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Variance Targeting Estimation of Multivariate GARCH Models

Author

Listed:
  • Christian Francq

    (CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - Groupe ENSAE-ENSAI - Groupe des Écoles Nationales d'Économie et Statistique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - Groupe ENSAE-ENSAI - Groupe des Écoles Nationales d'Économie et Statistique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique, IP Paris - Institut Polytechnique de Paris)

  • Lajos Horváth

    (Mathematics department - University of Utah)

  • Jean-Michel Zakoïan

    (CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - Groupe ENSAE-ENSAI - Groupe des Écoles Nationales d'Économie et Statistique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - Groupe ENSAE-ENSAI - Groupe des Écoles Nationales d'Économie et Statistique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

Abstract

We establish the strong consistency and the asymptotic normality of the variance-targeting estimator (VTE) of the parameters of the multivariate CCC-GARCH($p,q$) processes. This method alleviates the numerical difficulties encountered in the maximization of the quasi likelihood by using an estimator of the unconditional variance. It is shown that the distribution of the VTE can be consistently estimated by a simple residual bootstrap technique. We also use the VTE for testing the model adequacy. A test statistic in the spirit of the score test is constructed, and its asymptotic properties are derived under the null assumption that the model is well specified. An extension of the VT method to asymmetric CCC-GARCH models incorporating leverage effects is studied. Numerical illustrations are provided and an empirical application based on daily exchange rates is proposed.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Christian Francq & Lajos Horváth & Jean-Michel Zakoïan, 2016. "Variance Targeting Estimation of Multivariate GARCH Models," Post-Print hal-05417486, HAL.
    • Handle: RePEc:hal:journl:hal-05417486
    DOI: 10.1093/jjfinec/nbu030
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    Cited by:

    1. Thieu, Le Quyen, 2016. "Variance targeting estimation of the BEKK-X model," MPRA Paper 75572, University Library of Munich, Germany.
    2. Francq, Christian & Zakoïan, Jean-Michel, 2025. "Inference on dynamic systemic risk measures," Journal of Econometrics, Elsevier, vol. 247(C).
    3. Beutner, Eric & Heinemann, Alexander & Smeekes, Stephan, 2024. "A residual bootstrap for conditional Value-at-Risk," Journal of Econometrics, Elsevier, vol. 238(2).
    4. Giuseppe Cavaliere & Rasmus Søndergaard Pedersen & Anders Rahbek, 2018. "The Fixed Volatility Bootstrap for a Class of Arch(q) Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(6), pages 920-941, November.
    5. Francq, Christian & Zakoïan, Jean-Michel, 2020. "Virtual Historical Simulation for estimating the conditional VaR of large portfolios," Journal of Econometrics, Elsevier, vol. 217(2), pages 356-380.
    6. Marco Barassi & Lajos Horváth & Yuqian Zhao, 2020. "Change‐Point Detection in the Conditional Correlation Structure of Multivariate Volatility Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(2), pages 340-349, April.
    7. Thomas Giroux & Julien Royer & Olivier David Zerbib, 2024. "Empirical Asset Pricing with Score-Driven Conditional Betas," Post-Print hal-05415058, HAL.
    8. Yannick Hoga, 2023. "The Estimation Risk in Extreme Systemic Risk Forecasts," Papers 2304.10349, arXiv.org.
    9. Qi Li & Fukang Zhu, 2020. "Mean targeting estimator for the integer-valued GARCH(1, 1) model," Statistical Papers, Springer, vol. 61(2), pages 659-679, April.
    10. 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.
    11. 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.
    12. BAUWENS, Luc & BRAIONE, Manuela & STORTI, Giuseppe, 2016. "Multiplicative Conditional Correlation Models for Realized Covariance Matrices," LIDAM Discussion Papers CORE 2016041, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    13. Stanislav Anatolyev & Stanislav Khrapov, 2015. "Right on Target, or Is it? The Role of Distributional Shape in Variance Targeting," Econometrics, MDPI, vol. 3(3), pages 1-23, August.
    14. Billio, Monica & Caporin, Massimiliano & Frattarolo, Lorenzo & Pelizzon, Loriana, 2023. "Networks in risk spillovers: A multivariate GARCH perspective," Econometrics and Statistics, Elsevier, vol. 28(C), pages 1-29.
    15. Lai T. Hoang & Dirk G. Baur, 2021. "Spillovers and Asset Allocation," JRFM, MDPI, vol. 14(8), pages 1-31, July.
    16. Lyubimov, Ivan L. (Любимов, Иван) & Kazakova, Maria V. (Казакова, Мария), 2017. "The Demand for Production Inputs as the Reflection of the Level of Property Rights Protection [Структура Спроса На Факторы Производства Как Отражение Защищенности Прав Собственности]," Ekonomicheskaya Politika / Economic Policy, Russian Presidential Academy of National Economy and Public Administration, vol. 4, pages 30-59, August.
    17. Simos G. Meintanis & Joseph Ngatchou-Wandji & Šárka Hudecová, 2025. "Omnibus diagnostic procedures for vector multiplicative errors models," Statistical Papers, Springer, vol. 66(2), pages 1-44, February.
    18. Francq, C. & Jiménez-Gamero, M.D. & Meintanis, S.G., 2017. "Tests for conditional ellipticity in multivariate GARCH models," Journal of Econometrics, Elsevier, vol. 196(2), pages 305-319.
    19. Timo Dimitriadis & Yannick Hoga, 2022. "Dynamic CoVaR Modeling and Estimation," Papers 2206.14275, arXiv.org, revised Jan 2025.
    20. Hetland, Simon & Pedersen, Rasmus Søndergaard & Rahbek, Anders, 2023. "Dynamic conditional eigenvalue GARCH," Journal of Econometrics, Elsevier, vol. 237(2).
    21. Loïc Cantin & Christian Francq & Jean-Michel Zakoïan, 2022. "Estimating dynamic systemic risk measures," Working Papers 2022-11, Center for Research in Economics and Statistics.

    More about this item

    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

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