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Asymptotics of Cholesky GARCH Models and Time-Varying Conditional Betas

Author

Listed:
  • Serge Darolles

    (DRM-Finance - DRM - Dauphine Recherches en Management - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

  • Christian Francq

    (CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - CNRS - Centre National de la Recherche Scientifique, Université de Lille, Sciences Humaines et Sociales)

  • Sébastien Laurent

    (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique, Aix-Marseille Graduate School of Management)

Abstract

This paper proposes a new model with time-varying slope coefficients. Our model, called CHAR, is a Cholesky-GARCH model, based on the Cholesky decomposition of the conditional variance matrix introduced by Pourahmadi (1999) in the context of longitudinal data. We derive stationarity and invertibility conditions and prove consistency and asymptotic normality of the Full and equation-by-equation QML estimators of this model. We then show that this class of models is useful to estimate conditional betas and compare it to the approach proposed by Engle (2016). Finally, we use real data in a portfolio and risk management exercise. We find that the CHAR model outperforms a model with constant betas as well as the dynamic conditional beta model of Engle (2016).

Suggested Citation

  • Serge Darolles & Christian Francq & Sébastien Laurent, 2018. "Asymptotics of Cholesky GARCH Models and Time-Varying Conditional Betas," Working Papers halshs-01944656, HAL.
    • Handle: RePEc:hal:wpaper:halshs-01944656
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    Cited by:

    1. Boubacar Maïnassara, Y. & Kadmiri, O. & Saussereau, B., 2022. "Estimation of multivariate asymmetric power GARCH models," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    2. 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.
    3. Simon Hediger & Jeffrey Näf & Marc S. Paolella & Paweł Polak, 2023. "Heterogeneous tail generalized common factor modeling," Digital Finance, Springer, vol. 5(2), pages 389-420, June.
    4. Blasques, F. & Francq, Christian & Laurent, Sébastien, 2024. "Autoregressive conditional betas," Journal of Econometrics, Elsevier, vol. 238(2).
    5. Stefano Grassi & Francesco Violante, 2021. "Asset Pricing Using Block-Cholesky GARCH and Time-Varying Betas," Working Papers 2021-05, Center for Research in Economics and Statistics.
    6. Xiaoning Kang & Xinwei Deng & Kam‐Wah Tsui & Mohsen Pourahmadi, 2020. "On variable ordination of modified Cholesky decomposition for estimating time‐varying covariance matrices," International Statistical Review, International Statistical Institute, vol. 88(3), pages 616-641, December.
    7. David Ardia & S'ebastien Laurent & Rosnel Sessinou, 2024. "High-Dimensional Mean-Variance Spanning Tests," Papers 2403.17127, arXiv.org.
    8. Timo Dimitriadis & Yannick Hoga, 2022. "Dynamic CoVaR Modeling," Papers 2206.14275, arXiv.org, revised Feb 2024.
    9. Gribisch, Bastian & Hartkopf, Jan Patrick, 2023. "Modeling realized covariance measures with heterogeneous liquidity: A generalized matrix-variate Wishart state-space model," Journal of Econometrics, Elsevier, vol. 235(1), pages 43-64.
    10. Insana, Alessandra, 2022. "Does systematic risk change when markets close? An analysis using stocks’ beta," Economic Modelling, Elsevier, vol. 109(C).
    11. Hsiang‐Tai Lee, 2022. "A Markov regime‐switching Cholesky GARCH model for directly estimating the dynamic of optimal hedge ratio," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(3), pages 389-412, March.

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    More about this item

    Keywords

    multivariate-GARCH; conditional betas; covariance;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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