Robust minimum distance estimators for the CARR(1,1) model

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.