ARMA–GARCH models are used to predict returns on risky assets, with heavy-tailed innovations. Extreme value theory helps estimate extreme quantiles of residuals. By analyzing the distribution of extreme conditional Value-at-Risk and conditional expected shortfall estimates, researchers found that using self-normalization for confidence intervals improves coverage compared to normal approximation. Including more upper order statistics in the estimation process enhances accuracy, as shown in simulations and applied to stock index returns.