And my point was that this is an irrelevant comparison. When you look at the data sets, you want to know if they are mutually informative (if learning one can tell you about the other). A linear statistical correlation -- which Kennaway showed is absent -- is one way that the datasets can be mutually informative, but it is not the only way.

If you know the ordered, timewise development of each variable, you have extra information to use. If you discard this knowledge of the time ordering, and are left with just simultaneous pairs (pairs of the form [A(t0),B(t0)] ) then yes, as Kennaway points out, you're hosed. So?