This note considers a three‐step non‐Gaussian quasi‐maximum likelihood estimation (TS‐NGQMLE) of the double autoregressive model with its asymptotics, which improves efficiency of the GQMLE and circumvents inconsistency of the NGQMLE when the innovation is heavy‐tailed. Under mild conditions, the estimator not only can achieve consistency and asymptotic normality regardless of density misspecification of the innovation, but also outperforms the existing estimators, such as the GQMLE and the (weighted) least absolute deviation estimator, when the innovation is indeed heavy‐tailed.

中文翻译：

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重尾双自回归模型的三步非高斯拟极大似然估计

本说明考虑了具有渐近性的双自回归模型的三步非高斯拟最大似然估计（TS-NGQMLE），该模型提高了GQMLE的效率并避免了创新繁重时NGQMLE的不一致。在适度的条件下，无论创新密度不正确，估算器不仅可以实现一致性和渐近正态性，而且在创新确实很繁重时，其性能也优于现有估算器，例如GQMLE和（加权）最小绝对偏差估算器。尾巴。