This paper considers the ability of the power ARCH model to capture the stylized features of volatility in 17 heavily traded bilateral exchange rates. This power ARCH model nests a number of models from the ARCH family. The relative merits of these nested ARCH models can be considered using the standard log likelihood ratio test. The results of this paper suggest that in the presence of symmetric responses to innovations in the market, the GARCH(1,1) model is preferred. Where asymmetry is present, than the inclusion of a leverage term is worthwhile as long as a power term is also included.