For my thesis, I made a real-time ship's engine room simulator on a Z80 Big Board. The idea behind it was to create a low cost trainer for ship's engineers-to-be. One of the things that the system required to be capable of was to simulate faults in all kinds of processes, e.g. pumps, electric motors, generators, diesel engines, etc. For that purpose, we couldn't find much data readily available, other than our own observations over the previous years. So what we did is to define where the process would "end" and, using polynomial equations, extrapolate the known functions to that point. Although the resulting datasets will strictly speaking be incorrect, it is the only feasible way to get somewhere and we found that the results looked very real in this situation.
What I mean to say is that it depens on what you want to establish: extrapolation may not always be that bad, as long as you are aware of its limitations.