Robust estimation in vector autoregressive moving-average models (Q2703241)

A robust estimation procedure for a VARMA(p,q) processes is presented which is a generalization of the residual autocovariance (RA) estimates but produces estimates which are affine equivariant. The authors cite at least two advantages of their affine equivariant approach. At first, their approach modifies observations on the basis of an affine equivariant innovation norm which is large if at least one arbitrary linear combination of the innovation components is atypical. Secondly, they prove that their affine equivariant RA 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. NEWLINENEWLINE\textit{O.H. Bustos} and \textit{V.J. Yohai} [J. Am. Stat. Assoc. 81, No. 393, 155--168 (1986)] proposed a class of robust estimates for autoregressive moving-average (ARMA) model based on RA estimates. 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.