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

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.

Automated summary

This study introduces an efficient backtest method for risk variables modeled by ARMA-GARCH processes, requiring fewer finite moments for robustness to heavier tails. By adding a constraint on the goodness of fit for the error distribution, more accurate risk forecasts and improved test power are provided. Both simulation and empirical analyses confirm the good performance of the new backtests in monitoring financial crises.