# How a strong trend could be mean-reverting?

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:

f<-jitter(1:1000)


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.

Thank you!

(??) Surely, you realize that you perform the (regression whose coefficients are used in the calculation of the) (a)df (& pp for that matter) test on the differentiated series $y_t=f_t-f_{t-1}$ (the 'surely' is there, not to sound brash, but given that you interpret the p-value, i would assume you know what it corresponds to --otherwise why would you be surprised by the result[?]).