PETER R. HANSENa* AND ASGER LUNDE

SUMMARY
We compare 330 ARCH-type models in terms of their ability to describe the conditional variance. The models
are compared out-of-sample using DM–$ exchange rate data and IBM return data, where the latter is based
on a new data set of realized variance. We find no evidence that a GARCH(1,1) is outperformed by more
sophisticated models in our analysis of exchange rates, whereas the GARCH(1,1) is clearly inferior to models
that can accommodate a leverage effect in our analysis of IBM returns. The models are compared with the
test for superior predictive ability (SPA) and the reality check for data snooping (RC). Our empirical results
show that the RC lacks power to an extent that makes it unable to distinguish ‘good’ and ‘bad’ models in
our analysis. Copyright  2005 John Wiley & Sons, Ltd.