st: cointegration and unit choice

[Ricardo Fernandez <Ricardo.Fernandez@eea.europa.eu>]

I have a little bit of trouble with the interpretation of how different unit-choices affect whether two variables can be cointegrated:

In case a) I run a unit root test on a variable Y, measured as % change compared to the previous year. The dfuller test rejects the null of a unit root, implying a stationary process I(0) and therefore no cointegration would be possible with variable X.

In case b) I run a unit root test on the same variable Y measured in logs o f the absolute values. The dfuller test does NOT reject the unit root. In addition, I take first differences and find an I(1) process for Y. My variable X is also I(1) so I can therefore test for cointegration. In my example, X and Y are cointegrated. 

So, Y cannot be cointegrated with variable X  when measured in % (because the process is stationary) but cointegration exists when measured in logs. The puzzling thing is that the first difference of the logs is almost identical to the % change. Thus, it looks like the unit root is case a) is rejected because I am already looking at a differenced series (i.e. the difference of the logs). Does this make sense at all?

Thanks!
Ricardo

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