We compare two time series models: an ARMA(1,1)-ACD(1,1)-NIG model against an ARMA(1,1)-GARCH(1,1)-NIG model. Their out-of-sample performance is of interest rather than their in-sample properties. The models produce one-day ahead forecasts which are evaluated using three statistical tests: VaR-test, VaRdur-test and Berkowitz-test. All three tests are concerned with the the tail events, since our time series models are often used to estimate downside risk. When the two models are applied to data on Canadian stock market returns, our three statistical tests point in the direction that the ACD model and the GARCH model perform similarly. The difference between the models is small. We finish with comments on the model uncertainty inherit in the comparison.