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.

中文翻译：

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EGARCH模型中最大似然估计的有限样本理论和偏差校正

摘要我们推导了EGARCH（1,1）参数的最大似然（ML）和拟最大似然（QML）估计量的偏差近似值的解析表达式，这使我们能够在所有估计量都有偏差之后进行校正。偏置校正机制是在两种分析方法的规范下构造的。我们还评估了剩余的自举估计器作为性能的度量。蒙特卡洛模拟表明，对于给定的参数值集，偏差校正对于所有参数均令人满意。提出的全步估计器的性能优于经典估计器，并且也比自举算法快。结果还可以用于制定估计量的近似Edgeworth分布。