I have a data set for a variable, for which I have run some unit-root tests:
- ADF (constant/without trend): t-stat=-1.0816, p-val=0.7218 - DNR
- ADF (constant & trend): t-stat=-4.5203, p-val=0.0021 - REJECT @5% level
- PP (constant/without trend): t-stat=-1.3507, p-val=0.6044 - DNR
- PP (constant & trend): t-stat=-3.6030, p-val=0.0334 - REJECT @5% level
(Note I have also run all of the above tests with the first-differenced values, and they ALL reject the null of the presence of a unit root.)
As I understand, I fail-to-reject the null on both the ADF & PP tests with ONLY a constant (no trend), but statistically reject the null for both tests when a trend is included.
What should I conclude about the data series - is this indicative of any statistical property I may be ignoring/oblivious to? What does this indicate as to the presence of a unit-root in the series given the contradictory results of the tests?
EDIT: Just have run into the opposite problem on another data series: ADF & PP (no trend) Rejects the null but ADF & PP WITH trend Does Not Reject the null.
What would this case of the problem mean?
I feel like I'm missing something - the Alternative Hypotheses?