Efficiently Backtesting Conditional Value-at-Risk and Conditional Expected Shortfall

Abstract–Given the importance of backtesting risk models and forecasts for financial institutions and regulators, we develop an efficient empirical likelihood backtest for either conditional value-at-risk or conditional expected shortfall when the given risk variable is modeled by an ARMA-GARCH process. Using a two-step procedure, the proposed backtests require less finite moments than existing backtests, allowing for robustness to heavier tails. Furthermore, we add a constraint on the goodness of fit of the error distribution to provide more accurate risk forecasts and improved test power. A simulation study confirms the good finite sample performance of the new backtests, and empirical analyses demonstrate the usefulness of these efficient backtests for monitoring financial crises.