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

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  • John Galbraith

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  • Dongming Zhu

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Abstract

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.

Suggested Citation

  • John Galbraith & Dongming Zhu, 2009. "A Generalized Asymmetric Student-T Distribution With Application To Financial Econometrics," Departmental Working Papers 2009-02, McGill University, Department of Economics.
  • Handle: RePEc:mcl:mclwop:2009-02
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    JEL classification:

    • 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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