For 2004-2014, I have monthly measurements of my outcome of interest - some kind of physical exposure - for a collective of many thousand persons. The main determinant for the average exposure level is the intensity of the physical source (correlation ~ 0.7). This intensity was measured 1993-2014 in monthly intervals - it is periodic with a known cycle length.
The collective has three groups (A, B, C) which differ in their behavior such that their average time within proximity of the physical source differs - and thus their average exposure level. Yet, the correlation between their average monthly exposure is very high (~ 0.95). The smoothed monthly group averages look like this:
For group A, I have individual exposure measurements also for 1993-2004, but for B and C, no measurements exist for this period. I would like to retrospectively forecast the missing exposure given a) the intensity of the toxic source and b) the measured exposure for A. How can I do that?
I am only interested in prediction, not in testing. However, I also need a quantification of the forecast error variance. Pointers to relevant R functions / packages would be highly appreciated as well.