Package 'maxbootR'

Compute Block Maxima from a Time Series

Description

Extracts block maxima from a univariate numeric vector or matrix using disjoint, sliding, or circular (k-dependent) block schemes.

Usage

blockmax(xx, block_size, type = "sb", k = 2)

Arguments

xx	A numeric vector or matrix. For matrix input, each row is treated as a separate univariate series.
block_size	Positive integer. Size of each block for maxima extraction.
type	Character. Type of block maxima to compute. One of: "db" (disjoint blocks), "sb" (sliding blocks), or "cb" (circular blocks with k offsets).
k	Integer (only used if type = "cb"). Blocking parameter which controls the number of blocks contained in a block of blocks. Must be an integer between 1 and floor(length(xx) / block_size).

Value

A numeric vector (if xx is a vector) or a matrix (if xx is a matrix). Each entry contains block maxima computed according to the selected method.

Examples

if (requireNamespace("maxbootR", quietly = TRUE)) {
  set.seed(42)
  x <- rnorm(100)

  # Disjoint blocks of size 10
  bm_db <- blockmax(xx = x, block_size = 10, type = "db")

  # Sliding blocks of size 10
  bm_sb <- blockmax(xx = x, block_size = 10, type = "sb")

  # Circular blocks of size 10 with blocking parameter k = 2
  bm_cb <- blockmax(xx = x, block_size = 10, type = "cb", k = 2)
}

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Example Log Return Time Series

Description

A tibble containing daily negative log returns of closing prices for the S&P 500 stock market index. The observation period spans 20 trading years: 1995-01-01 to 2024-12-31.

Usage

data(logret_data)

Format

A tibble with 7,550 rows and 2 columns:

day

Date of observation (class Date)

neg_log_ret

Negative log return (numeric)

Details

The data was obtained using the quantmod package with Yahoo Finance as the source.

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Bootstrap Estimation for Block Maxima

Description

Performs bootstrap resampling for various block maxima estimators (mean, variance, GEV parameters, quantile, return level) using either disjoint or sliding block methods.

Usage

maxbootr(
  xx,
  est,
  block_size,
  B = 1000,
  type = "sb",
  seed = 1,
  p = NULL,
  annuity = NULL
)

Arguments

xx	A numeric vector or array containing univariate samples. For multivariate cases, samples should be arranged in rows.
est	A string specifying the estimator to apply. Must be one of "mean", "var", "gev", "quantile", or "rl".
block_size	Integer. Size of each block used in the block maxima extraction.
B	Integer. Number of bootstrap replicates to generate.
type	Type of block bootstrapping: "db" for disjoint blocks or "sb" for sliding blocks (internally approximated via circular blocks).
seed	Integer. Seed for reproducibility.
p	Optional numeric value in (0,1). Required if est = "quantile".
annuity	Optional numeric value > 1. Required if est = "rl" for return level estimation.

Value

A numeric vector with B rows for scalar estimators. If est = "gev", a matrix with B rows is returned. Each row contains 3 estimated GEV parameters (location, scale, shape).

Examples

if (requireNamespace("maxbootR", quietly = TRUE)) {
  library(maxbootR)
  set.seed(123)
  x <- rnorm(100)

  # Bootstrap mean using sliding blocks
  boot_mean <- maxbootr(x, est = "mean", block_size = 10, B = 20, type = "sb")

  # Bootstrap variance using disjoint blocks
  boot_var <- maxbootr(x, est = "var", block_size = 10, B = 20, type = "db")

  # Bootstrap 95%-quantile of block maxima using sliding blocks
  boot_q <- maxbootr(x, est = "quantile", block_size = 10, B = 20, type = "db", p = 0.95)
}

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Example Temperature Time Series

Description

This dataset contains daily temperature measurements in °C from the Hohenpeißenberg weather station in Germany, covering 145 years: 1878-01-01 to 2023-12-31.

Usage

data(temp_data)

Format

A tibble with 52,960 rows and 2 columns:

day

Date of observation (class Date)

temp

Temperature measured in °C (numeric)

Details

The data was obtained from the Open Data Server of the German Meteorological Service (Deutscher Wetterdienst, DWD): https://opendata.dwd.de/ and thus, is protected by law. It is reused under the Creative Commons license CC BY 4.0.

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