[Let the time series Y_t satisfy extlesstex-math extgreater$Y_ \= extbackslashalpha + extbackslashrho Y_ -1\+e_ $ extless/tex-math extgreater, where Y_1 is fixed and the e_t are normal independent (0, σ ^2) random variables. The likelihood ratio test of the hypothesis that (α, ρ) = (0, 1) is investigated and a limit representation for the test statistic is presented. Percentage points for the limiting distribution and for finite sample distributions are estimated. The distribution of the least squares estimator of α is also discussed. A similar investigation is conducted for the model containing a time trend.]