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Asymptotic theory for a factor GARCH model

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  • HAFNER, Christian
  • PREMINGER, Arie

Abstract

This paper investigates the asymptotic theory for a factor GARCH model. Sufficient conditions for strict stationarity, existence of certain moments, geometric ergodicity and - mixing with exponential decay rates are established. These conditions allow for volatility spill-over and integrated GARCH. We then show the strong consistency and asymptotic normality of the quasi-maximum likelihood estimator (QMLE) of the model parameters. The results are obtained under the finiteness of the fourth order moment of the innovations.

Suggested Citation

  • HAFNER, Christian & PREMINGER, Arie, 2006. "Asymptotic theory for a factor GARCH model," LIDAM Discussion Papers CORE 2006071, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2006071
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    Cited by:

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    2. Hecq Alain & Laurent Sébastien & Palm Franz C., 2016. "On the Univariate Representation of BEKK Models with Common Factors," Journal of Time Series Econometrics, De Gruyter, vol. 8(2), pages 91-113, July.
    3. Sucarrat, Genaro & Grønneberg, Steffen & Escribano, Alvaro, 2016. "Estimation and inference in univariate and multivariate log-GARCH-X models when the conditional density is unknown," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 582-594.
    4. Pedersen, Rasmus Søndergaard, 2017. "Inference and testing on the boundary in extended constant conditional correlation GARCH models," Journal of Econometrics, Elsevier, vol. 196(1), pages 23-36.
    5. Jean-Claude Hessing & Rutger-Jan Lange & Daniel Ralph, 2022. "This article establishes the Poisson optional stopping times (POST) method by Lange et al. (2020) as a near-universal method for solving liquidity-constrained American options, or, equivalently, penal," Tinbergen Institute Discussion Papers 22-007/IV, Tinbergen Institute.
    6. 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.
    7. Resende, Paulo Angelo Alves & Dorea, Chang Chung Yu, 2016. "Model identification using the Efficient Determination Criterion," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 229-244.
    8. Ricardo P. Masini & Marcelo C. Medeiros & Eduardo F. Mendes, 2022. "Regularized estimation of high‐dimensional vector autoregressions with weakly dependent innovations," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(4), pages 532-557, July.
    9. Avarucci, Marco & Beutner, Eric & Zaffaroni, Paolo, 2013. "On Moment Conditions For Quasi-Maximum Likelihood Estimation Of Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 29(3), pages 545-566, June.
    10. Li, Degui, 2024. "Estimation of Large Dynamic Covariance Matrices: A Selective Review," Econometrics and Statistics, Elsevier, vol. 29(C), pages 16-30.
    11. Francq, Christian & Zakoian, Jean-Michel, 2010. "QML estimation of a class of multivariate GARCH models without moment conditions on the observed process," MPRA Paper 20779, University Library of Munich, Germany.
    12. D’Innocenzo, Enzo & Lucas, Andre, 2024. "Dynamic partial correlation models," Journal of Econometrics, Elsevier, vol. 241(2).
    13. Benjamin Poignard & Manabu Asai, 2023. "High‐dimensional sparse multivariate stochastic volatility models," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(1), pages 4-22, January.
    14. Barigozzi, Matteo & Hallin, Marc, 2017. "Generalized dynamic factor models and volatilities: estimation and forecasting," Journal of Econometrics, Elsevier, vol. 201(2), pages 307-321.
    15. Yip, Iris W.H. & So, Mike K.P., 2009. "Simplified specifications of a multivariate generalized autoregressive conditional heteroscedasticity model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(2), pages 327-340.
    16. Hafner, Christian M. & Preminger, Arie, 2009. "On asymptotic theory for multivariate GARCH models," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2044-2054, October.
    17. Bojan Basrak & Danijel Krizmanić, 2015. "A Multivariate Functional Limit Theorem in Weak $$M_{1}$$ M 1 Topology," Journal of Theoretical Probability, Springer, vol. 28(1), pages 119-136, March.
    18. Hetland, Simon & Pedersen, Rasmus Søndergaard & Rahbek, Anders, 2023. "Dynamic conditional eigenvalue GARCH," Journal of Econometrics, Elsevier, vol. 237(2).
    19. Yuanyuan Zhang & Rong Liu & Qin Shao & Lijian Yang, 2020. "Two‐Step Estimation for Time Varying Arch Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(4), pages 551-570, July.

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    More about this item

    Keywords

    multivariate GARCH; factor model; geometric ergodicity; maximum likelihood; consistency; asymptotic normality;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: 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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