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An almost closed form estimator for the EGARCH model

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  • HAFNER, Christian

    (Université catholique de Louvain, CORE & ISBA, Belgium)

  • LINTON, Oliver

    (Faculty of Economics, Cambridge University, UK)

Abstract

The EGARCH 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 is 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 optimation algorithm, etc. We present an alter- native 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 inde- pendent 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.

Suggested Citation

  • HAFNER, Christian & LINTON, Oliver, 2013. "An almost closed form estimator for the EGARCH model," LIDAM Discussion Papers CORE 2013022, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2013022
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    References listed on IDEAS

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    8. Hafner C. & Linton, O., 2013. "An Almost Closed Form Estimator for the EGARCH," LIDAM Discussion Papers ISBA 2013010, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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).
    8. 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).
    9. 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.
    10. 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).
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    More about this item

    Keywords

    autocorrelations; generalized error distribution; method of moments estimator; Newton-Raphson;
    All these keywords.

    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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