Specifically: Is it okay to have a p value of zero or one. In this example I have a p-value of zero. Also in a different case I am having a p value = 1.0000. Is that alright?

Dickey-Fuller test for unit root Number of obs = 21

                           ---------- Interpolated Dickey-Fuller ---------
              Test         1% Critical       5% Critical      10% Critical
           Statistic           Value             Value             Value

Z(t) -14.272 -4.380 -3.600 -3.240

MacKinnon approximate p-value for Z(t) = 0.0000

D.TotalS | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- TotalS | L1. | -.9774459 .0684873 -14.27 0.000 -1.121332 -.8335593 _trend | .4713369 .0326362 14.44 0.000 .4027708 .539903 _cons | 48.50135 3.370879 14.39 0.000 41.41939 55.5833

Dickey-Fuller test for unit root                   Number of obs   =        21

                               ---------- Interpolated Dickey-Fuller ---------
                  Test         1% Critical       5% Critical      10% Critical
               Statistic           Value             Value             Value
------------------------------------------------------------------------------
 Z(t)            -14.272            -4.380            -3.600            -3.240
------------------------------------------------------------------------------
MacKinnon approximate p-value for Z(t) = 0.0000

------------------------------------------------------------------------------
D.TotalS     |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      TotalS |
         L1. |  -.9774459   .0684873   -14.27   0.000    -1.121332   -.8335593
      _trend |   .4713369   .0326362    14.44   0.000     .4027708     .539903
       _cons |   48.50135   3.370879    14.39   0.000     41.41939     55.5833
------------------------------------------------------------------------------