> > cross correlation function of the X vs y
Is this supposed to be combined somehow with the f_{i} outputs?
I'd rank the variables by their CCF, and use the top(n) to try to predict the series of interest.
Like, split Y in half, then use the X(1:(t/2)+n) to predict Y(t+n) to see if it works, and then if it works OK, actually model the top n X series and use them to really predict the Y.
It's a pretty manual approach, but you could automate it once you have a better idea what you're aiming for.