The Augmented Dickey-Fuller Test can be used to measure how well ranked certain pairs are against others for co-integration.
So then say we have a known co-integration between
Y and between
Z, is there a constraint to the range of co-integration between
For example, if we know
coint(X,Y) = -0.1 and
coint(Y,Z) = -0.3 can we then use these in some formula which would then say with certainty that
-x.x < coint(X,Z) < -x.x?
This is similar to the correlation constraint of the same scenario given by (Olkin, 1981).
EDIT - As Richard has pointed out, I may have misunderstood the ADF Test. I'll rephrase the question here:
If we know $X$ is cointegrated (via some test e.g. Engle Granger) with $Y$ and $Y$ with $Z$, is there some measure of how probable $X$ will be cointegrated with $Z$?