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Merits and Drawbacks of Variance Targeting in GARCH Models

  • Christian FRANCQ

    (Crest)

  • Lajos HORVATH

    (Crest)

  • Jean-Michel ZAKOIAN

    (Crest)

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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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. 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. 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, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
  4. 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.
  5. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
  6. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  7. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
  8. 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.
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