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Conditionally Heteroskedastic Factor Models: Identification and Instrumental Variables Estimation

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  • Catherine Doz
  • Éric Renault

    ()

Abstract

This paper provides a semiparametric framework for modelling multivariate conditional heteroskedasticity. First, we show that stochastic volatility factor models with possibly cross-correlated disturbances cannot be identified from returns conditional variance structure only, except when strong restrictions on the support of the probability distribution of latent factors volatility are maintained. Second, we provide an alternative way to maintain identifying restrictions through either higher order moments or through a specification of risk premiums based on constant prices of factor risks. In both cases, identification is obtained with conditional moment restrictions which pave the way for instrumental variables estimation and inference. A preliminary step of determination of the number of factors and identification of mimicking portfolios is proposed through a sequence of GMM overidentification tests which encompass Engle and Kozicki (1993) tests for common features. Cet article propose un cadre semi-paramétrique adapté à la modélisation de l'hétéroscédasticité conditionnelle multivariée. Nous montrons d'abord qu'un modèle factoriel à volatilité stochastique ne peut pas être identifié seulement à partir de la structure de variance conditionnelle des rendements, sauf si l'on impose des restrictions importantes au support de la loi de probabilité des facteurs latents. Nous proposons ensuite des restrictions alternatives permettant d'identifier le modèle de volatilité multivariée. Ces restrictions portent soit sur les moments d'ordre supérieur, soit sur une spécification de la prime de risque fondée sur un prix constant du risque des facteurs. Dans les deux cas, l'identification du modèle est obtenue à partir de restrictions sur les moments conditionnels, ce qui permet l'estimation par variables instrumentales. Une étape préliminaire de détermination du nombre de facteurs et d'identification de portefeuilles représentatifs est proposée. Elle est fondée sur une séquence de tests de sur-identification qui englobe les tests de caractéristiques communes d'Engle et Kozicki (1993).

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Bibliographic Info

Paper provided by CIRANO in its series CIRANO Working Papers with number 2004s-37.

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Date of creation: 01 Jun 2004
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Handle: RePEc:cir:cirwor:2004s-37

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Keywords: asset pricing; stochastic volatility; conditional factor models; multivariate conditional heteroskedasticity; common features; multiperiod conditional moment restrictions; Generalized Method of Moments.; évaluation d'actifs financiers; volatilité stochastique; modèles conditionnels à facteurs; hétéroscédasticité conditionnelle multivariée; caractéristiques communes; restrictions de moments conditionnels avec retards; Méthode des Moments Généralisés;

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References

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  1. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
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  3. Sentana, E., 2000. "Factor Representing Portfolios in Large Asset Markets," Papers 0001, Centro de Estudios Monetarios Y Financieros-.
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  8. Neil Shephard & Gabriele Fiorentini Enrique Sentana, 2002. "Likelihood-based estimation of latent generalised ARCH structures," Economics Series Working Papers 2002-W19, University of Oxford, Department of Economics.
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  10. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  11. Robert F. Engle & Sharon Kozicki, 1990. "Testing For Common Features," NBER Technical Working Papers 0091, National Bureau of Economic Research, Inc.
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  14. Darrell Duffie & Jun Pan & Kenneth Singleton, 1999. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," NBER Working Papers 7105, National Bureau of Economic Research, Inc.
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  17. Enrique Sentana, 1998. "The relation between conditionally heteroskedastic factor models and factor GARCH models," Econometrics Journal, Royal Economic Society, vol. 1(RegularPa), pages 1-9.
  18. Sargan, J D, 1983. "Identification and Lack of Identification," Econometrica, Econometric Society, vol. 51(6), pages 1605-33, November.
  19. Dovonon, Prosper, 2008. "Conditionally heteroskedastic factor models with skewness and leverage effects," MPRA Paper 40206, University Library of Munich, Germany, revised Feb 2012.
  20. Diebold, Francis X & Nerlove, Marc, 1989. "The Dynamics of Exchange Rate Volatility: A Multivariate Latent Factor Arch Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(1), pages 1-21, Jan.-Mar..
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  22. Engle, Robert F & Kozicki, Sharon, 1993. "Testing for Common Features: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(4), pages 393-95, October.
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  24. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Wiley Blackwell, vol. 61(2), pages 247-64, April.
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Cited by:
  1. Heather Anderson & Fashid Vahid, 2005. "Forecasting the Volatility of Australian Stock Returns: Do Common Factors Help?," ANU Working Papers in Economics and Econometrics 2005-451, Australian National University, College of Business and Economics, School of Economics.

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