The difference $Y_{1t}-Y_{2t}$ is known with certainty; after all, you just measured it (unless you are measuring with uncertainty), so confidence bands around the difference seem to make little sense without an underlying model. I assume I may be misunderstanding your question - perhaps you want to edit it?
That said, you could fit, say, a state space model to the difference (e.g., with ets()
in the R forecast
package) and then simulate it to get the distribution of the underlying states at particular time points. Unfortunately, simulate.ets()
only works for out-of-sample simulations, but you could probably extract what you need from the fitted model. Or you could fit the state space model to initial segments of the difference, then simulate out from there, sort of a "rolling origin" forecasting approach.