The purpose of this paper is to present a decomposition into trend or permanent component and cycle or transitory component of a time series that follows a nonstationary autoregressive fractionally integrated moving average (ARFlMA(p,d,q)) model. As a particular case, for d=l we obtain the well known BeveridgeNelson decomposition of a series. For d=2 we get the decomposition of an 1(2) series given by Newbold and Vougas (1996). The decomposition depends only on past data and is thus computable in real time. Computational issues are also discusse
