Robust Estimation in Vector Autoregressive Moving‐Average Models

Abstract

Bustos and Yohai proposed a class of robust estimates for autoregressive moving‐average (ARMA) models based on residual autocovariances (RA estimates). In this paper an affine equivariant generalization of the RA estimates for vector ARMA processes is given. These estimates are asymptotically normal and, when the innovations have an elliptical distribution, their asymptotic covariance matrix differs only by a scalar factor from the covariance matrix corresponding to the maximum likelihood estimate. A Monte Carlo study confirms that the RA estimates are efficient under normal errors and robust when the sample contains outliers. A robust multivariate goodness‐of‐fit test based on the RA estimates is also obtained.