The (Generalized) AutoRegressive Conditional Heteroscedasticity [(G)ARCH] model is tested for daily data on 22 exchange rates and 13 stock market indices using the standard Lagrange Multiplier [LM] test for GARCH and a LM test that is resistant to patches of additive outliers. The data span two samples of five years ranging from 1986 to 1995. Using asymptotic arguments and Monte Carlo simulations, in which the empirical method is evaluated, it is shown that patches of outliers can have significant effects on test outcomes. The main empirical result is that spurious GARCH is found in about 40% of the cases, while in many other cases evidence of GARCH is found even though such sequences of extraordinary observations seem to be present. © 2004 Taylor and Francis Ltd.