modernBoot (version 0.1.1)

stationary_boot: Stationary Bootstrap (Politis & Romano)

Description

Performs stationary bootstrap for dependent data with random block lengths. More flexible than fixed-block bootstrap for time series with variable dependence.

Usage

stationary_boot(x, p = 0.1, R = 1000)

Value

A list of length R. Each element is a numeric vector of length n (matching original series). Unlike moving block bootstrap, block lengths vary randomly following geometric distribution, avoiding artificial periodicity. Replicates preserve local dependence structure more flexibly than fixed-block methods.

Arguments

x

numeric vector or time series object. Should be univariate time series with temporal dependence. Length n >= 2 required. If ts object, frequency information is not preserved in output.

p

numeric probability parameter controlling average block length (default 0.1). Must satisfy 0 < p <= 1. Average block length approximately 1/p: set p = 0.1 for average blocks of ~10 observations, p = 0.05 for ~20 observations. Smaller p values preserve longer-range dependence; larger p values reduce distortion.

R

integer number of bootstrap replicates (default 1000). Each replicate is complete time series of length n with random block structure. Must be >= 1.

Details

The stationary bootstrap uses random block lengths drawn from a geometric distribution. This avoids artificial periodicity inherent in fixed-block methods. Set p = 1/m to have average block length approximately m.

Examples

set.seed(42)
x <- arima.sim(n = 100, list(ar = 0.7))
# Average block length of 10: p = 0.1
result <- stationary_boot(x, p = 0.1, R = 100)
length(result)  # 100 bootstrap replicates