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I have calculated the confidence intervals of the VaR for two assets using iid bootstrap. I compute VaR using historical simulation (non-parametric). So I have two bootstrap confidence intervals (in my case percentile intervals). How can I infer on them? For example, let's say that the two intervals are overlapped: can I say that they represent the same VaR (thus the same risk)? And if they are not overlapped? Do you know if there is some statistical test useful in this case?

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  • $\begingroup$ If they overlap each other, you may say they are statistically the same, but if they do not overlap, then they are different and one must be wrong. $\endgroup$ – Gordon Mar 9 '17 at 21:01
  • $\begingroup$ @Gordon: why would you say that if the confidence intervals do not overlap, one must be wrong? I am considering VaR on two different assets so it is possibe that the risk of one asset is statistically different from the risk of another asset. I do not undertand why one must be wrong. $\endgroup$ – user22108 Mar 14 '17 at 17:20
  • $\begingroup$ I overlooked. they are not really related, and we can not tell which is wrong. $\endgroup$ – Gordon Mar 14 '17 at 21:41

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