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Merits and Drawbacks of Variance Targeting in GARCH Models

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  • Christian FRANCQ

    (Crest)

  • Lajos HORVATH

    (Crest)

  • Jean-Michel ZAKOIAN

    (Crest)

Abstract

Variance targeting estimation (VTE) is a technique used to alleviate the numerical difficultiesencountered in the quasi-maximum likelihood (QML) estimation of GARCH models. It relieson 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 establishesthe asymptotic distribution of the estimators obtained by this method. Comparisons with thestandard QML are provided. In particular, when the model is misspecified the VTE can besuperior to the QMLE for long-term prediction or Value-at-Risk calculation. An empiricalapplication based on stock market indices is proposed.

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Bibliographic Info

Paper provided by Centre de Recherche en Economie et Statistique in its series Working Papers with number 2009-17.

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Length: 33
Date of creation: 2009
Date of revision:
Handle: RePEc:crs:wpaper:2009-17

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  1. 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.
  2. 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.
  3. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
  4. 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).
  5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  6. 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.
  7. 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.
  8. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
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Citations

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Cited by:
  1. Stanislav Khrapov, 2011. "Pricing Central Tendency in Volatility," Working Papers w0168, Center for Economic and Financial Research (CEFIR).
  2. Rasmus S. Pedersen & Anders Rahbek, 2014. "Multivariate variance targeting in the BEKK–GARCH model," Econometrics Journal, Royal Economic Society, vol. 17(1), pages 24-55, 02.
  3. 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.
  4. 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.
  5. 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.).
  6. 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.
  7. 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.
  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. Todd, Prono, 2010. "Simple GMM Estimation of the Semi-Strong GARCH(1,1) Model," MPRA Paper 20034, University Library of Munich, Germany.
  10. Rasmus Søndergaard Pedersen, 2014. "Targeting estimation of CCC-Garch models with infinite fourth moments," Discussion Papers 14-04, University of Copenhagen. Department of Economics.
  11. 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.
  12. Luis García-Álvarez & Richard Luger, 2011. "Dynamic Correlations, Estimation Risk, And Porfolio Management During The Financial Crisis," Working Papers wp2011_1103, CEMFI.

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