  The exact maximum likelihood estimate (MLE) provides a test statistic for the
unit root test that is more powerful \citep[p. 577]{Fuller96} than the usual
least squares approach. In this paper a new derivation is given for the
asymptotic distribution of this test statistic that is simpler and more direct
than the previous method. The response surface regression method is used to
obtain a fast algorithm that computes accurate finite-sample critical values.
This algorithm is available in the R package {\tt mleur} that is available on
CRAN. The empirical power of the new test is shown to be much better than the
usual test not only in the normal case but also for innovations generated from
an infinite variance stable distribution as well as for innovations generated
from a GARCH$(1,1)$ process.
