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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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Author Info
Jean-Marie Dufour ()
Lynda Khalaf
Marie-Claude Beaulieu ()

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Abstract

Dans cet article, nous proposons des tests sur la forme de la distribution des erreurs dans un modèle de régression linéaire multivarié (RLM). Les tests que nous développons sont fonction des résidus obtenus par moindres carrés multivariés, lesquels sont standardisés de façon à ce que leur distribution soit invariante à la matrice de covariance, inconnue, des erreurs. Notre approche utilise des mesures empiriques d'asymétrie et d'aplatissement de la distribution des erreurs, que nous comparons à des estimations engendrées par simulation de ces caractéristiques sous cette même hypothèse distributionnelle. Les cas spécifiques que nous étudions comprennent des tests sur les erreurs du modèle dans le cadre des lois normale, t de Student, mélange de normales et stable. Dans le cas gaussien, nous obtenons des versions exactes de tests d'ajustement standards sur l'asymétrie et l'aplatissement des erreurs dans le cas multivarié. À cette fin, nous utilisons des tests de Monte Carlo simples, doubles et multiples. Dans les cas non-gaussiens, comme les familles de lois dépendent de paramètres de nuisance, nous proposons des régions de confiance pour ces derniers et la distribution des erreurs. Les procédures introduites dans cet article sont alors évalulées par une simulation de petite taille. Finalement, les tests proposés sont appliqués à un modèle d'évaluation d'actifs impliquant un taux d'intérêt sans risque observable et utilisant les rendements de portefeuilles mensuels de titres inscrits à la bourse de New York, sur des sous-périodes de cinq ans allant de janvier 1926 à décembre 1995.

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Paper provided by CIRANO in its series CIRANO Working Papers with number 2003s-33.

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Date of creation: 01 Mar 2003
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Handle: RePEc:cir:cirwor:2003s-33

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Keywords: ; modèle de régression multivarié; test d'ajustement; test de normalité; normalité multivariée; t de Student; mélange de lois normales; distribution stable; test de spécification; diagnostic; test exact; test de Monte Carlo; bootstrap; paramètre de nuisance; modèle d'évaluation d'actifs financiers; CAPM;

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Find related papers by JEL classification:
C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data
C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Statistical Simulation Methods
G1 - Financial Economics - - General Financial Markets
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing
G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies

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  1. Dufour, Jean-Marie & Kiviet, Jan F., 1996. "Exact tests for structural change in first-order dynamic models," Journal of Econometrics, Elsevier, vol. 70(1), pages 39-68, January. [Downloadable!] (restricted)
  2. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February. [Downloadable!] (restricted)
  3. Kilian, Lutz & Demiroglu, Ufuk, 2000. "Residual-Based Tests for Normality in Autoregressions: Asymptotic Theory and Simulation Evidence," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(1), pages 40-50, January.
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  5. Affleck-Graves, John & McDonald, Bill, 1989. " Nonnormalities and Tests of Asset Pricing Theories," Journal of Finance, American Finance Association, vol. 44(4), pages 889-908, September. [Downloadable!] (restricted)
  6. Shanken, Jay, 1990. "Intertemporal asset pricing : An Empirical Investigation," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 99-120. [Downloadable!] (restricted)
  7. Berk, Jonathan B., 1997. "Necessary Conditions for the CAPM," Journal of Economic Theory, Elsevier, vol. 73(1), pages 245-257, March. [Downloadable!] (restricted)
  8. Nielsen, Lars Tyge, 1990. "Existence of equilibrium in CAPM," Journal of Economic Theory, Elsevier, vol. 52(1), pages 223-231, October. [Downloadable!] (restricted)
  9. Allingham, Michael, 1991. "Existence Theorems in the Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 59(4), pages 1169-74, July. [Downloadable!] (restricted)
  10. Zhou, Guofu, 1995. "Small sample rank tests with applications to asset pricing," Journal of Empirical Finance, Elsevier, vol. 2(1), pages 71-93, March. [Downloadable!] (restricted)
  11. Dufour, Jean-Marie & Khalaf, Lynda & Bernard, Jean-Thomas & Genest, Ian, 2004. "Simulation-based finite-sample tests for heteroskedasticity and ARCH effects," Journal of Econometrics, Elsevier, vol. 122(2), pages 317-347, October. [Downloadable!] (restricted)
    Other versions:
  12. Fiorentini, Gabriele & Sentana, Enrique & Calzolari, Giorgio, 2003. "Maximum Likelihood Estimation and Inference in Multivariate Conditionally Heteroscedastic Dynamic Regression Models with Student t Innovations," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(4), pages 532-46, October.
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  14. BONTEMPS, Christian & MEDDAHI, Nour, 2002. "Testing Normality : A GMM Approach," Cahiers de recherche 2002-14, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
  15. Richardson, Matthew & Smith, Tom, 1993. "A Test for Multivariate Normality in Stock Returns," Journal of Business, University of Chicago Press, vol. 66(2), pages 295-321, April. [Downloadable!] (restricted)
  16. Bontemps, C. & Meddahi, N., 2002. "Testing Normality : A GMM Approach," Cahiers de recherche 14-2002, Centre interuniversitaire de recherche en économie quantitative, CIREQ. [Downloadable!]
  17. DUFOUR, Jean-Marie & FARHAT, Abdeljelil & GARDIOL, Lucien, 1998. "Simulation-Based Finite-Sample Normality Tests in Linear Regressions," Cahiers de recherche 9811, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
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  18. Gibbons, Michael R & Ross, Stephen A & Shanken, Jay, 1989. "A Test of the Efficiency of a Given Portfolio," Econometrica, Econometric Society, vol. 57(5), pages 1121-52, September. [Downloadable!] (restricted)
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  20. Zhou, Guofu, 1991. "Small sample tests of portfolio efficiency," Journal of Financial Economics, Elsevier, vol. 30(1), pages 165-191, November. [Downloadable!] (restricted)
  21. Jobson, J. D. & Korkie, Bob, 1989. "A Performance Interpretation of Multivariate Tests of Asset Set Intersection, Spanning, and Mean-Variance Efficiency," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(02), pages 185-204, June. [Downloadable!]
  22. Dufour, Jean-Marie & Khalaf, Lynda, 2002. "Exact tests for contemporaneous correlation of disturbances in seemingly unrelated regressions," Journal of Econometrics, Elsevier, vol. 106(1), pages 143-170, January. [Downloadable!] (restricted)
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  23. Jobson, J. D. & Korkie, Bob, 1982. "Potential performance and tests of portfolio efficiency," Journal of Financial Economics, Elsevier, vol. 10(4), pages 433-466, December. [Downloadable!] (restricted)
  24. Fama, Eugene F & French, Kenneth R, 1995. " Size and Book-to-Market Factors in Earnings and Returns," Journal of Finance, American Finance Association, vol. 50(1), pages 131-55, March. [Downloadable!] (restricted)
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  26. Jean-Marie Dufour & Jan F. Kiviet, 1998. "Exact Inference Methods for First-Order Autoregressive Distributed Lag Models," Econometrica, Econometric Society, vol. 66(1), pages 79-104, January.
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  27. Dufour, Jean-Marie & Khalaf, Lynda, 2002. "Simulation based finite and large sample tests in multivariate regressions," Journal of Econometrics, Elsevier, vol. 111(2), pages 303-322, December. [Downloadable!] (restricted)
    Other versions:
  28. Shanken, Jay, 1986. " Testing Portfolio Efficiency When the Zero-Beta Rate Is Unknown: A Note," Journal of Finance, American Finance Association, vol. 41(1), pages 269-76, March. [Downloadable!] (restricted)
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Cited by:
(explanations, 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. 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 06-2003, Centre interuniversitaire de recherche en économie quantitative, CIREQ. [Downloadable!]
    Other versions:
  2. Oussama Chakroun & Georges Dionne & Amélie Dugas-Sampara, 2006. "Empirical Evaluation of Investor Rationality in the Asset Allocation Puzzle," Cahiers de recherche 0635, CIRPEE. [Downloadable!]
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