# Picking block length in a block bootstrap

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?) • This answer by @conjugateprior might be helpful. Two further sources are Bühlmann & Künsch (1999) and Politis & White (2004). Unfortunately I'm not knowledgeable enough about the subject to actually write an answer. Nov 3, 2018 at 15:32
• I have seen it written that an optimal block size is given by $O(n^{1/3})$ (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! Nov 30, 2018 at 11:07
• forgot to leave page number above, page 587. Nov 30, 2018 at 11:17