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Got a question regarding the usefulness of the bootstrap in generating scenarios. Say we have a random walk with drift process:

x = 0.005 + 0.01dZ

where dZ is a N(0,1) process. Now, assume we generate 1000 observations from this process, but by slim chance, the data sample actually has a negative drift (i.e. one of the unlikely events that can be generated by the process). Now further assume this data sample is what we observe so far in real life and we do not know what the underlying data generating process is.

So, if we use the bootstrap to generate mutilple scenarios using the data sample to estimate its mean, we will surely get a negative number although the actual mean or drift is +0.005.

Am I using the bootstrap in the wrong way? Perhaps the use of the bootstrap is more to do with simulating the variance and not the mean? Would appreciate any thoughts and do let me know if any part of my problem is unclear. Thanks!

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# Question on the bootstrap

Can you offer guidance or do you also need help?

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