  We present a new framework for robust estimation and inference on
second-order stationary time series and random fields. This framework is based
on the Generalized Method of Wavelet Moments which uses the wavelet variance to
achieve parameter estimation for complex models. Using an M-estimator of the
wavelet variance, this method can be made robust therefore allowing to estimate
the parameters of a wide range of time series and spatial models when the data
suffers from outliers or different forms of contamination. The paper presents a
series of simulation studies as well as a range of applications where this new
approach can be considered as a computationally efficient, numerically stable
and robust method which performs at least as well as existing methods in
bounding the influence of outliers on the estimation procedure.
