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An Almost Closed Form Estimator For The EGARCH Model

Author

Listed:
  • Hafner, Christian
  • Linton, Oliver

Abstract

The exponential GARCH (EGARCH) model introduced by Nelson (1991) is a popular model for discrete time volatility since it allows for asymmetric effects and naturally ensures positivity even when including exogenous variables. Estimation and inference are usually done via maximum likelihood. Although some progress has been made recently, a complete distribution theory of MLE for EGARCH models is still missing. Furthermore, the estimation procedure itself may be highly sensitive to starting values, the choice of numerical optimization algorithm, etc. We present an alternative estimator that is available in a simple closed form and which could be used, for example, as starting values for MLE. The estimator of the dynamic parameter is independent of the innovation distribution. For the other parameters we assume that the innovation distribution belongs to the class of Generalized Error Distributions (GED), profiling out its parameter in the estimation procedure. We discuss the properties of the proposed estimator and illustrate its performance in a simulation study and an empirical example.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Hafner, Christian & Linton, Oliver, 2017. "An Almost Closed Form Estimator For The EGARCH Model," LIDAM Reprints ISBA 2017040, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvar:2017040
    Note: In : Econometric Theory, vol. 33, no. 4, p. 1013-1038 (2017)
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    Cited by:

    1. Demos Antonis & Kyriakopoulou Dimitra, 2019. "Finite-Sample Theory and Bias Correction of Maximum Likelihood Estimators in the EGARCH Model," Journal of Time Series Econometrics, De Gruyter, vol. 11(1), pages 1-20, January.
    2. Prono Todd, 2018. "Closed-form estimators for finite-order ARCH models as simple and competitive alternatives to QMLE," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 22(5), pages 1-25, December.
    3. GOERTZ, Johanna & MANIQUET, François, 2013. "Large elections with multiple alternatives: a Condorcet Jury Theorem and inefficient equilibria," LIDAM Discussion Papers CORE 2013023, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. NESTEROV, Yurii, 2013. "Universal gradient methods for convex optimization problems," LIDAM Discussion Papers CORE 2013026, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. CORNUEJOLS, Gérard & WOLSEY, Laurence & YILDIZ, Sercan, 2013. "Sufficiency of cut-generating functions," LIDAM Discussion Papers CORE 2013027, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Ahsan, Md. Nazmul & Dufour, Jean-Marie, 2021. "Simple estimators and inference for higher-order stochastic volatility models," Journal of Econometrics, Elsevier, vol. 224(1), pages 181-197.
    7. Chiara Canta & Marie-Louise Leroux, 2016. "Public and Private Hospitals, Congestion, and Redistribution," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 18(1), pages 42-66, February.
    8. Carnero M. Angeles & Pérez Ana, 2021. "Outliers and misleading leverage effect in asymmetric GARCH-type models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 25(1), pages 1-19, February.
    9. Bocart, Fabian Y.R.P. & Hafner, Christian M., 2015. "Fair Revaluation of Wine as an Investment," Journal of Wine Economics, Cambridge University Press, vol. 10(2), pages 190-203, November.
    10. Yongdeng Xu, 2025. "Extended Multivariate EGARCH Model: A Model for Zero‐Return and Negative Spillovers," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 44(4), pages 1266-1279, July.
    11. MLINAR, Tanja B. & CHEVALIER, Philippe, 2013. "Pooling in manufacturing: do opposites attract?," LIDAM Discussion Papers CORE 2013040, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    12. 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.
    13. Christian M. Hafner & Dimitra Kyriakopoulou, 2021. "Exponential-Type GARCH Models With Linear-in-Variance Risk Premium," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(2), pages 589-603, March.

    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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