Description Usage Arguments Details Value Author(s) References See Also Examples

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.

1 |

`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 |

`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. |

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).

An object of class `wd`

but containing coefficients with
respect to the squared wavelets.

Guy Nason

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.

`genwwn.thpower`

,
`sqcoefvec`

,
`sqndwd`

,
`sqndwdecomp`

1 2 3 4 5 6 7 8 | ```
#
# A made-up sequence
#
x <- 1:32
#
# Work out its expansion wrt squared wavelets
#
x.sqwd <- sqwd(1:32)
``` |

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