IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/15143.html
   My bibliography  Save this paper

Merits and drawbacks of variance targeting in GARCH models

Author

Listed:
  • 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.

Suggested Citation

  • Francq, Christian & Horvath, Lajos & Zakoian, Jean-Michel, 2009. "Merits and drawbacks of variance targeting in GARCH models," MPRA Paper 15143, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:15143
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/15143/1/MPRA_paper_15143.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(1), pages 122-150, February.
    2. Ling, Shiqing, 2007. "Self-weighted and local quasi-maximum likelihood estimators for ARMA-GARCH/IGARCH models," Journal of Econometrics, Elsevier, vol. 140(2), pages 849-873, October.
    3. Kristensen, Dennis & Linton, Oliver, 2004. "03.5.2. Consistent Standard Errors for Target Variance Approach to GARCH Estimation—Solution," Econometric Theory, Cambridge University Press, vol. 20(5), pages 990-993, October.
    4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    5. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    6. Lajos Horváth & Piotr Kokoszka & Ricardas Zitikis, 2006. "Sample and Implied Volatility in GARCH Models," Journal of Financial Econometrics, Oxford University Press, vol. 4(4), pages 617-635.
    7. Christoffersen, Peter, 2011. "Elements of Financial Risk Management," Elsevier Monographs, Elsevier, edition 2, number 9780123744487.
    8. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(1), pages 17-39, February.
    9. 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.
    10. L. Bauwens & J. V. K. Rombouts, 2007. "Bayesian Clustering of Many Garch Models," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 365-386.
    11. Francq, Christian & Zakoïan, 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(5), pages 815-834, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Francq, Christian & Zakoïan, Jean-Michel, 2009. "Testing the Nullity of GARCH Coefficients: Correction of the Standard Tests and Relative Efficiency Comparisons," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 313-324.
    2. Dominique Guegan & Bertrand K. Hassani, 2019. "Risk Measurement," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02119256, HAL.
    3. Jiang, Feiyu & Li, Dong & Zhu, Ke, 2021. "Adaptive inference for a semiparametric generalized autoregressive conditional heteroskedasticity model," Journal of Econometrics, Elsevier, vol. 224(2), pages 306-329.
    4. Luc Bauwens & Sébastien Laurent & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109, January.
    5. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, Department of Economics and Business Economics, Aarhus University.
    6. Meitz, Mika & Saikkonen, Pentti, 2008. "Ergodicity, Mixing, And Existence Of Moments Of A Class Of Markov Models With Applications To Garch And Acd Models," Econometric Theory, Cambridge University Press, vol. 24(5), pages 1291-1320, October.
    7. Wu, Guojun & Xiao, Zhijie, 2002. "A generalized partially linear model of asymmetric volatility," Journal of Empirical Finance, Elsevier, vol. 9(3), pages 287-319, August.
    8. Meitz, Mika & Saikkonen, Pentti, 2011. "Parameter Estimation In Nonlinear Ar–Garch Models," Econometric Theory, Cambridge University Press, vol. 27(6), pages 1236-1278, December.
    9. de Almeida, Daniel & Hotta, Luiz K. & Ruiz, Esther, 2018. "MGARCH models: Trade-off between feasibility and flexibility," International Journal of Forecasting, Elsevier, vol. 34(1), pages 45-63.
    10. So, Mike K.P. & Chan, Thomas W.C. & Chu, Amanda M.Y., 2022. "Efficient estimation of high-dimensional dynamic covariance by risk factor mapping: Applications for financial risk management," Journal of Econometrics, Elsevier, vol. 227(1), pages 151-167.
    11. Saidi, Youssef & Zakoian, Jean-Michel, 2006. "Stationarity and geometric ergodicity of a class of nonlinear ARCH models," MPRA Paper 61988, University Library of Munich, Germany, revised 2006.
    12. F Blasques & P Gorgi & S Koopman & O Wintenberger, 2016. "Feasible Invertibility Conditions for Maximum Likelihood Estimation for Observation-Driven Models," Papers 1610.02863, arXiv.org.
    13. Phoebe Koundouri & Nikolaos Kourogenis & Nikitas Pittis, 2012. "Statistical Modeling of Stock Returns: A Historical Survey with Methodological Reflections," DEOS Working Papers 1226, Athens University of Economics and Business.
    14. Fernandes, Marcelo & de Sa Mota, Bernardo & Rocha, Guilherme, 2005. "A multivariate conditional autoregressive range model," Economics Letters, Elsevier, vol. 86(3), pages 435-440, March.
    15. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2005. "Volatility forecasting," CFS Working Paper Series 2005/08, Center for Financial Studies (CFS).
    16. Koundouri, Phoebe & Kourogenis, Nikolaos & Pittis, Nikitas, 2012. "Statistical Modeling of Stock Returns: A Historical Survey with Some Methodological Reflections," MPRA Paper 122422, University Library of Munich, Germany.
    17. Patton, Andrew, 2013. "Copula Methods for Forecasting Multivariate Time Series," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 899-960, Elsevier.
    18. Gospodinov, Nikolay, 2008. "Asymptotic and bootstrap tests for linearity in a TAR-GARCH(1,1) model with a unit root," Journal of Econometrics, Elsevier, vol. 146(1), pages 146-161, September.
    19. Rob van den Goorbergh, 2004. "A Copula-Based Autoregressive Conditional Dependence Model of International Stock Markets," DNB Working Papers 022, Netherlands Central Bank, Research Department.
    20. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.

    More about this item

    Keywords

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

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:15143. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.