I am working with a large timeseries (millions data points) spread across 5 years from which I would like to estimate the annual maxima distribution and subsequently a quantile of this distribution.
My approach is as follows:
- First estimate the daily maxima distribution using the Block Maxima method, from which it would be reasonable to obtain a good fit with 365*5 points.
- From this daily maxima distribution, generate 1000 samples of size 365 and extract the maximum for every sample.
- Fit an extreme value distribution to estimate the annual maxima distribution on this generated synthetic data.
I read here and there that bootstrapping was usually not advised to estimate extreme statistics. Given my approach is slightly hybrid, would it make sense to estimate the annual maxima distribution in such a way?
