Ok, of course....I think it just hit me. Of course, right after I write it out. (That's probably what did it.)

Is this it: The goal of MRA is to de-correlate between time-scales, so you sometimes pay for that in correlation within scale. If I want to (basically) reverse that filter on that scale and de-correlate it, than that's dandy, but now it will be more correlated with the other scales?

Let me also say a bit more about what I'm doing. I'm trying to break down a few series, separate the time scales and then do some multivariate regression. I get some okay results and I've seen worse in the literature, but the fact that I've got this correlation structure, that I -know- the structure of, hanging around is annoying me.

Help! (And, many, many thanks!)