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Asymptotic Theory For A Factor Garch Model

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  • Hafner, Christian M.
  • Preminger, Arie

Abstract

This paper investigates the asymptotic theory for a factor GARCH (generalized autoregressive conditional heteroskedasticity) model. Sufficient conditions for asymptotic stability and existence of moments are established. These conditions allow for volatility spillover 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.

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  • Hafner, Christian M. & Preminger, Arie, 2009. "Asymptotic Theory For A Factor Garch Model," Econometric Theory, Cambridge University Press, vol. 25(2), pages 336-363, April.
    • Handle: RePEc:cup:etheor:v:25:y:2009:i:02:p:336-363_09
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    2. 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.
    3. Woźniak, Tomasz, 2015. "Testing causality between two vectors in multivariate GARCH models," International Journal of Forecasting, Elsevier, vol. 31(3), pages 876-894.
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    5. 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.
    6. 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.
    7. 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.
    8. Barigozzi, Matteo & Hallin, Marc, 2017. "Generalized dynamic factor models and volatilities: estimation and forecasting," Journal of Econometrics, Elsevier, vol. 201(2), pages 307-321.
    9. 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.
    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. 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.
    12. 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.
    13. Li, Degui, 2024. "Estimation of Large Dynamic Covariance Matrices: A Selective Review," Econometrics and Statistics, Elsevier, vol. 29(C), pages 16-30.
    14. 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.
    15. D’Innocenzo, Enzo & Lucas, Andre, 2024. "Dynamic partial correlation models," Journal of Econometrics, Elsevier, vol. 241(2).
    16. 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.
    17. Hetland, Simon & Pedersen, Rasmus Søndergaard & Rahbek, Anders, 2023. "Dynamic conditional eigenvalue GARCH," Journal of Econometrics, Elsevier, vol. 237(2).
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    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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    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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