An adaptive orthonormal basis is selected in order to perform the
naive bootstrap within nodes of the wavelet packet tree. A bootstrap
realization of the time series is produce by applying the inverse
DWPT.
Name of the wavelet filter to use in the decomposition. See
wave.filter for those wavelet filters available.
J
Depth of the discrete wavelet packet transform.
p
Level of significance for the white noise testing procedure.
frac
Fraction of the time series that should be used in
constructing the likelihood function.
Details
A subroutines is used to select an adaptive orthonormal basis for the
piecewise-constant approximation to the underlying spectral density
function (SDF). Once selected, sampling with replacement is performed
within each wavelet packet coefficient vector and the new collection
of wavelet packet coefficients are reconstructed into a bootstrap
realization of the original time series.
Value
Time series of length $N$, where $N$ is the length of y.
Author(s)
B. Whitcher
References
Percival, D.B., S. Sardy, A. Davision (2000)
Wavestrapping Time Series: Adaptive Wavelet-Based Bootstrapping,
in B.J. Fitzgerald, R.L. Smith, A.T. Walden, P.C. Young (Eds.)
Nonlinear and Nonstationary Signal Processing, pp. 442-471.
Whitcher, B. (2001)
Simulating Gaussian Stationary Time Series with Unbounded Spectra,
Journal of Computational and Graphical Statistics, 10,
No. 1, 112-134.
Whitcher, B. (2004)
Wavelet-Based Estimation for Seasonal Long-Memory Processes,
Technometrics, 46, No. 2, 225-238.