I have created an artificial stock market where different groups of traders trade with each other and therefore influence the asset price as well as the returns on the asset. The model generates 10k+ observations of prices and returns which I will split into subsamples of about 500 observations.
My main interest lies in the comparison of two generated datasets. The first one is without any additional constraints and the second one contains a special constraint. What are the possibilities to compare these 2 datasets? The easiest thing I can think of is to compare the mean and standard deviation of these series. By visual inspection it is possible that the second dataset is more volatile than the first one. How do I test for the significance of this?
Is it possible to use the t-test, subtract the e.g. returns of dataset2 from the returns of dataset1 and test for $H_0$: µ = 0 vs. $H_1$: µ != 0 even though returns exhibit fat tails?