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Merits and drawbacks of variance targeting in GARCH models

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  • Francq, Christian
  • Horvath, Lajos
  • Zakoian, Jean-Michel

Abstract

Variance targeting estimation is a technique used to alleviate the numerical difficulties encountered in the quasi-maximum likelihood (QML) estimation 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 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.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 15143.

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Date of creation: 2009
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Handle: RePEc:pra:mprapa:15143

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Keywords: Consistency and Asymptotic Normality; GARCH; Heteroskedastic Time Series; Quasi Maximum Likelihood Estimation; Value-at-Risk; Variance Targeting Estimator.;

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References

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  1. 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.
  2. 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.
  3. 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.
  4. BAUWENS, Luc & ROMBOUTS, Jeroen, 2003. "Bayesian clustering of many GARCH models," CORE Discussion Papers 2003087, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  6. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
  7. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
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Citations

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Cited by:
  1. 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.
  2. Rasmus Søndergaard Pedersen, 2014. "Targeting estimation of CCC-Garch models with infinite fourth moments," Discussion Papers 14-04, University of Copenhagen. Department of Economics.
  3. 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).
  4. Todd, Prono, 2010. "Simple GMM Estimation of the Semi-Strong GARCH(1,1) Model," MPRA Paper 20034, University Library of Munich, Germany.
  5. Rasmus Søndergaard Pedersen & Anders Rahbek, 2012. "Multivariate Variance Targeting in the BEKK-GARCH Model," Discussion Papers 12-23, University of Copenhagen. Department of Economics.
  6. Luis García-Álvarez & Richard Luger, 2011. "Dynamic Correlations, Estimation Risk, And Porfolio Management During The Financial Crisis," Working Papers wp2011_1103, CEMFI.
  7. Stanislav Khrapov, 2011. "Pricing Central Tendency in Volatility," Working Papers w0168, Center for Economic and Financial Research (CEFIR).
  8. 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.).
  9. 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.
  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. 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.

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