Using both semiparametric and parametric estimation methods, this paper corroborates earlier findings of fractionally integrated behaviour in the forward premium. Two new explanations are also proposed to help reconcile earlier conflicting empirical evidence on the time series properties of the forward premium. Traditional regression approaches used to test the forward rate unbiasedness hypothesis are then evaluated, including regression in levels, in returns (Fama's, 1984, regression), and in error-correction format. Interesting statistical and/or interpretive implications are found in all three cases. For example, the predictions of the appropriate nonstandard limit theory are consistent with many of the standard empirical results reported from Fama's regression, including the commonly occurring, yet puzzling negative correlations between spot returns and the forward premium. It is suggested that the principal failure of unbiasedness, may be due instead to the difference in persistence between these two series.