<p>Evaluating forecasts of risk measures, such as value–at–risk (VaR) and expected shortfall (ES), is an important process for financial institutions. Backtesting procedures were introduced to assess the efficiency of these forecasts. In this paper, we compare the empirical power of new classes of backtesting, for VaR and ES, from the statistical literature. Further, we employ these procedures to evaluate the efficiency of the forecasts generated by both the Historical Simulation method and two methods based on the Generalized Pareto Distribution. To evaluate VaR forecasts, the empirical power of the Geometric–VaR class of backtesting was, in general, higher than that of other tests in the simulated scenarios. This supports the advantages of using defined time periods and covariates in the test procedures. On the other hand, to evaluate ES forecasts, backtesting methods based on the conditional distribution of returns to the VaR performed well with large sample sizes. Additionally, we show that the method based on the generalized Pareto distribution using durations and covariates has optimal performance in forecasts of VaR and ES, according to backtesting.</p>
Quantile estimation for the generalized pareto distribution with application to finance