Convergence tests for experimental data I ran a simulation for the critical density at which traffic flow transitions from laminar flow to start-stop-waves. The results for different road lengths are:

From the graph we can see that the critical density decreases as the road length increases. Is there any test I can do that guides me into a point where my data may converge?
All I can be sure is that it converges at least to 0 (which physically makes sense to me). How can I test that it does not converge to any other value greater than 0?
PS: It takes me about a week of the code running to get very high values (1 single point at $10^4$ took 5 days of the program running).
PPS: I add a link to the data Data in case someone wants to try something.
 A: You could try hypothesis testing.  The first thing I would do is estimate the non-stationary mean of the data.  Least square fit it with a model (e.g., exponential or something nonparametric).  This is an estimate of the mean.  You could also just apply a running (mean, say) filter over the data to get an estimate of the mean.  Once you have this, subtract the mean from the data.  This gives you an estimate of the population variance, assuming you've removed all the obvious structure.  Of course you want to make sure that the mean and variance are insensitive to the model you use.  Then you can compute asymptotes that are consistent with the uncertainty in the data.  In other words, once your mean decays to the level of the noise then you stop.  You can estimate the uncertainty of the asymptote by seeing how sensitive it is among all the mean-estimates that don't overfit the data.  There is a vast statistics literature on this problem, and I've just given an oversimplified version.  Talk to a statistician.  But I think what I've said will give you a reasonably defensible start at your answer.  It's also possible to pose the test:  is the asymptote consistent with zero given the uncertainties in the data.  You can also estimate confidence intervals on the asymptote itself.  If you like, you could post a link to the data and I could give it a go, since I have a lot of statistical tools for doing similar calculations.  Finally, a caveat.  With enough degrees of freedom you can fit any model.  So you need to make sure that only add degrees of freedom if they are required by the data.  Occam's Razor.
