smooth.over.scale {CNLTtsa}

Function to perform smoothing over scale of spectral quantities

Description

This function uses simple averaging or smoothing splines to smooth spectra over scale

Usage

smooth.over.scale(x, det1, det2, lre, lreA, scale.range = NULL, Arange = NULL, 
Jstar = 20, splines = FALSE, positive = FALSE, dfS = 10, interpolate = FALSE)

Arguments

x

A vector corrsponding to the sampling grid of the component of a univariate series, or both components of a bivariate series with identical sampling grids.

det1

A list of (real or imaginary parts of) the component 1 detail coefficients from a CNLT decomposition, such as from the output of cnlt.biv.

det2

A list of (real or imaginary parts of) the component 2 detail coefficients from a CNLT decomposition, such as from the output of cnlt.biv.

lre

A list of scales (removed integral lengths) corresponding to det from a CNLT decomposition, such as from the output of cnlt.biv.

lreA

A list of asymmetry values from a CNLT decomposition, such as from the output of cnlt.biv.

scale.range

An optional two-vector specifying the range of scales to be considered in the resulting output spectrum.

Arange

An optional two-vector specifying whether the values used in forming the output spectrum should be limited to those from a specific range of asymmetry values, see Sanderson (2010), chapter 6.2.

Jstar

The number of artificial scales in the output spectrum.

splines

An indicator variable whether smoothing splines should be used for the scale-based smoothing, or simple averaging (splines = FALSE).

positive

An indicator variable whether the smoothing should ensure that the resulting output is positive or not (e.g. for spectra).

dfS

An argument, if splines = TRUE, specifying the number of degrees of freedom for the smoothing spline.

interpolate

An indicator variable for whether interpolation should be used in the smoothing spline method for predicting values outside the range of the data.

Details

For a univariate series or a bivariate series where the two components have the same sampling grids, the co- /quadrature periodogram values are first formed. They are then smoothed over scale (per timepoint), to give spectral values corresponding to equal artificial levels by setting Jstar and optionally scale.range.

Value

A list with the following components:

spec

A matrix of dimension Jstar x length(x) corrsponding to a periodogram / co-periodogram / quadrature periodogram.

mscale

A vector of scales (of length Jstar) corresponding to the rows of the spectrum spec.

Author(s)

Jean Hamilton, Matt Nunes

References

Hamilton, J., Nunes, M. A., Knight, M. I. and Fryzlewicz, P. (2018) Complex-valued wavelet lifting and applications. Technometrics, 60 (1), 48-60, DOI 10.1080/00401706.2017.1281846.

See Also

cnlt.spec.SG

Examples

x<-sort(runif(100))

y <-sin(2*pi*(1/25)*x) + sin(2*pi*(1/50)*x)

## Not run: 
xy.dec<-cnlt.univ(x,y,P=300)

# compute the real part of the spectrum (real details^2) and smooth over scale
ReS <- smooth.over.scale(x, sapply(xy.dec$det1,Re), sapply(xy.dec$det1,Re), xy.dec$lre, 
xy.dec$lreA, positive = TRUE)

## End(Not run)