I have a few questions, if you don't mind.
1. What do you mean by "overlapping" data populations? Do you mean that, say, I have one time series that runs from t= 0 to 10, and another that runs from t = 5 to 15?
2. Can you exhibit the "simple linear equation" or do you not know it in advance?
3. What do you mean by "difference"? If I'm looking at a plot of your two data populations, what sort of thing am I doing by taking a difference?