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In this paper, the stochastic characteristics of the electric consumption in France are analyzed. It is shown that the load time series exhibit lasting abrupt changes in the stochastic pattern, termed breaks. The goal is to propose an efficient and robust load forecasting method for prediction up to a day-ahead. To this end, two new robust procedures for outlier identification and suppression are developed. They are termed the multivariate ratio-of-medians-based estimator (RME) and the multivariate minimum-Hellinger-distance-based estimator (MHDE). The performance of the proposed methods has been evaluated on the French electric load time series in terms of execution times, ability to detect and suppress outliers, and forecasting accuracy. Their performances are compared with those of the robust methods proposed in the literature to estimate the parameters of SARIMA models and of the multiplicative double seasonal exponential smoothing. A new robust version of the latter is proposed as well. It is found that the RME approach outperforms all the other methods for “normal days” and presents several interesting properties such as good robustness, fast execution, simplicity, and easy online implementation. Finally, to deal with heteroscedasticity, we propose a simple novel multivariate modeling that improves the quality of the forecast.