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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,

    (Athens University of Economics and Business)

  • KYRIAKOPOULOU Dimitra,

    (CORE, Université catholique de Louvain)

Abstract

We derive 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,, 2018. "Finite sample theory and bias correction of maximum likelihood estimators in the EGARCH model," LIDAM Discussion Papers CORE 2018007, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2018007
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    Cited by:

    1. Yongdeng Xu, 2025. "The exponential HEAVY model: an improved approach to volatility modeling and forecasting," Review of Quantitative Finance and Accounting, Springer, vol. 65(2), pages 727-748, August.
    2. Stelios Arvanitis & Sofia Anyfantaki, 2020. "On the limit theory of the Gaussian SQMLE in the EGARCH(1,1) model," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(2), pages 341-350, March.

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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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