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AbstractThis paper introduces an asymmetric robust weighted least squares (ARLS) approach to improve the forecasting performance of the heterogeneous autoregressive model for realized volatility. The ARLS approach down‐weights extreme observations to limit the bad influence of outliers on the estimated parameters. Compared with existing robust regression methods, our model further takes into account the asymmetry of outliers using a class of kernel functions. Out‐of‐sample results show the ARLS approach can generate more accurate forecasts of the S&P 500 index realized volatility in the statistical and economic senses. The model that considers the asymmetry of outliers gains superior performance among various robust regression competitors. The forecasting improvements also hold in other international stock markets. More importantly, the source of the predictive ability of the ARLS model comes from the less biased and more efficient parameter estimation.