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Factor Stochastic Volatility in Mean Models: A GMM Approach


  • Catherine Doz
  • Eric Renault


This paper provides a semiparametric framework for modeling multivariate conditional heteroskedasticity. We put forward latent stochastic volatility (SV) factors as capturing the commonality in the joint conditional variance matrix of asset returns. This approach is in line with common features as studied by Engle and Kozicki (1993), and it allows us to focus on identication of factors and factor loadings through first- and second-order conditional moments only. We assume that the time-varying part of risk premiums is based on constant prices of factor risks, and we consider a factor SV in mean model. Additional specification of both expectations and volatility of future volatility of factors provides conditional moment restrictions, through which the parameters of the model are all identied. These conditional moment restrictions pave the way for instrumental variables estimation and GMM inference.

Suggested Citation

  • Catherine Doz & Eric Renault, 2006. "Factor Stochastic Volatility in Mean Models: A GMM Approach," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 275-309.
  • Handle: RePEc:taf:emetrv:v:25:y:2006:i:2-3:p:275-309 DOI: 10.1080/07474930600713325

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    References listed on IDEAS

    1. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-1339, November.
    2. Rong Chen & Jun S. Liu, 2000. "Mixture Kalman filters," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(3), pages 493-508.
    3. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
    4. Michael K Pitt & Neil Shephard, 1996. "Analytic convergence rates and parameterisation issues for the Gibbs sampler applied to state space models," Economics Papers 20 & 113, Economics Group, Nuffield College, University of Oxford.
    5. Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2006. "Analysis of high dimensional multivariate stochastic volatility models," Journal of Econometrics, Elsevier, vol. 134(2), pages 341-371, October.
    6. Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2006. "Analysis of high dimensional multivariate stochastic volatility models," Journal of Econometrics, Elsevier, vol. 134(2), pages 341-371, October.
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    Cited by:

    1. Dovonon, Prosper & Renault, Eric, 2011. "Testing for Common GARCH Factors," MPRA Paper 40224, University Library of Munich, Germany.
    2. Sentana, Enrique & Calzolari, Giorgio & Fiorentini, Gabriele, 2008. "Indirect estimation of large conditionally heteroskedastic factor models, with an application to the Dow 30 stocks," Journal of Econometrics, Elsevier, vol. 146(1), pages 10-25, September.
    3. Peter Boswijk, H. & van der Weide, Roy, 2011. "Method of moments estimation of GO-GARCH models," Journal of Econometrics, Elsevier, vol. 163(1), pages 118-126, July.
    4. Bastian Gribisch, 2016. "Multivariate Wishart stochastic volatility and changes in regime," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(4), pages 443-473, October.
    5. repec:bla:irvfin:v:17:y:2017:i:3:p:479-490 is not listed on IDEAS
    6. Mike K. P. So & C. Y. Choi, 2009. "A threshold factor multivariate stochastic volatility model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 28(8), pages 712-735.
    7. repec:eee:econom:v:201:y:2017:i:1:p:43-71 is not listed on IDEAS
    8. M. Hashem Pesaran & Paolo Zaffaroni, 2009. "Optimality and Diversifiability of Mean Variance and Arbitrage Pricing Portfolios," CESifo Working Paper Series 2857, CESifo Group Munich.
    9. Kuruppuarachchi, Duminda & Premachandra, I.M., 2016. "Information spillover dynamics of the energy futures market sector: A novel common factor approach," Energy Economics, Elsevier, vol. 57(C), pages 277-294.
    10. Zhou, Xiaocong & Nakajima, Jouchi & West, Mike, 2014. "Bayesian forecasting and portfolio decisions using dynamic dependent sparse factor models," International Journal of Forecasting, Elsevier, vol. 30(4), pages 963-980.
    11. repec:rim:rimwps:40-07 is not listed on IDEAS


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