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Newbie question. I am reading about stationary series and understand that it has many forms:

  • mean stationary
  • variance stationary
  • covariance stationary

If I run an augmented dicky fuller test and find that the series is stationary is that sufficient to say that the series is stationary in all respects?

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Rejecting the null hypothesis of a unit root after applying the ADF test does not imply that the series is stationary in all respects. The ADF test is devised to detect non-stationarity in the long-term cycle, i.e. the trend of the series. Non-stationarity in other cycles are not inspected by this test. As long as the series exhibits a stationary trend pattern, sources of non-stationarity such as a changing seasonal pattern or a switch in the variance of the series will most likely result in rejecting the null hypothesis of the ADF test.

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