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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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Bibliographic Info

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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References

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  1. BAUWENS, Luc & ROMBOUTS, Jeroen VK, . "Bayesian clustering of many GARCH models," CORE Discussion Papers RP -1916, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
  3. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  4. 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, vol. 22(05), pages 815-834, October.
  5. 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.
  6. Lajos Horváth & Piotr Kokoszka & Ricardas Zitikis, 2006. "Sample and Implied Volatility in GARCH Models," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(4), pages 617-635.
  7. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
  8. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(01), pages 17-39, February.
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Citations

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Cited by:
  1. Rasmus Søndergaard Pedersen, 2014. "Targeting estimation of CCC-Garch models with infinite fourth moments," Discussion Papers 14-04, University of Copenhagen. Department of Economics.
  2. Boudt, Kris & Daníelsson, Jón & Laurent, Sébastien, 2013. "Robust forecasting of dynamic conditional correlation GARCH models," International Journal of Forecasting, Elsevier, vol. 29(2), pages 244-257.
  3. Rasmus Søndergaard Pedersen & Anders Rahbek, 2012. "Multivariate Variance Targeting in the BEKK-GARCH Model," CREATES Research Papers 2012-53, School of Economics and Management, University of Aarhus.
  4. 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.
  5. Todd, Prono, 2010. "Simple GMM Estimation of the Semi-Strong GARCH(1,1) Model," MPRA Paper 20034, University Library of Munich, Germany.
  6. Stanislav Khrapov, 2011. "Pricing Central Tendency in Volatility," Working Papers w0168, Center for Economic and Financial Research (CEFIR).
  7. 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.
  8. HAFNER, Christian & LINTON, Oliver, 2013. "An almost closed form estimator for the EGARCH model," CORE Discussion Papers 2013022, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  9. Luis García-Álvarez & Richard Luger, 2011. "Dynamic Correlations, Estimation Risk, And Porfolio Management During The Financial Crisis," Working Papers wp2011_1103, CEMFI.
  10. Hafner, Christian M. & Reznikova, Olga, 2012. "On the estimation of dynamic conditional correlation models," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3533-3545.
  11. Celso Brunetti & David Reiffen, 2011. "Commodity index trading and hedging costs," Finance and Economics Discussion Series 2011-57, Board of Governors of the Federal Reserve System (U.S.).
  12. 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.

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