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(This is related to my (so far unanswered) last question)

I want to use residual bootstrap to examine uncertainty and robustness of a model that fits a series of environmental measurements. I know close to nothing about the structure of my data's noise. It appears to be heteroskedastic and may (!) be autocorrelated in some cases (I have a few different data sets). Would the most simple form of the wild bootstrap (switching signs of the residuals with 50 % probability) be valid in this context, or would I have to rely on harder to implement methods like (moving) block bootstrapping because of possible autocorrelation?

Please stop me if I'm completely off the track; while the idea of bootstrapping is more or less easy to understand, the many available variants are extremely confusing to a newcomer.

/edit: Just to be clear: I want to resample the residuals (as an estimate for the error), not the time-series itself.

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Have you read this paper:

Cameron, A. C., Gelbach, J. B., & Miller, D. L. (2008). Bootstrap-Based Improvements for Inference with Clustered Errors. Review of Economics and Statistics, 90(3), 414–427. https://doi.org/10.1162/rest.90.3.414

For wild bootstrapping when you suspect clustering, this is probably the most comprehensive review. Essentially yes, you may have to use block wild bootstrapping. Luckily, block wild bootstrapping is implemented in the multiwayvcov (cluster.boot() function) and clusterSEs packages (cluster.wild.glm() function) in R.

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