R: A function to compute CNLT spectral quantities for univariate...

cnlt.spec

R Documentation

A function to compute CNLT spectral quantities for univariate and bivariate series

Description

The function takes a nondecimated complex lifting decomposition of a univariate or bivariate series, and uses smoothing before computing spectral quantities such as the complex periodograms, coherence and phase

Usage

cnlt.spec(x, ...)
## S3 method for class 'SG'
cnlt.spec(x, M = 50, fact = 1, ...)
## S3 method for class 'DG'
cnlt.spec(x, M = 50, fact = 1, ...)

Arguments

`x`	An object of class `cnlt`, i.e. the output from either `cnlt.univ` or `cnlt.biv`.
`M`	The smoothing parameter (binwidth) or vector of smoothing parameters (one for each scale) for the time-domain kernel smoothing method, see `smooth.over.time`.
`fact`	If `length(M)==1`, a factor indicating how the smoothing parameter (binwidth) in the time-domain kernel smoothing method should increase from one scale to the next, see `smooth.over.time`.
`...`	Any other parameters to be passed to the scale smoothing function, see the documentation for `smooth.over.scale` for univariate `cnlt` objects, or `pre.per` for bivariate `cnlt` objects.

Details

For univariate series, the nondecimated complex lifting object can be used to form a spectral object by smoothing the squared details over scale (with smooth.over.scale), and then smoothing over time (using smooth.over.time). Smoothing over scale is done via smooth.spline; smoothing over time is done with a kernel smoother (e.g. a "box" kernel for a moving average). See Hamilton et al. (2018) for more details.

Value

An object of class cnlt.spec (subclasses: DG, SG, univ, biv).

For subclass univ, a list with components:

`S1`	A spectral object (matrix) of dimension `length(mscale) x length(mtime)`, corresponding to the spectrum of the univariate series.
`mscale`	A vector of scales corresponding to the rows of the spectrum `S1` (after smoothing the periodogram), see `smooth.over.scale`.
`mtime`	The vector `cnltobj$x`, the vector of times corresponding to the columns of the spectrum `S1`.

For subclass biv, a list with components:

`coh`	A matrix of dimension `length(mscale) x length(mtime)`, corresponding to the coherence between the two components of the bivariate series.
`phase`	A matrix of dimension `length(mscale) x length(mtime)`, corresponding to the phase between the two components of the bivariate series.
`C`	A matrix of dimension `length(mscale) x length(mtime)`, corresponding to the co-periodogram of the bivariate series.
`Q`	A matrix of dimension `length(mscale) x length(mtime)`, corresponding to the quadrature periodogram of the bivariate series.
`S1`	A matrix of dimension `length(mscale) x length(mtime)`, corresponding to the spectrum of the first component of the bivariate series.
`S2`	A matrix of dimension `length(mscale) x length(mtime)`, corresponding to the spectrum of the second component of the bivariate series.
`mscale`	A vector of scales corresponding to the rows of the spectrum `S1` (after smoothing the periodogram), see `smooth.over.scale`.
`mtime`	A vector of times corresponding to the columns of the spectrum `S1`. If the class of `cnlt.obj` is `SG`, this is `cnlt.obj$x1`, else this is a vector formed by binning detail coefficients within equal intervals of time, see `pre.per` for more details.

Author(s)

Matt Nunes, Jean Hamilton

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.

Examples


# read some data in (a bivariate series)

## Not run: 

data(Baidu)
data(Google)

BaiGoo<-cnlt.biv(Baidu$Seconds[1:100], Google$Seconds[1:100], Baidu$Return[1:100], 
Google$Return[1:100], P = 500)

specobj<-cnlt.spec(BaiGoo,M=10,fact=1.05, Tstar=20)

## End(Not run)