I have a stochastic model used to simulate time series of some process. I am interested in the effect of changing one parameter to a specific value and want to show the difference between the time series (say model A and model B) and some sort of simulation based confidence interval.
I have been simply running a bunch of simulations from model A and a bunch from model B and then subtracting the medians at each time point to find the median difference throughout time. I used the same approach to find the 2.5 and 97.5 quantiles. This seems like a very conservative approach since I am not considering each time series jointly (e.g., each point is considered independent of all others at previous and future times).
Is there a better way to do this?