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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
DUFOUR, Jean-Marie
KHALAF, Lynda
BEAULIEU, Marie-Claude

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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 to simulation-based estimates of their expected value under the hypothesized distribution. Special cases considered include testing multivariate normal, Student t; normal mixtures and stable error models. 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 the nuisance parameters and the error distribution. The procedures considered are evaluated in a small simulation experiment. Finally, 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 five-year subperiods from 1926-1995.

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Paper provided by Centre interuniversitaire de recherche en économie quantitative, CIREQ in its series Cahiers de recherche with number 07-2003.

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Length: 29 pages
Date of creation: 2003
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Handle: RePEc:mtl:montec:07-2003

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Keywords: Multivariate linear regression goodness-of-fit normality test multivariate normality multinormality Student t normal mixture stable distribution specification test diagnostics exact test Monte Carlo test bootstrap nuisance parameter asset pricing model 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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  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!]
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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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  22. 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)
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  26. 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)
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  27. 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. Oussama Chakroun & Georges Dionne & Amélie Dugas-Sampara, 2006. "Empirical Evaluation of Investor Rationality in the Asset Allocation Puzzle," Cahiers de recherche 0635, CIRPEE. [Downloadable!]
  2. Jean-Marie Dufour & Lynda Khalaf & Marie-Claude Beaulieu, 2003. "Finite-Sample Diagnostics for Multivariate Regressions with Applications to Linear Asset Pricing Models," CIRANO Working Papers 2003s-34, CIRANO. [Downloadable!]
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