  The subject of robust estimation in time series is widely discussed in
literature. One of the approaches is to use GM-estimation. This method
incorporates a broad class of nonparametric estimators which under suitable
conditions includes estimators robust to outliers in data. For the linear
models the sensitivity of GM-estimators to outliers have been studied in the
work by Martin and Yohai [5], and influence functionals for this estimator were
derived. In this paper we follow this direction and examine the asymptotical
properties of the class of M-estimators, which is narrower than the class of
GM-estimators, but gives more insight into asymptotical properties of such
estimators. This paper gives an asymptotic expansion of the residual weighted
empirical process, which allows to prove asymptotic normality of these
estimators in case of non-smooth objective functions. For simplicity MA(1)
model is considered, but it will be shown that even in this case mathematical
techniques used to derive these asymptotic properties appear to be rather
complicated.However, the approach used in this paper could be applied to
GM-estimators and to more realistic models.
