1

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?

Ferdi
  • 4,882
  • 7
  • 42
  • 62
Darren Ignatius Lee
  • 11
  • 1
  • 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). – user603 Sep 21 '16 at 15:55
  • I can tell you in advance that the index is not stationary, regardless of your test results. – Aksakal Sep 21 '16 at 19:39
  • There are some good responses to a very similar question at [Log or no log when testing for unit root?](https://www.researchgate.net/post/Log_or_no_log_when_testing_for_unit_root) – Brian O'Donnell Sep 21 '16 at 15:58

1 Answers1

2

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?

Community
  • 1
Ferdi
  • 4,882
  • 7
  • 42
  • 62