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Conditionally Heteroskedastic Factor Models: Identification and Instrumental Variables Estimation

  • Catherine Doz
  • Éric Renault

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

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Length: 55 pages
Date of creation: 01 Jun 2004
Date of revision:
Handle: RePEc:cir:cirwor:2004s-37
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  1. Engle, Robert F. & Ng, Victor K. & Rothschild, Michael, 1990. "Asset pricing with a factor-arch covariance structure : Empirical estimates for treasury bills," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 213-237.
  2. Hansen, Lars Peter & Singleton, Kenneth J, 1996. "Efficient Estimation of Linear Asset-Pricing Models with Moving Average Errors," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 53-68, January.
  3. Ng, Victor & Engle, Robert F. & Rothschild, Michael, 1992. "A multi-dynamic-factor model for stock returns," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 245-266.
  4. Manuel Arellano & Lars Peter Hansen & Enrique Sentana, 2009. "Underidentification?," Working Papers wp2009_0905, CEMFI.
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  6. Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  7. Sargan, J D, 1983. "Identification and Lack of Identification," Econometrica, Econometric Society, vol. 51(6), pages 1605-33, November.
  8. 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..
  9. Neil Shephard & Gabriele Fiorentini & Enrique Sentana, 2003. "Likelihood-based estimation of latent generalised ARCH structures," FMG Discussion Papers dp453, Financial Markets Group.
  10. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Wiley Blackwell, vol. 61(2), pages 247-64, April.
  11. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
  12. Nour Meddahi, 2000. "Temporal Aggregation of Volatility Models," Econometric Society World Congress 2000 Contributed Papers 1903, Econometric Society.
  13. Prosper Dovonon, 2013. "Conditionally Heteroskedastic Factor Models With Skewness And Leverage Effects," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(7), pages 1110-1137, November.
  14. Sentana, Enrique & Fiorentini, Gabriele, 2001. "Identification, estimation and testing of conditionally heteroskedastic factor models," Journal of Econometrics, Elsevier, vol. 102(2), pages 143-164, June.
  15. Robert F. Engle & Sharon Kozicki, 1990. "Testing For Common Features," NBER Technical Working Papers 0091, National Bureau of Economic Research, Inc.
  16. Drost, F.C. & Nijman, T.E., 1990. "Temporal aggregation of GARCH processes," Discussion Paper 1990-66, Tilburg University, Center for Economic Research.
  17. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
  18. 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.
  19. Mervyn King & Enrique Sentana & Sushil Wadhwani, 1990. "Volatiltiy and Links Between National Stock Markets," NBER Working Papers 3357, National Bureau of Economic Research, Inc.
  20. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-31, February.
  21. Sentana, E., 2000. "Factor Representing Portfolios in Large Asset Markets," Papers 0001, Centro de Estudios Monetarios Y Financieros-.
  22. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
  23. 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.
  24. 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.
  25. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
  26. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  27. Drost, F.C. & Nijman, T.E., 1993. "Temporal aggregation of GARCH processes," Other publications TiSEM 0642fb61-c7f4-4281-b484-4, Tilburg University, School of Economics and Management.
  28. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
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