boot_local {boodd}R Documentation

TFT Local Bootstrap.

Description

The local bootstrap is used to bootstrap the Fourier coefficients for the Time Frequency Toggle (TFT)-Bootstrap (see Kirch and Politis (2011)).

Usage

boot_local(X, n = length(X), h, kernel, t)

Arguments

X

A numeric vector representing a time series.

n

An integer; by default is the length of time series X but allow for a smaller sample size m to perform moon bootstrap.

h

A numeric value specifying the bandwidth used to compute the kernel estimator in case of local bootstrap. By default it is equal to n^{-2/3}.

kernel

An integer value indicating the kernel type. Use 0 for the Daniell kernel or any other value for the Bartlett-Priestley (Epanechnikov) kernel (by default).

t

An integer indicating the number of bootstrap replications.

Details

The function first centers X by subtracting its mean, calculates the Fourier coefficients using the Fast Fourier Transform (FFT), and computes resampling probabilities based on the specified kernel kernel and bandwidth h. These probabilities are used to select random Fourier coefficients, which are then transformed back to generate standardized bootstrap replicates.

Value

A matrix where each column contains a bootstrap replicate of the time series X.

Author(s)

We are grateful to Claudia Kirch for providing the original code in R.

References

Bertail, P. and Dudek, A. (2025). Bootstrap for Dependent Data, with an R package (by Bernard Desgraupes and Karolina Marek) - submitted.

Kirch, C. and Politis, D. N. (2011). TFT-Bootstrap: Resampling time series in the frequency domain to obtain replicates in the time domain, Annals of Statistics, vol.

See Also

tft_boot, boot_res, boot_wild.

Examples

# see the mother function tft_boot

[Package boodd version 0.1 Index]