I am currently conducting a test of stationarity on the Shanghai Stock Exchange (SSE) index.

Clearly when graphing both the ln(SSE) and SSE series, I see an upward trend, which should clearly indicate a violation of stationarity. I conducted an Augmented Dickey Fuller tests on both, and found that in the case of ln(SSE), I was able to reject the null hypothesis that there is a unit root in ln(SSE). This was not the case for the SSE series.

Does this mean that when you take the logarithm of a variable, there is a slight chance of making the data stationary as what the test results suggest?

  • $\begingroup$ The common unit root tests are based on linear regressions which are not invariant to non linear transformations of the data. More generally, statistical tests of the form $\theta=\theta_0$ have in principle potentially arbitrary low power against alternatives of the form $\theta=\theta_0+\epsilon$. Therefore, specially in large samples the actual value of the test statistic is more interpretable than the p-value (except in small samples, you should be more concerned that $\gamma$ is meaningfully far from 0). $\endgroup$
    – user603
    Commented Sep 21, 2016 at 15:55
  • $\begingroup$ There are some good responses to a very similar question at Log or no log when testing for unit root? $\endgroup$ Commented Sep 21, 2016 at 15:58
  • $\begingroup$ I can tell you in advance that the index is not stationary, regardless of your test results. $\endgroup$
    – Aksakal
    Commented Sep 21, 2016 at 19:39

1 Answer 1


Note that the null hypothesis of the ADF test is that there is a Unit root.

The alternative hypothesis of the test is that there is a "root outside the unit circle". A "root outside the Unit circle" usually infers stationarity or trend-stationarity.

Trend-stationarity CANNOT be detected with an ADF test. The ADF test does not test a null hypothesis of trend stationarity against an alternative hypothesis of strict stationarity. Instead detrend the time series and test for stationarity in the detrended data set.

Edit: Note that a Unit root can be defined as a shock which shifts the time series permanently to a new level. Apparently your data does not have such shocks.

Edit2: In the following link I described cases in which an ADF-test might produce missleading results (i.e. if the time series contains components of both stationary and non-stationary time series or if the data set is two small for inference. In your case the first case might be a possibillity). Two solutions of these problems are either applying additionally for a Stationarity test such as KPSS or Leybourne-McCabe or applying a Variance ratio test .What is the difference between a stationary test and a unit root test?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.