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Exact Skewness-Kurtosis Tests for Multivariate Normality and Goodness-of-Fit in Multivariate Regressions with Application to Asset Pricing Models

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  • Jean-Marie Dufour
  • Lynda Khalaf
  • Marie-Claude Beaulieu

Abstract

We study the problem of testing the error distribution in a multivariate linear regression (MLR) model. The tests are functions of appropriately standardized multivariate least squares residuals whose distribution is invariant to the unknown cross-equation error covariance matrix. Empirical multivariate skewness and kurtosis criteria are then compared with a simulation-based estimate of their expected value under the hypothesized distribution. Special cases considered include testing multivariate normal and stable error distributions. In the Gaussian case, finite-sample versions of the standard multivariate skewness and kurtosis tests are derived. To do this, we exploit simple, double and multi-stage Monte Carlo test methods. For non-Gaussian distribution families involving nuisance parameters, confidence sets are derived for the nuisance parameters and the error distribution. The tests are applied to an asset pricing model with observable risk-free rates, using monthly returns on New York Stock Exchange (NYSE) portfolios over 5-year subperiods from 1926 to 1995. Copyright 2003 Blackwell Publishing Ltd.

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Bibliographic Info

Article provided by Department of Economics, University of Oxford in its journal Oxford Bulletin of Economics & Statistics.

Volume (Year): 65 (2003)
Issue (Month): s1 (December)
Pages: 891-906

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Handle: RePEc:bla:obuest:v:65:y:2003:i:s1:p:891-906

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Citations

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Cited by:
  1. Jean-Marie DUFOUR & Lynda KHALAF & Marcel VOIA, 2013. "Finite-Sample Resampling-Based Combined Hypothesis Tests, with Applications to Serial Correlation and Predictability," Cahiers de recherche 13-2013, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  2. Bai, Zhidong & Phoon, Kok Fai & Wang, Keyan & Wong, Wing-Keung, 2013. "The performance of commodity trading advisors: A mean-variance-ratio test approach," The North American Journal of Economics and Finance, Elsevier, vol. 25(C), pages 188-201.
  3. Araújo, Tanya & Dias, João & Eleutério, Samuel & Louçã, Francisco, 2013. "A measure of multivariate kurtosis for the identification of the dynamics of a N-dimensional market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3708-3714.
  4. Tanya Ara\'ujo & Jo\~ao Dias & Samuel Eleut\'erio & Francisco Lou\c{c}\~a, 2012. "How Fama Went Wrong: Measures of Multivariate Kurtosis for the Identification of the Dynamics of a N-Dimensional Market," Papers 1207.1202, arXiv.org.
  5. Beaulieu, Marie-Claude & Dufour, Jean-Marie & Khalaf, Lynda, 2009. "Finite sample multivariate tests of asset pricing models with coskewness," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2008-2021, April.
  6. Iqbal, Javed & Brooks, Robert & Galagedera, Don UA, 2007. "Robust Tests of the Lower Partial Moment Asset Pricing Model in Emerging Markets," MPRA Paper 25349, University Library of Munich, Germany, revised May 2007.
  7. Beaulieu, Marie-Claude & Dufour, Jean-Marie & Khalaf, Lynda, 2014. "Exact confidence sets and goodness-of-fit methods for stable distributions," Journal of Econometrics, Elsevier, vol. 181(1), pages 3-14.
  8. Bontemps, Christian, 2013. "Moment-Based Tests for Discrete Distributions," IDEI Working Papers 772, Institut d'Économie Industrielle (IDEI), Toulouse.
  9. DUFOUR, Jean-Marie & KHALAF, Lynda & BEAULIEU, Marie-Claude, 2003. "Finite-Sample Diagnostics for Multivariate Regressions with Applications to Linear Asset Pricing Models," Cahiers de recherche 2003-08, Universite de Montreal, Departement de sciences economiques.
  10. Galvao, Antonio F. & Montes-Rojas, Gabriel & Sosa-Escudero, Walter & Wang, Liang, 2013. "Tests for skewness and kurtosis in the one-way error component model," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 35-52.
  11. Jean-Marie Dufour & Lynda Khalaf & Marie-Claude Beaulieu, 2010. "Multivariate residual-based finite-sample tests for serial dependence and ARCH effects with applications to asset pricing models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(2), pages 263-285.
  12. Enrique Sentana, 2009. "The econometrics of mean-variance efficiency tests: a survey," Econometrics Journal, Royal Economic Society, vol. 12(3), pages C65-C101, November.
  13. Oussama Chakroun & Georges Dionne & Amélie Dugas-Sampara, 2006. "Empirical Evaluation of Investor Rationality in the Asset Allocation Puzzle," Cahiers de recherche 0635, CIRPEE.
  14. Bernard, Jean-Thomas & Idoudi, Nadhem & Khalaf, Lynda & Yelou, Clement, 2007. "Finite sample multivariate structural change tests with application to energy demand models," Journal of Econometrics, Elsevier, vol. 141(2), pages 1219-1244, December.

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