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I am working with time series data and wish to use bootstrapping to compute confidence intervals of the mean prediction of my model's accuracy.

My data is not i.i.d and therefore I need to use a variant of the bootstrapping technique, either Block Bootstrap (BB), Stationary Bootstrap (SB) or Moving Block Bootstrap (MBB). For the moment I am concerning myself with the SB.

To perform the stationary bootstrap I need to pick a block size with which the bootstrapped data sets will be constructed. As the SB only requires a mean block size to be specified this is my first choice.

I want to know how to pick what the block size $b$ should be? I assume it will be dependent on each time series. I found this question but it is as of yet unanswered.

I have seen it written here (page 587) that optimal $b$ is given by $O(n^{\frac{1}{3}})$ although no proof or explanation is provided.

I am aware this topic is discussed in the book 'Resampling methods for dependent data' chapter 7 but it is too technical for me to easily obtain an answer from.

What I am after is a set of rules which I could program to automatically determine a block size that is considered to be optimal. A justification for why $O(n^{\frac{1}{3}})$ would be great.

If the optimal $b$ is dependent on the use case of the datasets then I am using it to generate many similar time series so I can perform $B$ evaluations of my model. I then wish to compute uncertainties for the average accuracy of the $B$ measures.

Aesir
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Not sure if you still need this, but the classic texts are on subject are Hall and Horowitz "On Blocking Rules for the Bootstrap with Dependent Data", Lahiri "Theoretical Comparisons of Block Bootstrap Methods", in addition to the Lahiri book you mentioned. I found Hongyi Li and Maddala "Bootstrapping Time Series Models" useful as well. I'm writing my Masters dissertation on the subject so if I can be of any other help please let me know.

Michael R. Chernick
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John Siryj
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  • Lahiri also has a book on bootstrapping with dependent data. – Michael R. Chernick Jun 06 '19 at 23:49
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    The book he referenced in his original comment was the Lahiri book. To be honest if you are on this thread I have no right to talk. Your research into the topic is much better than mine. – John Siryj Jun 06 '19 at 23:58
  • I appreciate your answer. i think you gave the OP a lot to look at. – Michael R. Chernick Jun 07 '19 at 00:10
  • Thanks for the answer, sorry I haven't had time to respond. I emailed the author of the draft book that I posted in my question in the second link. He did reply to me and recommended the following resource for automatic bootstrap selection by Politis and White: http://www.math.ucsd.edu/~politis/SBblock-revER.pdf. I used it to solve the issue I was having at the time. I am not working on the project anymore so haven't posted a full answer as I can't remember the specifics, but the question got an upvote recently so thought I'd post this in the meantime. – Aesir Jan 07 '20 at 13:00