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 |
g |
A numeric function accepting |
B |
A positive integer; the number of bootstrap replications. |
kernel |
A character string specifying the smoothing kernel. The valid values are:
|
bandwidth |
A real number; the kernel bandwidth smoothing parameter.
If unspecified, an optimal value is computed using formula |
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)