This article considers tests for unit roots in time series models with varying parameters. The null hypothesis is that roots are unity against an alternative where they change over time. Tests statistics are based on recursive least squares (RLS) estimates having exponentially weighted (EW) observations. This method belongs to the class of nonparametric estimators and allows interesting computational and graphical aspects. Asymptotic properties are investigated as in kernel estimation, by allowing smoothing coefficients tending to zero. Under the null, we find that test statistics approach the distributions tabulated by Dickey and Fuller. Applications to real and simulated data show the validity of the method.