For background, I have a rudimentary understanding of self-similarity as it applies to observing network traffic as a stochastic process. I also have a robust mathematical background but not in stochastics.
Assume I am looking at two different self-similar processes, X and Y, with respective Hurst parameters: 0.57 and 0.62.
Would it be correct to say that Y is more self-similar than X?
Does being "more self-similar" have any physical meaning? (i.e. smoother more stable transitions)
Is there a distribution for the Hurst parameter itself? I have seen comparison similar to the example above, but no mention of statistical significance. For example would there be a significant change in degree of self-similarity due to a 0.05 change in the Hurst parameter, or a small one? Would that degree of change be different if the 0.05 change were in the middle of the range (like 0.75 to 0.8) or high in the range (0.88 to 0.93)?