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torbenstaud/maxbootR: Efficient Bootstrap Methods for Block Maxima

The maxbootR package provides fast and consistent bootstrap methods for block maxima, designed for applications in extreme value statistics. Under the hood, performance-critical parts are implemented in C++ via Rcpp, enabling efficient computation even for long time series.

These methods are based on the first consistent bootstrap approach for block maxima as introduced in Bücher & Staud (2024+): Bootstrapping Estimators based on the Block Maxima Method..

You can install the development version of maxbootR from GitHub with:

# install.packages("devtools")
devtools::install_github("torbenstaud/maxbootR")

or from the official CRAN repository in R with:

install.packages("maxbootR")

The following example demonstrates how to extract sliding block maxima from synthetic data.

library(ggplot2)
library(maxbootR)
library(dplyr)
#> 
#> Attache Paket: 'dplyr'
#> Die folgenden Objekte sind maskiert von 'package:stats':
#> 
#>     filter, lag
#> Die folgenden Objekte sind maskiert von 'package:base':
#> 
#>     intersect, setdiff, setequal, union

# Generate 100 years of daily observations
set.seed(91)
x <- rnorm(100 * 365)

# Extract sliding block maxima with 1-year window
bms <- blockmax(xx = x, block_size = 365, type = "sb")

# Create time-indexed tibble for plotting
df <- tibble(
  day = seq.Date(from = as.Date("1900-01-01"), by = "1 day", length.out = length(bms)),
  block_max = bms
)

# Plot the block maxima time series
ggplot(df, aes(x = day, y = block_max)) +
  geom_line(color = "steelblue") +
  labs(
    title = "Sliding Block Maxima from Simulated Data",
    x = "Year",
    y = "Block Maximum"
  ) 

Time series of block maxima from simulated normal data

We now use the maxbootr() function to bootstrap the 100-year return level of synthetic data, comparing the disjoint vs. sliding block bootstrap methods.

# Set block size (e.g., summer days)
bsize <- 92

# Generate synthetic time series
set.seed(1)
y <- rnorm(100 * bsize)

# Bootstrap using disjoint blocks (+timing)
system.time(
  bst.db <- maxbootr(xx = y, est = "rl", block_size = bsize, B = 500, 
                     type ="db", annuity = 100)
)
#>        User      System verstrichen 
#>        0.59        0.03        0.63

# Bootstrap using sliding blocks (+timing)
system.time(
  bst.sb <- maxbootr(xx = y, est = "rl", block_size = bsize, B = 500, 
                     type = "sb", annuity = 100)
)
#>        User      System verstrichen 
#>        6.91        0.08        7.08

# Compare variance
var(bst.sb) / var(bst.db)
#>           [,1]
#> [1,] 0.5502442

The sliding block method typically results in narrower bootstrap distributions, reducing statistical uncertainty.

Histogram of return level bootstrap replicates

For a full tutorial with real-world case studies (finance & climate), check out the vignette included in the package.

The implemented disjoint and sliding block bootstrap methods are grounded in the following foundational works:

• Gumbel, E. J. (1958). Statistics of Extremes. Columbia University Press.
• Ferro, C. A. T. & Segers, J. (2003). Inference for clusters of extreme values. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 65(2), 545–556.

The block bootstrap methodology itself is based on:

• Bücher, A. & Staud, T. (2024+). Bootstrapping estimators based on the block maxima method. arXiv:2409.05529.

I plan to further enhance maxbootR by:

• Adding functionality for computing (size-corrected) confidence intervals
• Providing built-in plotting and diagnostic functions
• Extending estimator support for multivariate block maxima

Your ideas and contributions are welcome — feel free to open an issue or pull request on GitHub!

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