freqboot {boodd}R Documentation

Frequency Domain Bootstrap

Description

Implements the Frequency Domain Bootstrap (FDB) for time series data.

Usage

freqboot(x, XI, g, B, kernel = "normal", bandwidth)

Arguments

x

A vector or time series.

XI

A list of functions defined on the interval [0, \pi].

g

A numeric function accepting length(XI) arguments, used to compute the statistic of interest.

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.

Details

The input series x is assumed to be a sample from a real-valued, zero-mean, stationary time series. The XI argument consists of functions \xi_i used to define linear functionals of the spectral density, say A(\xi,f)=\int\xi_i(\omega)f(\omega)d\omega. The statistic estimates T(f)=g(A(\xi,f)). The spectral density is estimated by smoothing the periodogram of the series, with the smoothing kernel specified by kernel and the smoothing parameter bandwidth. The FDB consists in resampling periodogram ordinates standardized by the spectral density estimates to recompute the bootstrap values of the statistics of interest.

Value

Returns an object of class boodd.

References

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

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.

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

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

See Also

aidedboot, func_fdb, per_boo, tft_boot.

Examples

set.seed(123)
n <- 120
x <- arima.sim(list(order=c(1,0,0),ar=0.7),n=n)
B <- 999
one <- function(x) {1}
XI <- list(cos,one)
g <- function(x,y) {return(x/y)}
# This gives an estimate for the autocorrelation of order 1
boo = freqboot(x,XI,g,B,"normal")
plot(boo)

[Package boodd version 0.1 Index]