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When testing the stationarity of residuals after OLS estimation, the ADF and KPSS test have opposing conclusions when it comes to rejecting the null:

  • ADF: Rejection of null concludes evidence of stationarity
  • KPSS: Rejection of null concludes evidence of non-stationarity.

In addition, the sample size is fairly low (approx 40 observations). Is this what's throwing off the test? From what I've read ADF has low power as well. In such a situation would it be appropriate to use DF-GLS instead?

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  • $\begingroup$ It depends on many things. Are you using trend? constant? What about the other tests? (there are many more) $\endgroup$ – luchonacho Aug 29 '16 at 17:39
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    $\begingroup$ Note that when KPSS rejects the null of stationarity it does not necessarily suggest presence of a unit root. It could be another type of nonstationarity. $\endgroup$ – Richard Hardy Aug 29 '16 at 17:46
  • $\begingroup$ @luchanacho, this is the conclusion on all cases, i.e. no constand or trend, constant, constant and trend $\endgroup$ – rayven1lk Aug 29 '16 at 17:54
  • $\begingroup$ @RichardHardy I'm not familiar with other forms of nonstationarity. Do you have a resource I could check out on this? $\endgroup$ – rayven1lk Aug 29 '16 at 17:55
  • $\begingroup$ Some times series textbook, e.g. Zivot "Modeling Financial Time Series with S-PLUS" (2006) or the original paper by the four authors (KPSS are their surnames' first letters). $\endgroup$ – Richard Hardy Aug 29 '16 at 17:59

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