This note defines a Beveridge-Nelson smoother, that is a two-sided signal e
xtraction filter for trends. The smoother is shown to be the optimal estima
tor of the trend when the ARIMA model can be decomposed into an uncorrelate
d random walk trend and stationary cycle components. The conditions under w
hich such a decomposition is possible are discussed. (C) 2000 Elsevier Scie
nce S.A. All rights reserved. JEL classification: C22.