func_fdb {boodd}R Documentation

Functional Bootstrap in the Frequency Domain (FDB)

Description

Uses the Frequency Domain Bootstrap (FDB) to compute the bootstrap spectral density, cumulative distribution function for the estimated spectral density, and the quantiles of the standardized distribution.

Usage

func_fdb(
  x,
  B,
  kernel = "normal",
  bandwidth,
  p = 0.5,
  PLT = c("spec", "cdf", NULL)
)

Arguments

x

A vector or time series.

B

A positive integer; the number of bootstrap replications.

kernel

A character string specifying the smoothing kernel. The valid values are:

  • "normal" - default,

  • "epanechnikov",

  • "box" - rectangular kernel.

bandwidth

A real number; the kernel bandwidth smoothing parameter. If unspecified, an optimal value is computed using formula sd(x)*n^(-1/3), which is smaller than the Silverman's rule-of-thumb bandwidth.

p

A vector of the quantiles to be calculated. Default is p = 0.5.

PLT

An argument specifying what to plot:

  • "spec" - spectral density,

  • "cdf" - cumulative distribution,

  • NULL - no plots - default.

Details

The function performs a bootstrap in the frequency domain and computes the specified functionals. It estimates the spectral density using a periodogram smoothed by the specified kernel and bandwidth. The function then computes the cumulative spectral density and quantiles based on this estimation.

Value

The function returns a list of two components:

  1. The boodd object:

    • s: A matrix of size B \times (2n_0 + l_p), where n_0 = \lfloor n/2 \rfloor and l_p is the length of vector p. The first n_0 columns contain bootstrap values of the spectral density at the frequency 2\pi n_0. The columns n_0+1 up to 2n_0 contain values of the cumulative distribution function corresponding to the bootstrap spectral density, and the last l_p columns contain the estimated quantiles.

    • Tn: Estimated values of the spectral density, the estimated cumulative distribution of the spectral density, and the quantiles.

  2. freqs: The vector of frequencies at which the functionals are computed for the process x.

References

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

Bertail, P. and Dudek, A.E. (2021). Consistency of the Frequency Domain Bootstrap for differentiable functionals, Electron. J. Statist., 15, 1-36.

Hurvich, C. M. and Zeger, S. L. (1987). Frequency domain bootstrap methods for time series, Technical Report 87-115, Graduate School of Business Administration, New York Univ.

Lahiri, S.N. (2003). Resampling Methods for Dependent Data. Springer, New York.

See Also

aidedboot,tft_boot, aidedboot, freqboot, per_boo.

Examples


# Choice of sample size 
n <- 1000
# Simulate AR(1) model with parameter 0.6
 x <- arima.sim(list(order=c(1,0,0),ar=0.6),n=n)
 n0=floor(n/2)
 bf=func_fdb(x,199, PLT="spec")
 

[Package boodd version 0.1 Index]