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Merits and Drawbacks of Variance Targeting in GARCH Models

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  • Christian Francq
  • Lajos Horváth

Abstract

Variance targeting estimation (VTE) is a technique used to alleviate the numerical difficulties encountered in the quasi-maximum likelihood estimation (QMLE) of GARCH models. It relies on a reparameterization of the model and a first-step estimation of the unconditional variance. The remaining parameters are estimated by quasi maximum likelihood (QML) in a second step. This paper establishes the asymptotic distribution of the estimators obtained by this method in univariate GARCH models. Comparisons with the standard QML are provided and the merits of the variance targeting method are discussed. In particular, it is shown that when the model is misspecified, the VTE can be superior to the QMLE for long-term prediction or value-at-risk calculation. An empirical application based on stock market indices is proposed. Copyright The Author 2011. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com., Oxford University Press.

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Article provided by Society for Financial Econometrics in its journal Journal of Financial Econometrics.

Volume (Year): 9 (2011)
Issue (Month): 4 ()
Pages: 619-656

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Handle: RePEc:oup:jfinec:v:9:y:2011:i:4:p:619-656

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  1. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, Elsevier, vol. 31(3), pages 307-327, April.
  2. Francq, Christian & Zako an, Jean-Michel, 2006. "Mixing Properties Of A General Class Of Garch(1,1) Models Without Moment Assumptions On The Observed Process," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 22(05), pages 815-834, October.
  3. Lajos Horváth & Piotr Kokoszka & Ricardas Zitikis, 2006. "Sample and Implied Volatility in GARCH Models," Journal of Financial Econometrics, Society for Financial Econometrics, Society for Financial Econometrics, vol. 4(4), pages 617-635.
  4. BAUWENS, Luc & ROMBOUTS, Jeroen, 2003. "Bayesian clustering of many GARCH models," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2003087, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 18(01), pages 17-39, February.
  6. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 11(01), pages 122-150, February.
  7. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, Econometric Society, vol. 50(4), pages 987-1007, July.
  8. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, Econometric Society, vol. 50(1), pages 1-25, January.
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Cited by:
  1. Boudt, Kris & Daníelsson, Jón & Laurent, Sébastien, 2013. "Robust forecasting of dynamic conditional correlation GARCH models," International Journal of Forecasting, Elsevier, Elsevier, vol. 29(2), pages 244-257.
  2. Rasmus Søndergaard Pedersen, 2014. "Targeting estimation of CCC-Garch models with infinite fourth moments," Discussion Papers, University of Copenhagen. Department of Economics 14-04, University of Copenhagen. Department of Economics.
  3. Esben Hedegaard & Robert J. Hodrick, 2014. "Estimating the Risk-Return Trade-off with Overlapping Data Inference," NBER Working Papers 19969, National Bureau of Economic Research, Inc.
  4. Rasmus Søndergaard Pedersen & Anders Rahbek, 2012. "Multivariate Variance Targeting in the BEKK-GARCH Model," CREATES Research Papers, School of Economics and Management, University of Aarhus 2012-53, School of Economics and Management, University of Aarhus.
  5. Todd, Prono, 2009. "Simple, Skewness-Based GMM Estimation of the Semi-Strong GARCH(1,1) Model," MPRA Paper 30994, University Library of Munich, Germany, revised 30 Jul 2011.
  6. Hafner, Christian M. & Reznikova, Olga, 2012. "On the estimation of dynamic conditional correlation models," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 56(11), pages 3533-3545.
  7. Luis García-Álvarez & Richard Luger, 2011. "Dynamic Correlations, Estimation Risk, And Porfolio Management During The Financial Crisis," Working Papers, CEMFI wp2011_1103, CEMFI.
  8. Celso Brunetti & David Reiffen, 2011. "Commodity index trading and hedging costs," Finance and Economics Discussion Series, Board of Governors of the Federal Reserve System (U.S.) 2011-57, Board of Governors of the Federal Reserve System (U.S.).
  9. Todd, Prono, 2010. "Simple GMM Estimation of the Semi-Strong GARCH(1,1) Model," MPRA Paper 20034, University Library of Munich, Germany.
  10. Francq, Christian & Sucarrat, Genaro, 2013. "An Exponential Chi-Squared QMLE for Log-GARCH Models Via the ARMA Representation," MPRA Paper 51783, University Library of Munich, Germany.
  11. Francq, Christian & Horvath, Lajos & Zakoian, Jean-Michel, 2014. "Variance targeting estimation of multivariate GARCH models," MPRA Paper 57794, University Library of Munich, Germany.
  12. Stanislav Khrapov, 2011. "Pricing Central Tendency in Volatility," Working Papers, Center for Economic and Financial Research (CEFIR) w0168, Center for Economic and Financial Research (CEFIR).
  13. HAFNER, Christian & LINTON, Oliver, 2013. "An almost closed form estimator for the EGARCH model," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2013022, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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