This paper introduces a new class of robust estimates for ARMA models. They are M-estimates, but the residuals are computed so the effect of one outlier is limited to the period where it occurs. These estimates are closely related to those based on a robust filter, but they have two important advantages: they are consistent and the asymptotic theory is tractable. We perform a Monte Carlo where we show that these estimates compare favorably with respect to standard M-estimates and to estimates based on a diagnostic procedure.
"Robust estimation for ARMA models." Ann. Statist. 37 (2) 816 - 840, April 2009. https://doi.org/10.1214/07-AOS570