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Equation-by-Equation Estimation of a Multivariate Log-GARCH-X Model of Financial Returns

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  • Francq, Christian
  • Sucarrat, Genaro

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.

Suggested Citation

  • Francq, Christian & Sucarrat, Genaro, 2015. "Equation-by-Equation Estimation of a Multivariate Log-GARCH-X Model of Financial Returns," MPRA Paper 67140, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:67140
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    Citations

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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. Christian Francq & Genaro Sucarrat, 2018. "An Exponential Chi-Squared QMLE for Log-GARCH Models Via the ARMA Representation," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 16(1), pages 129-154.
    3. Karanasos, Menelaos & Xu, Yongdeng, 2017. "Matrix Inequality Constraints for Vector (Asymmetric Power) GARCH/HEAVY Models and MEM with spillovers: some New (Mixture) Formulations," Cardiff Economics Working Papers E2017/14, Cardiff University, Cardiff Business School, Economics Section.
    4. Sucarrat, Genaro & Grønneberg, Steffen, 2016. "Models of Financial Return With Time-Varying Zero Probability," MPRA Paper 68931, University Library of Munich, Germany.
    5. 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.
    6. Escribano, Alvaro & Sucarrat, Genaro, 2018. "Equation-by-equation estimation of multivariate periodic electricity price volatility," Energy Economics, Elsevier, vol. 74(C), pages 287-298.
    7. Thieu, Le Quyen, 2016. "Equation by equation estimation of the semi-diagonal BEKK model with covariates," MPRA Paper 75582, University Library of Munich, Germany.

    More about this item

    Keywords

    Exponential GARCH; multivariate log-GARCH-X; VARMA-X; Equation-by-Equation Estimation (EBEE); Least Squares;

    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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