This paper proposes a robust forecasting method for non-stationary time series. The time series is modelled using non-parametric heteroscedastic regression, and fitted by a localized MM-estimator, combining high robustness and large efficiency. The proposed method is shown to produce reliable for… ecasts in the presence of outliers, non-linearity, and heteroscedasticity. In the absence of outliers, the forecasts are only slightly less precise than those based on a localized Least Squares estimator. An additional advantage of the MM-estimator is that it provides a robust estimate of the local variability of the time series.