- Zhu, Dongming & Galbraith, John W., 2011. "Modeling and forecasting expected shortfall with the generalized asymmetric Student-t and asymmetric exponential power distributions," Journal of Empirical Finance, Elsevier, vol. 18(4), pages 765-778, September.
- Harvey, Andrew & Sucarrat, Genaro, 2014.
"EGARCH models with fat tails, skewness and leverage,"
Computational Statistics & Data Analysis,
Elsevier, vol. 76(C), pages 320-338.
- Harvey, A. & Sucarrat, G., 2012. "EGARCH models with fat tails, skewness and leverage," Cambridge Working Papers in Economics 1236, Faculty of Economics, University of Cambridge.
- Rubio, Francisco Javier & Steel, Mark F. J., 2014. "Bayesian modelling of skewness and kurtosis with two-piece scale and shape transformations," MPRA Paper 57102, University Library of Munich, Germany.
- Nadarajah, Saralees & Chan, Stephen & Afuecheta, Emmanuel, 2013. "On the characteristic function for asymmetric Student t distributions," Economics Letters, Elsevier, vol. 121(2), pages 271-274.
- Colletaz, Gilbert & Hurlin, Christophe & Pérignon, Christophe, 2013.
"The Risk Map: A new tool for validating risk models,"
Journal of Banking & Finance,
Elsevier, vol. 37(10), pages 3843-3854.
- Gilbert Colletaz & Christophe Hurlin & Christophe Pérignon, 2012. "The Risk Map: A New Tool for Validating Risk Models," Working Papers halshs-00746273, HAL.
- 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.
- Dongming Zhu & John Galbraith, 2009. "Forecasting Expected Shortfall with a Generalized Asymmetric Student-t Distribution," CIRANO Working Papers 2009s-24, CIRANO.
- Stavros Degiannakis & Pamela Dent & Christos Floros, 2014. "A Monte Carlo Simulation Approach to Forecasting Multi-period Value-at-Risk and Expected Shortfall Using the FIGARCH-skT Specification," Manchester School, University of Manchester, vol. 82(1), pages 71-102, 01.
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