1. ## Analysis Question

Hi all,

I have a timeseries data set that converges to the exact (attached). I would like to have some sort of tolerance in my programs but would like to do it numerically. It would be something like min(max(distance_from_exact_of_timeseries)). It is difficult to explain but I hope the picture will help. If I fit a linear regression line to the data I get something along the lines of what I am looking for but I can only do this with the tools after the program has run which defies the point.

2. So, what is your question? Are you wanting to be able to approximate the exact solution in real-time, and not wait to post-process?

3. I apologise it's probably unclear. I would like a bound. As the approximate solution oscillates closer to the exact solution I would like to input a value say 0.01. When the approximate solution gets to the point where it is oscillating at 0.01 intervals about the exact solution it stops. So I know my approximate solution is within 0.01 error of the exact.

This would be easy if it was linear because it would just be

while abs(approx-exact)>0.01
continue program
end

however in my case the approximate solution passes through the exact solution and this statement doesn't work.

Is there a way to statistically or otherwise determine the minimum maximum value