Maximum Likelihood Estimation and Inference in Multivariate Conditionally Heteroscedastic Dynamic Regression Models with Student t Innovations

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Maximum Likelihood Estimation and Inference in Multivariate Conditionally Heteroscedastic Dynamic Regression Models with Student t Innovations

Author Info

Fiorentini, Gabriele
Sentana, Enrique
Calzolari, Giorgio

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Abstract

We provide numerically reliable analytical expressions for the score, Hessian, and information matrix of conditionally heteroscedastic dynamic regression models when the conditional distribution is multivariate t. We also derive one-sided and two-sided Lagrange multiplier tests for multivariate normality versus multivariate t based on the first two moments of the squared norm of the standardized innovations evaluated at the Gaussian pseudo-maximum likelihood estimators of the conditional mean and variance parameters. Finally, we illustrate our techniques through both Monte Carlo simulations and an empirical application to 26 U.K. sectoral stock returns that confirms that their conditional distribution has fat tails.

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Publisher Info
Article provided by American Statistical Association in its journal Journal of Business and Economic Statistics.

Volume (Year): 21 (2003)
Issue (Month): 4 (October)
Pages: 532-46
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Handle: RePEc:bes:jnlbes:v:21:y:2003:i:4:p:532-46

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Enrique Sentana & Giorgio Calzolari & Gabriele Fiorentini, 2004. "Indirect Estimation Of Conditionally Heteroskedastic Factor Models," Working Papers wp2004_0409, CEMFI. [Downloadable!]
Enrique Sentana & Dante Amegual, 2008. "A Comparison Of Mean-Variance Efficiency Tests," Working Papers wp2008_0806, CEMFI. [Downloadable!]
Trino-Manuel Ñíguez, 2003. "Volatility And Var Forecasting For The Ibex-35 Stock-Return Index Using Figarch-Type Processes And Different Evaluation Criteria," Working Papers. Serie AD 2003-33, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie). [Downloadable!]
DUFOUR, Jean-Marie & KHALAF, Lynda & BEAULIEU, Marie-Claude, 2003. "Exact Skewness-Kurtosis Tests for Multivariate Normality and Goodness-of-Fit in Multivariate Regressions with Application to Asset Pricing Models," Cahiers de recherche 07-2003, Centre interuniversitaire de recherche en économie quantitative, CIREQ. [Downloadable!]
Other versions:
- DUFOUR, Jean-Marie & KHALAF, Lynda & BEAULIEU, Marie-Claude, 2003. "Exact Skewness-Kurtosis Tests for Multivariate Normality and Goodness-of-fit in Multivariate Regressions with Application to Asset Pricing Models," Cahiers de recherche 2003-09, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
- Jean-Marie Dufour & Lynda Khalaf & Marie-Claude Beaulieu, 2003. "Exact skewness-kurtosis tests for multivariate normality and goodness-of-fit in multivariate regressions with application to asset pricing models," CIRANO Working Papers 2003s-33, CIRANO. [Downloadable!]
- Jean-Marie Dufour & Lynda Khalaf & Marie-Claude Beaulieu, 2003. "Exact Skewness-Kurtosis Tests for Multivariate Normality and Goodness-of-Fit in Multivariate Regressions with Application to Asset Pricing Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 65(s1), pages 891-906, December. [Downloadable!] (restricted)
Pesaran, B. & Pesaran, M.H., 2007. "Modelling Volatilities and Conditional Correlations in Futures Markets with a Multivariate t Distribution," Cambridge Working Papers in Economics 0734, Faculty of Economics, University of Cambridge. [Downloadable!]
Other versions:
- Bahram Pesaran & M. Hashem Pesaran, 2007. "Modelling Volatilities and Conditional Correlations in Futures Markets with a Multivariate t Distribution," IZA Discussion Papers 2906, Institute for the Study of Labor (IZA). [Downloadable!]
Rossi, Eduardo & Spazzini, Filippo, 2008. "Model and distribution uncertainty in multivariate GARCH estimation: a Monte Carlo analysis," MPRA Paper 12260, University Library of Munich, Germany. [Downloadable!]
Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109. [Downloadable!]
Other versions:
- BAUWENS, Luc & LAURENT, SŽbastien & ROMBOUTS, Jeroen, 2003. "Multivariate GARCH models: a survey," CORE Discussion Papers 2003031, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
Javier Mencía & Enrique Sentana, 2009. "Multivariate location-scale mixtures of normals and mean-variance-skewness portfolio allocation," Banco de EspaÃ±a Working Papers 0909, Banco de España. [Downloadable!]
Other versions:
- Enrique Sentana & Javier Mencía, 2008. "Multivariate Location-Scale Mixtures Of Normals And Mean-Variance-Skwness Portfolio Allocation," Working Papers wp2008_0805, CEMFI. [Downloadable!]
Enrique Sentana, 2008. "The Econometrics Of Mean-Variance Efficiency Tests: A Survey," Working Papers wp2008_0807, CEMFI. [Downloadable!]
Francisco Javier Mencía & Enrique Sentana, 2004. "Estimation And Testing Of Dynamic Models With Generalised Hyperbolic Innovations," Working Papers wp2004_0411, CEMFI. [Downloadable!]
Other versions:
- Mencía, Javier & Sentana, Enrique, 2005. "Estimation and Testing of Dynamic Models with Generalized Hyperbolic Innovations," CEPR Discussion Papers 5177, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
- Enrique Sentana, 2004. "Estimation and Testing of Dynamic Models with Generalised Hyperbolic Innovations," FMG Discussion Papers dp502, Financial Markets Group. [Downloadable!] (restricted)
Giorgio Canarella & Stephen M. Miller & Stephen K. Pollard, 2008. "Dynamic Stock Market Interactions between the Canadian, Mexican, and the United States Markets: The NAFTA Experience," Working papers 2008-49, University of Connecticut, Department of Economics. [Downloadable!]
Other versions:
- Giorgio Canarella & Stephen M. Miller & Stephen K. Pollard, 2009. "Dynamic Stock Market Interactions between the Canadian, Mexican, and the United States Markets: The NAFTA Experience," Working Papers 0905, University of Nevada, Las Vegas , Department of Economics. [Downloadable!]
Bahram Pesaran & M. Hashem Pesaran, 2007. "Volatilities and Conditional Correlations in Futures Markets with a Multivariate t Distribution," CESifo Working Paper Series CESifo Working Paper No. , CESifo Group Munich. [Downloadable!]
C.M. Hafner & H. Herwartz, 2003. "Analytical quasi maximum likelihood inference in multivariate volatility models," Econometric Institute Report 326, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
Other versions:
- Hafner, C.M. & Herwartz, H., 2003. "Analytical quasi maximum likelihood inference in multivariate volatility models," Econometric Institute Report EI 2003-21 Revision_Date:, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
- Christian Hafner & Helmut Herwartz, 2008. "Analytical quasi maximum likelihood inference in multivariate volatility models," Metrika, Springer, vol. 67(2), pages 219-239, March. [Downloadable!] (restricted)
Trino-Manuel Niguez & Javier Perote, 2004. "Forecasting the density of asset returns," STICERD - Econometrics Paper Series /2004/479, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
Enrique Sentana & Gabriele Fiorentini, 2007. "On The Efficiency And Consistency Of Likelihood Estimation In Multivariate Conditionally Heteroskedastic Dynamic Regression Models," Working Papers wp2007_0713, CEMFI. [Downloadable!]
Other versions:
- Gabriele Fiorentini & Enrique Sentana, 2007. "On the efficiency and consistency of likelihood estimation in multivariate conditionally heteroskedastic dynamic regression models," Working Paper Series 38-07, Rimini Centre for Economic Analysis, revised Jul 2007. [Downloadable!]

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