If time series $A, B$ and $A, C$ are cointegrated, is $B, C$ also cointegrated? And with similar confidence? While I am interested in the general case, let's consider the case of three series. So, suppose time series $A, B, C$. If I can show that $A, B$ and $A, C$ are cointegrated with a test statistic $\ge 95\%$ confidence interval level, can I be expect that $B, C$ are cointegrated? Similarly, can I make a good assumption about the strength of the cointegration test statistic, i.e. will the confidence level be similar? 
Intuitively I would think good assumptions can be made, but perhaps there is a chance of scenarios where cointegration is not the case. 
 A: If $A$ and $B$ are cointegrated, they're both $I(1)$ but a linear combination of them is $I(0)$. This suggests we should be able to write each of them in this form:
$A = aJ + Z_A$
$B = bJ + Z_B$
where $J$ is $I(1)$ and $Z$'s are $I(0)$.
Now a similar relationship exists between $A$ and $C$; consequently it seems  that $C$ must relate to the same integrated component, $J$, otherwise $A$ would have a second $I(1)$ component in it and in that case there wouldn't be a linear combination of $A$ and $B$ that was $I(0)$. So it looks like $C$ must be of the form
$C = cJ + Z_C$
and therefore should be cointegrated with $B$ also.
Edit: I did a bit of additional digging about and I see that apparently (and unsurprisingly) this transitivity is quite well known. It's proved, for example, in Appendix A of this paper.
It can certainly happen that a test can fail to detect cointegration between $B$ and $C$, even when it should be present.
See for example, Ferré (2004) [1] which uses the Johansen test in just such a setup (using simulation), where $A$ was "driving" the relationship between $B$ and $C$ (in a sense, $A=J$). With that setup, even though cointegration was usually detected between each of the two variables and $A$, it was usually not detected between $B$ and $C$.
(Note, however, that she calls the series X, Y and Z in her paper)
[1] Ferré, M. (2004),
"The Johansen Test and the Transitivity Property,"
Economics Bulletin, Vol. 3, No. 27, pp. 1-7   
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=870226
