# How to determine block size for a block bootstrap and it's variants?

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.