Compare time series of measured properties to control, no forecasting There are many time serious questions but I can't seem to find one that explains my case. I have a set of timeseries that are the output of many simulations where the value of the same parameter is changed in each simulation. I would like to compare each  time series with the time series from the control simulation. The frequency and duration of all time series is the same. The value at time t depends on the value at time t-1 (in most cases), so I guess you would call these auto-correlated time series. These are values of number of plants or kg of biomass produced, or average height. I would like to know if there is a statistical significance between each time series and the control to determine the magnitude of the effect that this parameter has on the simulation output. I was thinking of comparing the mean and standard deviation  using a  t-test,  but I am not sure if these timeseries are auto-correlated.


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*Here two example with difference distances between means from control
 A: To parametrically test the equivalence of two means one needs to have data that is i.i.d. as @Alex Burn pointed out. What this means (pun intended) is that each series (separately) needs to be i.i.d or the resultant of an ARIMA process with an i.i.d error variance. Additionally each series error process needs to be free of deterministic structure (pulses/step shifts/seasonal pulses/time trends) AND have a constant error process over time.
I took your first series (SIM) into AUTOBOX (my tool of choice). The program's heuristics iterated (studiously avoiding using a presumptive list-based procedure) to the following model.
 where a few pulses are identified AND a significant reduction in error variance see (http://docplayer.net/12080848-Outliers-level-shifts-and-variance-changes-in-time-series.html) ( visually obvious ) at period 43   . This reduction is also clear from your graph if you mentally  adjust for the few anomalies
The actual/cleansed graph is also very revealing . So in summary the underlying model/characterization is that of a random walk where the expected value or mean is 0.0. If your simulation used another starting point then that would be the expected value or mean.
Now as a second step I took the second series called CONTROL here  and AUTOBOX formed  . This second series had pulses at different points in time and did not evidence a change in error variance. Here is the actual/cleansed graph 
In summary both series ultimately had a white noise error process confirming the results of a tour de force to separate signal and noise. The identified pulses are different save for period 28.
In summary both model are fundamentally random walks and thus could be referred to as being similar (but with important differences) . In my opinion your comment that your "kind of question" had not been seriously addressed is largely true because one has to initially identify what might be a common DGF ( Data Generating Function) and if a constant mean could be detected then a test might be formuable.
Hope this helps.
