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An equation-by-equation estimator of a multivariate log-GARCH-X model of financial returns

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)

  • Genaro Sucarrat

    (BI Norwegian Business School [Oslo])

Abstract

Estimation of large financial volatility models is plagued by the curse of dimensionality: As the dimension grows, joint estimation of the parameters becomes infeasible in practice. This problem is compounded if covariates or conditioning variables (``X") are added to each volatility equation. In particular, the problem is especially acute for non-exponential volatility models (e.g. GARCH models), since there the variables and parameters are restricted to be positive. Here, we propose an estimator for a multivariate log-GARCH-X model that avoids these problems. The model allows for feedback among the equations, admits several stationary regressors as conditioning variables in the X-part (including leverage terms), and allows for time-varying covariances of unknown form. Strong consistency and asymptotic normality of an equation-by-equation least squares estimator is proved, and the results can be used to undertake inference both within and across equations. The flexibility and usefulness of the estimator is illustrated in two empirical applications.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Christian Francq & Genaro Sucarrat, 2017. "An equation-by-equation estimator of a multivariate log-GARCH-X model of financial returns," Post-Print hal-05417319, HAL.
    • Handle: RePEc:hal:journl:hal-05417319
    DOI: 10.1016/j.jmva.2016.09.010
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    Cited by:

    1. is not listed on IDEAS
    2. Thieu, Le Quyen, 2016. "Variance targeting estimation of the BEKK-X model," MPRA Paper 75572, University Library of Munich, Germany.
    3. Karanasos, Menelaos & Xu, Yongdeng & Yfanti, Stavroula, 2017. "Constrained QML Estimation for Multivariate Asymmetric MEM with Spillovers: The Practicality of Matrix Inequalities," Cardiff Economics Working Papers E2017/14, Cardiff University, Cardiff Business School, Economics Section.
    4. Raffaele Mattera & Philipp Otto, 2023. "Network log-ARCH models for forecasting stock market volatility," Papers 2303.11064, arXiv.org.
    5. Nguyen, Giang & Engle, Robert & Fleming, Michael & Ghysels, Eric, 2020. "Liquidity and volatility in the U.S. Treasury market," Journal of Econometrics, Elsevier, vol. 217(2), pages 207-229.
    6. Sucarrat, Genaro & Grønneberg, Steffen, 2016. "Models of Financial Return With Time-Varying Zero Probability," MPRA Paper 68931, University Library of Munich, Germany.
    7. 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.
    8. Boubacar Maïnassara, Y. & Kadmiri, O. & Saussereau, B., 2022. "Estimation of multivariate asymmetric power GARCH models," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    9. Xu, Yongdeng, 2024. "Extended multivariate EGARCH model: A model for zero†return and negative spillovers," Cardiff Economics Working Papers E2024/24, Cardiff University, Cardiff Business School, Economics Section.
    10. Mattera, Raffaele & Otto, Philipp, 2024. "Network log-ARCH models for forecasting stock market volatility," International Journal of Forecasting, Elsevier, vol. 40(4), pages 1539-1555.
    11. Escribano, Alvaro & Sucarrat, Genaro, 2018. "Equation-by-equation estimation of multivariate periodic electricity price volatility," Energy Economics, Elsevier, vol. 74(C), pages 287-298.
    12. Thieu, Le Quyen, 2016. "Equation by equation estimation of the semi-diagonal BEKK model with covariates," MPRA Paper 75582, University Library of Munich, Germany.
    13. Sucarrat, Genaro, 2018. "The Log-GARCH Model via ARMA Representations," MPRA Paper 100386, University Library of Munich, Germany.
    14. Christian Francq & Genaro Sucarrat, 2018. "An Exponential Chi-Squared QMLE for Log-GARCH Models Via the ARMA Representation," Journal of Financial Econometrics, Oxford University Press, vol. 16(1), pages 129-154.
    15. Bonnier, Jean-Baptiste, 2022. "Forecasting crude oil volatility with exogenous predictors: As good as it GETS?," Energy Economics, Elsevier, vol. 111(C).

    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
    • 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
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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