We revisited the definitions of Expected Shortfall (ES) backtesting procedures based on exceedance residuals with the objective of making them effective for evaluating risk forecasts of Range Value at Risk (RVaR). To assess the performance of all procedures, we conducted Monte Carlo simulations to evaluate the size and power properties across different scenarios. In addition, we executed an empirical exercise with different asset classes, rolling window estimations and significance levels. Jointly with each backtest, we applied the loss function of RVaR to assess the results and verify if they remained following both methods. We identified that none of the proposed backtesting procedures display significant superiority over the others in numerical and empirical analyses. Besides, the size and power of the tests deteriorate as the out-of-sample size increases. Also, with the increase of in-sample observations, we noted a degradation of sizes and improvement of powers for data generated with normal distribution at the significance levels of $\alpha = 1\%,\beta=2.5\%$. For data generating processes with third and fourth moments, the proposed procedures exhibit higher powers when the predictions are conducted using the normal distribution. Regarding the empirical application, we identified that the results closely follow both methods in the best-performing scenarios, exhibiting the opposite in the worst-performing ones.
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