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Efficient Estimation of Conditional Asset Pricing Models

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Abstract

A semiparametric efficient estimation procedure is developed for the parameters of multivariate GARCH-in-mean models when the disturbances have a distribution that is assumed to be elliptically symmetric but is otherwise unrestricted. Under high level restrictions, the resulting estimator achieves the asymptotic semiparametric efficiency bound. The elliptical symmetry assumption allows us to avert the curse of dimensionality problem that would otherwise arise in estimating the unknown error distribution. This framework is suitable for the estimation and testing of conditional asset pricing models such as the conditional CAPM, and we apply our estimator in an empirical study of stock prices, with Monte Carlo simulation results also being reported. Nous développons un nouvel estimateur pour les paramètres d'un modèle de GARCH en moyenne (" GARCH-M ") avec plusieurs variables. L'estimateur a l'efficacité semiparamétrique quand les erreurs suivent une loi de probabilité qui est elliptiquement symétrique mais n'aucune autre restriction. Sous les hypothèses de haut niveau, notre estimateur obtient la limite d'efficacité semiparamétrique. L'hypothèse de la symétrie elliptique nous permet d'éviter le problème d'estimer non-paramétriquement une fonction de haut dimension, parce qu'on peut écrire la densité d'un loi elliptique comme un fonction d'une transformation unidimensionnelle de la variable aléatoire multidimensionnelle. Ce cadre est approprié pour analyser des modèles conditionnels des prix des actifs financiers, comme le CAPM conditionnel. Nous appliquons notre méthodologie à l'étude des prix des actions, et nous rendons compte des résultats d'une étude simulation "Monte-Carlo".

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  • Douglas J. Hodgson & Keith Vorkink, 2001. "Efficient Estimation of Conditional Asset Pricing Models," Cahiers de recherche CREFE / CREFE Working Papers 144, CREFE, Université du Québec à Montréal.
  • Handle: RePEc:cre:crefwp:144
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    Cited by:

    1. Gabriele Fiorentini & Enrique Sentana, 2009. "Dynamic Specification Tests for Static Factor Models," Working Papers wp2009_0912, CEMFI.
    2. Christensen, Bent Jesper & Dahl, Christian M. & Iglesias, Emma M., 2012. "Semiparametric inference in a GARCH-in-mean model," Journal of Econometrics, Elsevier, vol. 167(2), pages 458-472.
    3. Fiorentini, Gabriele & Sentana, Enrique, 2018. "Specification tests for non-Gaussian maximum likelihood estimators," CEPR Discussion Papers 12934, C.E.P.R. Discussion Papers.
    4. Huffer, Fred W. & Park, Cheolyong, 2007. "A test for elliptical symmetry," Journal of Multivariate Analysis, Elsevier, vol. 98(2), pages 256-281, February.
    5. Dahl Christian M & Iglesias Emma, 2011. "Modeling the Volatility-Return Trade-Off When Volatility May Be Nonstationary," Journal of Time Series Econometrics, De Gruyter, vol. 3(1), pages 1-32, February.
    6. repec:rim:rimwps:38-07 is not listed on IDEAS
    7. BEAULIEU, Marie-Claude & DUFOUR, Jean-Marie & KHALAF, Lynda, 2005. "Exact Multivariate Tests of Asset Pricing Models with Stable Asymmetric Distributions," Cahiers de recherche 2005-04, Universite de Montreal, Departement de sciences economiques.
    8. Hafner, Christian M. & Rombouts, Jeroen V.K., 2007. "Semiparametric Multivariate Volatility Models," Econometric Theory, Cambridge University Press, vol. 23(02), pages 251-280, April.
    9. Beaulieu, Marie-Claude & Dufour, Jean-Marie & Khalaf, Lynda, 2010. "Asset-pricing anomalies and spanning: Multivariate and multifactor tests with heavy-tailed distributions," Journal of Empirical Finance, Elsevier, vol. 17(4), pages 763-782, September.
    10. Keith Vorkink & Douglas J. Hodgson & Oliver Linton, 2002. "Testing the capital asset pricing model efficiently under elliptical symmetry: a semiparametric approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(6), pages 617-639.
    11. Hallin, Marc & van den Akker, Ramon & Werker, Bas J.M., 2016. "Semiparametric error-correction models for cointegration with trends: Pseudo-Gaussian and optimal rank-based tests of the cointegration rank," Journal of Econometrics, Elsevier, vol. 190(1), pages 46-61.
    12. Alexeev, Vitali & Maynard, Alex, 2012. "Localized level crossing random walk test robust to the presence of structural breaks," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3322-3344.
    13. Amengual, Dante & Fiorentini, Gabriele & Sentana, Enrique, 2013. "Sequential estimation of shape parameters in multivariate dynamic models," Journal of Econometrics, Elsevier, vol. 177(2), pages 233-249.
    14. Douglas Hodgson & Barrett Slade & Keith Vorkink, 2006. "Constructing Commercial Indices: A Semiparametric Adaptive Estimator Approach," The Journal of Real Estate Finance and Economics, Springer, vol. 32(2), pages 151-168, March.
    15. Gabriele Fiorentini & Enrique Sentana, 2012. "Tests for Serial Dependence in Static, Non-Gaussian Factor Models," Working Papers wp2012_1211, CEMFI.
    16. Hallin, M. & Werker, B.J.M. & van den Akker, R., 2015. "Optimal Pseudo-Gaussian and Rank-based Tests of the Cointegration Rank in Semiparametric Error-correction Models," Discussion Paper 2015-001, Tilburg University, Center for Economic Research.

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    Keywords

    Capital asset pricing model; elliptical symmetry; semiparametric efficiency; GARCH.;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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