sqwd {hwwntest}

Compute expansion with respect to squared wavelets.

Description

Compute expansion with respect to squared wavelets. See help for sqndwd. The coefficients are the projection of the input sequence onto the set of functions being the squares of the usual wavelets. This operation is most useful for computing variances of wavelet coefficients.

Usage

sqwd(x, filter.number = 10, family = "DaubExPhase", type = "station", m0 = 3)

Arguments

x

Sequence that you wish to compute expansion for.

filter.number

Base wavelet family (no. of vanishing moments) you wish to use.

family

The base wavelet family you wish to use.

type

Either station for the non-decimated transform or wavelet for the regular wavelet transform.

m0

The number of scales down (finer) from the scale of the squared wavelet being approximated. Usually, 2 or 3 is enough. Many more scales results in a better approximation but at a higher cost as the number of coefficients at consecutive scales doubles.

Details

This function is an implementation of the ‘powers of wavelets’ idea from Herrick (2000), Barber, Nason and Silverman (2002) and, for the associated mod-wavelets by Fryzlewicz, Nason and von Sachs (2008).

Value

An object of class wd but containing coefficients with respect to the squared wavelets.

Author(s)

Guy Nason

References

Barber, S., Nason, G.P. and Silverman, B.W. (2002) Posterior probability intervals for wavelet thresholding. J. R. Statist. Soc. B, 64, 189-206.

Fryzlewicz, P., Nason, G.P. and von Sachs, R. (2008) A wavelet-Fisz approach to spectrum estimation. J. Time Ser. Anal., 29, 868-880.

Herrick, D.R.M. (2000) Wavelet Methods for Curve Estimation, PhD thesis, University of Bristol, U.K.

See Also

genwwn.thpower, sqcoefvec, sqndwd, sqndwdecomp

Examples

#
# A made-up sequence
#
x <- 1:32
#
# Work out its expansion wrt squared wavelets
#
x.sqwd <- sqwd(1:32)