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I have an agent-based simulation that generates a time series in its output for my different treatments. I am measuring performance through time, and at each time tick the performance is the mean of 30 runs (30 samples). In all of the treatments the performance starts from near 0 and ends in 100%, but with different speed. I was wondering if there is any stochastic model or probabilistic way to to compare the speed or growth of these time series. I want to find out which one "significantly" grows faster.

Thanks.

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Assuming you're using a pre-canned application, then there will be an underlying distribution generating your time series. I would look in the help file of the application to find this distribution.

Once you know the underlying distribution, then "significance" is determined the usual way, namely pick a confidence level, and test for the difference between two random variables.

The wrinkle is to do with the time element. If your "treatments" are the result of an accumulation of positive outcomes, then each time series is effectively a sum of random variables, and each term in that sum is itself the result of a mean of 30 samples from the underlying distribution.

So, although the formulation is different, the treatment of significance is the same.

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