John W. Galbraith, Dongming Zhu

This code estimates the parameters of an AST-NGARCH(1,1) model, which is a non-linear asymmetric NGARCH process of Engle and Ng where the conditional distribution of return is the Asymmetric Student-t distribution (AST) proposed by Zhu and Galbraith.

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.

John W. Galbraith,
Dongming Zhu,
et al.
"A Generalized Asymmetric Student-t Distribution with Application to Financial Econometrics."
*Journal of Econometrics (2010)*.
doi:10.1016/j.jeconom.2010.01.013.
Retrieved 10/23/2018 from researchcompendia.org/compendia/2013.97/

**Primary Research Field**: Econometrics

created 11/12/2013

modified 01/16/2014

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