This paper proposes a minimum distance estimator (MDE) for the CARR(1,1) model, which is based on the minimization of the quadratic distance between sample and population autocorrelations. It is shown that the estimator is consistent and asymptotically normal distributed under regularity conditions. Considering the impact of outliers, we robustify the MDE by replacing sample mean and autocorrelations by robust estimators of them to obtain some robust MDEs. The performances of these MDEs are investigated and compared via Monte Carlo simulations and empirical application. Both results show that these robust MDEs outperform the quasi-maximum likelihood estimator(QMLE) in the presence of outliers.

本文提出了CARR（1,1）模型的最小距离估计器（MDE），该模型基于样本和总体自相关之间的二次距离最小化。结果表明，在正则条件下，估计量是一致的且渐近正态分布。考虑到异常值的影响，我们通过用样本的均值和自相关替换它们的鲁棒估计量来对MDE进行鲁棒化，以获得一些鲁棒的MDE。通过蒙特卡洛模拟和经验应用研究和比较了这些MDE的性能。两项结果均表明，在存在异常值的情况下，这些鲁棒的MDE优于拟最大似然估计器（QMLE）。