I'm testing ADF, PP and KPSS unit tests with tseries library. I get strange result with ADF and PP.
I have this vector:
x <- rnorm(1000)
obviously this vector is trend stationary. OK, I've done ADF, PP and KPSS tests and all of these confirm it.
I have noticed that if I have a strong trend like:
ADF: adf.test(f, alternative='stationary')
Dickey-Fuller = -9.8989, Lag order = 9, p-value = 0.01
PP: pp.test(f, alternative='stationary')
Dickey-Fuller Z(alpha) = -994.6171, Truncation lag parameter = 7, p-value = 0.01
KPSS: kpss.test(f, null='Level')
KPSS Level = 12.5992, Truncation lag parameter = 7, p-value = 0.01
Why ADF and PP have 0.01 as p-value when there is a strong trend? This strong trend obviously is not "mean-reverting", so i don't understand why they reject the null.
In these tests only kpss has 'Level' type, ADF and PP not.