If we try to estimate the parameters of the AR process {Xn} using the observed process {Xn+Zn} then these estimates will be badly biased and not consistent but we can minimize the damage using a robust estimation procedure such as GM-estimation. The question is does additive contamination affect estimates of “core” parameters in the infinite variance case to the same extent that it does in the finite variance case? We will see that if the contamination {Zn} has higher tails than the core process {Xn}, the estimation of parameters of the core process will not be greatly affected; that at least its consistency is preserved.