# Augmented Dickey-Fuller unit root test & cointegration

I have a pair of variables (x, y) over time. I want to regress y on x.

• Do I have to perform a ADF test 1st on x and y to find if both are stationary in their 1st difference (i.e. I(1))?
• What if they are non-stationary? Or 1 variable is stationary and the other isn't?

I am confused as to why I need to perform the ADF test and the implication of it. Correct me if I am wrong.

1. I think I am to perform ADF on x & y to find that both are I(1).
2. Next, perform a cointegration test to check if their linear combination is I(0), or stationary. If the conintegration test is I(0), it implies that the results of the regression of y on x is acceptable, as their linear combination is stationary.

So the next question is:

• How do I perform a cointegration test on the residuals? I am supposed to use the Levin, Lin and Chua (2002) test. But I understand that this test is a panel unit root test (xtunitroot), does it test for cointegration?

Note: I am using Stata 13.

Perform the ADF test first. If it's found one series is stationary and the other is not, you need to take the first difference of that series and then run the regression.

If it's found that both have unit root, run the cointegration test. Levin, Lin, Chua is indeed a panel unit root test. Use that for the unit root test if you have panel data. Note that cointegration test tests whether the residual is stationary, so indeed you may use a unit root test to do that. The significance threshold values won't be right though so you will have to get the right values. For testing cointegration I would rather use the Johansen's test instead.

Now, if the series is cointegrated run the regression using an error correction model. If it's not, take the first difference of the variables instead and then run the regression. Do note that there is a difference in running a regression with differenced variables, long term relationships may be lost.