# About 2 unit root tests and null hypothesis

I have been looking at unit root testing. Specifically 2 tests:

1. The ADF test. The ADF (augmented Dickey Fuller) test has the null hypothesis that "the time series has a unit root" (meaning that the time series is not weakly stationary)

2. The KPSS test. The KPSS is a (Lagrange Multiplier type) test which has the null hypothesis that "the time series is weakly stationary" (so no unit root here).

What I am looking for when applying those tests is to say whether a process is stationary, so I can do things with it. Somebody told me that because of how the null hypothesis was specified, on average one test would give more stationary processes than the other.

Could anybody explain to me why ?

This is what I think: because the ADF test has as $H_0$ "the process has a unit root", what I can say is "With a given confidence, say 99%, I cannot reject the fact that this process has a unit root"; because of this I can be pretty sure that a process is not stationary, but this is not the same that saying that a process is stationary, so the ADF test should "keep" more processes as stationary than the KPSS test ...

• What do you mean by "I can do things with it"? In general, I would suggest that you consult a general discussion of what means to reject or not to reject a null hypothesis, see e.g. here and posts that are related (see the column on the right side of the page). – Christoph Hanck Mar 12 '15 at 17:15
• The following link should answer your question perfectly stats.stackexchange.com/questions/30569/… – Ferdi Sep 20 '16 at 9:13