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Consider the following: I have sampled yearly stock returns from a specified distribution.

What I want to do is compare how well my sampled distribution fits the empirical distribution of yearly returns. I am not interested in doing goodness of fit tests (e.g. Kolmogorov Smirnov test). Rather, I am interested in comparing the central moments of the sampled and the empirical distribution, say the first 4. However, I only have 30 observations of empirical annual returns, so I cannot have high confidence in my estimates.

Hence, I would like to increase my confidence, and to me it seems like bootstrapping would be a smart way to do this. However, since there is serial correlation in stock returns I cannot apply standard bootstrapping, as it would remove the serial correlation in the data. I have been looking at different types of Block bootstrapping, for example non-overlapping Block, Moving Block and Stationary Block. However, I find it hard to decide on which of the methods is most appropriate for the comparison I want to make.

Obviously, I am not looking for a perfect solution, but I am looking for an acceptable amount of accuracy, with a relatively low degree of complexity. I also emphasize that I am interested in estimating the parameters for the yearly return distribution. Are there any of the above Block bootstrapping techniques which are most appropriate for my usage, and if so, why?

My issue is a bit similar to this post: Empirical distribution function of overlapping time series data

However, I did manage to come to any conclusion by investigating the sources which were referred to in the post above. Hence, I wonder if anyone with more experience regarding bootstrapping methods could shed some light on the above.

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