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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?)

autocorrelation plot

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  • $\begingroup$ 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. $\endgroup$
    – Candamir
    Commented Nov 3, 2018 at 15:32
  • $\begingroup$ 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! $\endgroup$
    – Aesir
    Commented Nov 30, 2018 at 11:07
  • $\begingroup$ forgot to leave page number above, page 587. $\endgroup$
    – Aesir
    Commented Nov 30, 2018 at 11:17

1 Answer 1

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Old thread, worthy question. I've treated block length as a hyperparameter to tune, and plotted how it affected the parameter estimate. $n=1$ is a standard i.i.d. bootstrap, so it helped me visualize how the block bootstrap was affecting the results. Here's a figure to demonstrate, I ended up picking a block size around 20 for this data. Maybe not rigorous, but makes sense to my brain. a plot of the standard deviation of mean error versus block length, converging at a block length of 20

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