ISSN 1440-771X

A semiparametric model is proposed in which a parametric \u85ltering of a non-stationary time series, incorporating fractionally di¤erencing with short mem-ory correction, removes correlation but leaves a nonparametric deterministic trend. Estimates of the memory parameter and other dependence parameters are proposed, and shown to be consistent and asymptotically normally distrib-uted with parametric rate. Unit root tests with standard asymptotics are thereby justi\u85ed. Estimation of the trend function is also considered. We include a Monte Carlo study of \u85nite-sample performance