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The Score Of Conditionally Heteroskedastic Dynamic Regression Models With Student T Innovations, An Lm Test For Multivariate Normality

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Author Info
Gabriele Fiorentini () (Universidad de Alicante)
Enrique Sentana (CEMFI)
Giorgio Calzolari (University of Florence)

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Abstract

We provide numerically reliable analytical expressions for the score of conditionally heteroskedastic dynamic regression models when the conditional distribution is multivariate $t$. We also derive one-sided and 2-sided LM tests for multivariate normality versus multivariate $t$ based on the first two moments of the (squared) norm of the standardised innovations evaluated at the Gaussian quasi-ML estimators of the conditional mean and variance parameters. We reinterpret them as specification tests for multivariate excess kurtosis, and show that they have power against leptokurtic alternatives. Finally, we analyse UK stock returns, and confirm that their conditional distribution has fat tails.

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File URL: http://www.ivie.es/downloads/docs/wpasad/wpasad-2000-33.pdf
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Publisher Info
Paper provided by Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) in its series Working Papers. Serie AD with number 2000-33.

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Length: 32 pages
Date of creation: Dec 2000
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Publication status: Published by Ivie
Handle: RePEc:ivi:wpasad:2000-33

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Related research
Keywords: Kurtosis; Inequality Constraints; ARCH; Financial Returns.;

Find related papers by JEL classification:
C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation and Testing

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Baillie, Richard T & Bollerslev, Tim, 1989. "The Message in Daily Exchange Rates: A Conditional-Variance Tale," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(3), pages 297-305, July.
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  2. Jurgen A Doornik & Henrik Hansen, . "An omnibus test for univariate and multivariate normalit," Economics Papers W4&91., Economics Group, Nuffield College, University of Oxford. [Downloadable!]
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  3. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59. [Downloadable!] (restricted)
  4. B. D. McCullough & H. D. Vinod, 1999. "The Numerical Reliability of Econometric Software," Journal of Economic Literature, American Economic Association, vol. 37(2), pages 633-665, June. [Downloadable!] (restricted)
  5. Tim Bollerslev & Jeffrey Wooldridge, 1992. "Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances," Econometric Reviews, Taylor and Francis Journals, vol. 11(2), pages 143-172. [Downloadable!] (restricted)
  6. Davidson, Russel & MacKinnon, James G., 1983. "Small sample properties of alternative forms of the Lagrange Multiplier test," Economics Letters, Elsevier, vol. 12(3-4), pages 269-275. [Downloadable!] (restricted)
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  7. Kiefer, Nicholas M. & Salmon, Mark, 1983. "Testing normality in econometric models," Economics Letters, Elsevier, vol. 11(1-2), pages 123-127. [Downloadable!] (restricted)
  8. Demos, Antonis & Sentana, Enrique, 1998. "Testing for GARCH effects: a one-sided approach," Journal of Econometrics, Elsevier, vol. 86(1), pages 97-127, June. [Downloadable!] (restricted)
  9. Engle, Robert F., 1984. "Wald, likelihood ratio, and Lagrange multiplier tests in econometrics," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 13, pages 775-826 Elsevier. [Downloadable!] (restricted)
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  1. BONTEMPS, Christian & MEDDAHI, Nour, 2002. "Testing Normality : A GMM Approach," Cahiers de recherche 2002-14, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
  2. Josep Pijoan-Mas, 2003. "Precautionary Savings Or Working Longer Hours?," Working Papers wp2003_0311, CEMFI. [Downloadable!]
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