We derive the limit theory of the Gaussian stable quasi maximum likelihood estimator for the stationary EGARCH(1,1) model when the squared innovation process has marginals with regularly varying tails. We derive regularly varying rates and limiting stable distributions. We perform Monte Carlo experiments to assess the extent of the parameter space corresponding to the invertibility condition, and the quality of the asymptotic approximation.

中文翻译：

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EGARCH(1,1)模型中高斯SQMLE的极限理论

当平方创新过程具有尾端规律变化的边际时，我们推导出稳态 EGARCH(1,1) 模型的高斯稳定拟最大似然估计量的极限理论。我们得出有规律的变化率和极限稳定分布。我们执行蒙特卡罗实验来评估对应于可逆条件的参数空间的范围，以及渐近近似的质量。