I am using the Mann-Kendall test to assess trends in a data time-series. I believe there is autocorrelation in my data and therefore need to use a block bootstrap to correct for it. I have plotted the autocorrelation to try to determine the block size to use in my block bootstrap. I have not found many resources on how to select this block? Comparing one example to my data I thought I should pick a length of $15$ as at lag $=15$ the points stay within the autocorrelation intervals (blue lines) but another source said $2-4$ is usually a sufficient block length and that a block length of $1/4$ of the sample size ($n$) can make the test insignificant. My data $n=64$ so $15$ is approaching $1/4$ of the sample size. How can I tell the best block size to pick from this plot (or another method?)
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[This answer by @conjugateprior](https://stats.stackexchange.com/a/25721/182174) might be helpful. Two further sources are [Bühlmann & Künsch (1999)](https://pdfs.semanticscholar.org/5a4e/382cf6ed63b9fbdcad66338cc4f516926676.pdf) and [Politis & White (2004)](https://public.econ.duke.edu/~ap172/Politis_White_2004.pdf). Unfortunately I'm not knowledgeable enough about the subject to actually write an answer. – Candamir Nov 03 '18 at 15:32
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I have seen it written that an optimal block size is given by $O(n^{1/3})$ (http://www.stat.cmu.edu/~cshalizi/ADAfaEPoV/ADAfaEPoV.pdf) although no proof is provided. $n$ is the length of the data. Chapter 7 in 'Resampling methods for dependent data' discusses it at length but so far it is too theoretical for me! – Aesir Nov 30 '18 at 11:07
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forgot to leave page number above, page 587. – Aesir Nov 30 '18 at 11:17