# 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. – Candamir Nov 3 '18 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! – Aesir Nov 30 '18 at 11:07
• forgot to leave page number above, page 587. – Aesir Nov 30 '18 at 11:17