The RATS Software Forum

Dear members,

I want to examine cointegration relationship between two variables (in logs). But I am confused about ADF test results. When I perform ADF without any constant and trend, results show that variables are nonstationary. But when I include constant (or trend) in the equation test, results show that variables are stationary.
Which one could be correct? What about Johansen cointegration test (by assuming that variables are nonstationary)?
I would be grateful if anyone could possibly guide me. Thanks.

Here is my data.

Your series don't appear to have a trend, so adding a trend will reduce the power of the unit root test.

Tom
Thank you for your quick reply.

You mean that I should include a constant in the equation test? In this case variables are stationary.
But when I use Elliott-Rothenberg-Stock test, it seems that they are non-stationary.
I would be grateful if I have your idea about this issue. Are they stationary?

It looks like they're borderline. If your main interest is in studying cointegration, you're probably fine in working with them as integrated.

Thank you a lot Tom.
when I do Johansen MLE test, results show they are not cointegrated except when I do not include any deterministic components (none option).
Dose it seams reasonable to have a cointegration equation without any deterministic components? Because in this case variables should have zero mean while my variables' mean is clearly grater than zero.

Integrated processes don't have a unconditional "mean" so it's possible to have DET=NONE as a possibility. However, if your two series are at best only marginally non-stationary and only marginally "cointegrated", it would probably be hard to conclude that there is anything very interesting going on.

You are wonderful Tom. Just another question and I am really sorry for asking so many questions.
When I plot the graph of my variables together, they track each other very closely and they move just together. Dose this co-moving is a sign of cointegration of variables? I am really sorry again

First, it's possible for two stationary processes to have a linear combination which is very small compared to the two inputs. It's also possible for two non-stationary series to have a linear combination which is "economically" trivial but statistically I(1). (A random walk with variance .000001 increments is still an I(1) series, but is effectively zero for almost any practical purpose). You're not showing cointegration by a Johansen test because the series are only borderline I(1), so you get no unit roots rather than one.

However, the DF tests are being thrown off by the behavior of the first 100 or so data points. A DF test assumes constant variance, and the variance over the beginning of the sample is quite different from that over the last 80%. If you restrict yourself to roughly the period starting entry (roughly) 101, you will probably get more reasonable results. You'll just need an explanation of why those first data points are different.