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Finite-Sample Theory and Bias Correction of Maximum Likelihood Estimators in the EGARCH Model

Author

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  • Demos Antonis

    (Department of International European Economic Studies, Athens University of Economics and Business (AUEB), Athens, Greece)

  • Kyriakopoulou Dimitra

    (Center for Operations Research and Econometrics (CORE), Université catholique de Louvain, Louvain-la-Neuve, Belgium)

Abstract

We derive the analytical expressions of bias approximations for maximum likelihood (ML) and quasi-maximum likelihood (QML) estimators of the EGARCH (1,1) parameters that enable us to correct after the bias of all estimators. The bias-correction mechanism is constructed under the specification of two methods that are analytically described. We also evaluate the residual bootstrapped estimator as a measure of performance. Monte Carlo simulations indicate that, for given sets of parameters values, the bias corrections work satisfactory for all parameters. The proposed full-step estimator performs better than the classical one and is also faster than the bootstrap. The results can be also used to formulate the approximate Edgeworth distribution of the estimators.

Suggested Citation

  • 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.
    • Handle: RePEc:bpj:jtsmet:v:11:y:2019:i:1:p:20:n:4
    DOI: 10.1515/jtse-2018-0010
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    More about this item

    Keywords

    exponential GARCH; maximum likelihood estimation; finite-sample properties; bias approximations; bias correction; Edgeworth expansion; bootstrap;
    All these keywords.

    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

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