I have a question concerning bootstrap technique. So I have been working with one trading strategy and I have a sample of observations that relate the volatility of the stock to its return, roughly. So I have 2-tuple observations of the form $(x_i,y_i), \ (i: 1 \leq i \leq 500)$, where $x_i$ is the volatility and $y_i$ is the return associated with that volatility. There is a small bump in the range of zero to $10\%$ volatility and I would like to investigate whether it is statistically significant. Since there is only one strategy, my sample is my population, so I thought I should perform the bootstrapping on these 2-tuples. I obtain the samples of the same length for each bootstrap run with the randomized observations from the initial sample (however if bootstrap picks $x_2$ for example, then I have to select $y_2$ to complete the pair, so I perform the bootstrapping on the pairs).

How would I now actually test that that bump is significant? Would I perform the bootstrap just on observations that have volatility less than $10\%$ and then construct some sorts of skewness measure and compute that skewness measure for each of the bootstrap runs? And how would I then be able to conclude that the bump is significant, what kind of statistical confidence measure would I have to construct?

Here is how the graph looks like, when the tuples are plotted.

enter image description here

EDIT: Perhaps compute the skewness and then compute the confidence interval of the skewness measures and inspect whether the skewness of the "genuine" sample is in that confidence interval?


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