A dominance approach for comparing the performance of VaR forecasting models

We introduce three dominance criteria to compare the performance of alternative value at risk (VaR) forecasting models. The three criteria use the information provided by a battery of VaR validation tests based on the frequency and size of exceedances, offering the possibility of efficiently summarizing a large amount of statistical information. They do not require the use of any loss function defined on the difference between VaR forecasts and observed returns, and two of the criteria are not conditioned by the choice of a particular significance level for the VaR tests. We use them to explore the potential for 1-day ahead VaR forecasting of some recently proposed asymmetric probability distributions for return innovations, as well as to compare the asymmetric power autoregressive conditional heteroskedasticity (APARCH) and the family of generalized autoregressive conditional heteroskedasticity (FGARCH) volatility specifications with more standard alternatives. Using 19 assets of different nature, the three criteria lead to similar conclusions, suggesting that the unbounded Johnson SU, the skewed Student-t and the skewed Generalized-t distributions seem to produce the best VaR forecasts. The unbounded Johnson SU distribution performs remarkably well, while symmetric distributions seem clearly inappropriate for VaR forecasting. The added flexibility of a free power parameter in the conditional volatility in the APARCH and FGARCH models leads to a better fit to return data, but it does not improve upon the VaR forecasts provided by GARCH and GJR-GARCH volatilities.