This paper, estimates FIGARCH models introduced by Baillie et al. (1996a) for the four major daily exchange rates against the USD (DEM, FRF, YEN and the GBP). The former contributions are extended by accounting for the observed kurtosis through a Student-t based maximum likelihood estimation and by including variables capturing the effect of closing days. These estimations suggest that the introduction of these features improves the goodness of fit properties of the model on the one hand, and may lead to different interest parameters estimates on the other hand. In particular, it is shown that in the case of the DEM, volatility shocks may display much less persistence than documented by previous studies. Finally, it is shown that an ARFIMA-FIGARCH framework turns out to be relevant for all the currencies (except the GBP), without inducing any significant changes in the inference of the stochastic volatility process.