This paper empirically investigates the contribution of the term structure of the forward premium to explain the long memory behavior that can characterize the forward premium. We apply our empirical study on1-month, 3-month, 6-month, 9-month and 1-year forward premiums of the EUR/USD over 17 years with a daily frequency from 08 January 1999 to 08 January 2016. Therefore, we estimate the ARFIMA model by a semi-parametric method that is Geweke and Porter-Hudak (1983) and a parametric model namely the maximum likelihood method. The estimation results of long memory parameter confirm the persistence and the fractional dynamics of the forward premium. Moreover, both approaches are consistent when it is the case of 6, 9 and 12 months horizons. These findings bring into question the relevance of the term structure of the foreign exchange forward premium in the determination of the long memory attitude.