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Finite-sample theory and bias correction of maximum likelihood estimators in the EGARCH model

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  • Antonis Demos
  • Dimitra Kyriakopoulou

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.
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Suggested Citation

  • Antonis Demos & Dimitra Kyriakopoulou, 2018. "Finite-sample theory and bias correction of maximum likelihood estimators in the EGARCH model," LIDAM Reprints CORE 2983, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:2983
    DOI: https://doi.org/10.1515/jtse-2018-0010
    Note: In : Journal of Time Series Econometrics, 2018
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    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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