Augmented Dickey Fuller output conflicting in Stata I am required to perform unit root testing on a given time series. The output obtained in Stata is somewhat confusing me. To the best of my knowledge I am obtaining two conflicting results, Stata indicating that the time series fits a unit root process while also seemingly saying that the coefficient is significantly different from zero, hence contradicting the idea that the time series indeed follows a unit root process. This is the output obtained in Stata:
. dfuller series3, noconstant regress lags(0)

Dickey-Fuller test for unit root                   Number of obs   =        48

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

------------------------------------------------------------------------------
 Z(t)              8.943            -2.623            -1.950            -1.609
------------------------------------------------------------------------------
 D.series3 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
 series3 |
     L1. |   .1314633   .0147005     8.94   0.000     .1018897    .1610369
-----------------------------------------------------------------------------

Clearly the test statistic is indicating that the null hypothesis is accepted and hence the time series fits a unit root process. However, the p-value obtained for L1 is 0.000 indicating that it is significantly different from zero (0.1314633 cannot be treated as being 0). I read somewhere that this might be related to the Augmented Dickey Fuller test itself; however, I cannot seem to find this link again. I also ran the Augmented Dickey Fuller test using lags as well as the Philips-Perron test and obtained similar results.
Would anyone have any idea why the ADF is giving such results and what might be the cause of this anomaly?
 A: You'r test indicates that the series does follow a unit root. Note that the DF-test is one sided so you should not think in absolute values. You'r test statistic is 8.943 which clearly is higher than -1.950
  so you cannot reject the null of a unit root in the series. That being said I think that you will have very low power because you only have 48 observations. When you have so few observations it will look like the series does not mean revert when in fact, with more observations, it will be mean reverting. Second I would try to augment the ADF regression with a trend and more lags. Autocorrelation in the error term will invalidate the DF test! Hence use the ADF test with more lags to account for the autocorrelation.
1) Look at the ACF to determine approximately how many lags you need to include. 2) Remove insignificant lags 3) When all included lags are significant look at the t-value of the variable of interest. If its lower than -1.950
  then you do not have a unit root, if its higher then you do have a unit root (which you in fact do have). As mentioned, you'r problem is with the low observations and the lack of lags and probably also a time trend in the regression.
A: 
Clearly the test statistic is indicating that the null hypothesis is accepted and hence the time series fits a unit root process.

How is that clear to you? To me it's clear that the test statistics is beyond 1% critical value, i.e. $H_0$ has to be rejected, see Stata's dfuller command's help with examples
UPDATE: thanks @whuber, fixed typo in link
A: It would seem that a possible result for this would be the inadequacy of either autoregressive or unit root processes to model the given data. This is only a conclusion I have come to based on consultation with my lecturer as well as comparing the data's behaviour under further analysis. Any comments or criticism is more than welcome.
Indeed, for the given data, when using the Expert Modeller in SPSS Holt's Exponential Smoothing was chosen as the model which fit the given data best with a normalized BIC of 6.857. When fitting an ARIMA model, ARIMA(2,2,0) was the best fitting model and gave a BIC of 6.856. Both ARIMA(2,2,0) and the Holt's Exponential Smoothing gave a similar BIC and had fitted values which were very close to the observed data values. 
