How can one evaluate the similarity of non-independent data-sets I have a set of time series from different runs of a computational model. I know that the computational model is highly historical in the sense that the state early in a trial heavily influences (in a non-linear, difficult to summarise way) what the state will be later in that same trial. Accordingly, I understand the data in these time series to be non-independent.
My goal is to show that when I change a particular parameter in the model from Value A to Value B, it has a consistent influence upon the dynamics. When I plot histograms of the state variables, it is clear to me that this is the case, but I am looking for a statistical test that will allow me to say so with less subjectivity.
I don't know how to do so. I have searched around for non-independent statistical tests, but most of what I find are tests for detecting if your data is independent or not. I know that my data is not independent, and this non-independence is an essential feature of my model, so I can't get rid of it.
I have 10 trials of each parameter value. I thought I might divide each of those sets into two groups of 5 trials, thus:

*

*Data Set # 1 : Parameter Value A, trials 0-4

*Data Set # 2 : Parameter Value A, trials 5-9

*Data Set # 3 : Parameter Value B, trials 0-4

*Data Set # 4 : Parameter Value B, trials 5-9

I then could (somehow!) show that Data Set #1 is more similar to Data Set #2 than the amalgamation of Data Set #1 and #2 is to the amalgamation of Data Sets #3 and #4.
...and similarly show that Data Set #3 is more similar to Data Set #4 than the amalgamation of Data Set #1 and #2 is to the amalgamation of Data Sets #3 and #4.
Is that a good plan? If so, what measures of similarity should I learn about that can be applied to non-independent data?

You say: "My goal is to show that when I change a particular parameter in the model from Value A to Value B, it has a consistent influence upon the dynamics." For doing that, you need some metric $M$ (e.g. some numeric value) that describes this "influence upon the dynamics". E.g., if the change in dynamics is a change in variance (fluctuation, volatility) in the time series, then this would be your metric $M$.
Once you have that, the rest is fairly standard statistics. You simply check whether the ten values of $M$ obtained with A are significantly different from the ten values of $M$ obtained with B. Depending on what you can assume about the data, you could look into e.g. the t-test or the Mann–Whitney U test.
Note, that the question of what inner dependencies (auto-correlation) your time series are having is not really relevant in this approach.
