ewspec: Compute evolutionary wavelet spectrum estimate.

Description

This function computes the evolutionary wavelet spectrum (EWS) estimate from a time series (or non-decimated wavelet transform of a time series). The estimate is computed by taking the non-decimated wavelet transform of the time series data, taking its modulus; smoothing using TI-wavelet shrinkage and then correction for the redundancy caused by use of the non-decimated wavelet transform. Options below beginning with smooth. are passed directly to the TI-wavelet shrinkage routines.

Usage

ewspec(x, filter.number = 10, family = "DaubLeAsymm",
        UseLocalSpec = TRUE, DoSWT = TRUE, WPsmooth = TRUE, verbose = FALSE,
        smooth.filter.number = 10, smooth.family = "DaubLeAsymm", smooth.levels = 3:(nlevelsWT(WPwst) - 1), smooth.dev = madmad, smooth.policy =
        "LSuniversal", smooth.value = 0, smooth.by.level = FALSE, smooth.type = "soft", smooth.verbose = FALSE, smooth.cvtol = 0.01, smooth.cvnorm = l2norm, smooth.transform = I, smooth.inverse = I)

Arguments

The time series that you want to analyze. (See DETAILS below on how to supply preprocessed versions of the time series which bypass early parts of the ewspec function).

filter.number

This selects the index of the wavelet used in the analysis of the time series (i.e. the wavelet basis functions used to model the time series). For Daubechies compactly supported wavelets the filter number is the number of vanishing moments.

family

This selects the wavelet family to use in the analysis of the time series (i.e. which wavelet family to use to model the time series). Only use the Daubechies compactly supported wavelets DaubExPhase and DaubLeAsymm.

UseLocalSpec

If you input a time series for x then this argument should always be T. (However, you can precompute the modulus of the non-decimated wavelet transform yourself and supply it as x in which case the

DoSWT

If you input a time series for x then this argument should always be T. (However, you can precompute the non-decimated wavelet transform yourself and supply it as x in which case the wd call within the f

WPsmooth

Normally a wavelet periodogram is smoothed before it is corrected. Use WPsmooth=F is you do not want any wavelet periodogram smoothing (correction is still done).

verbose

If this option is T then informative messages are printed as the function progresses.

smooth.filter.number

This selects the index number of the wavelet that smooths each scale of the wavelet periodogram. See filter.select for further details on which wavelets you can use. Generally speaking it is a good id

smooth.family

This selects the wavelet family that smooths each scale of the wavelet periodogram. See filter.select for further details on which wavelets you can use. There is no need to use the same family as you used to analyse the time series.

smooth.levels

The levels to smooth when performing the TI-wavelet shrinkage smoothing.

smooth.dev

The method for estimating the variance of the empirical wavelet coefficients for smoothing purposes.

smooth.policy

The recipe for smoothing: determines how the threshold is chosen. See threshold for TI-smoothing and choice of potential policies. For EWS estimation LSuniversal is recommended for thi Chi-sq

smooth.value

When a manual policy is being used this argument is used to supply a threshold value. See threshold for more information.

smooth.by.level

If TRUE then the wavelet shrinkage is performed by computing and applying a separate threshold to each level in the non-decimated wavelet transform of each scale. Note that each scale in the EWS is smoothed separately and independently: and e

smooth.type

The type of shrinkage: either "hard" or "soft".

smooth.verbose

If T then informative messages concerning the TI-transform wavelet shrinkage are printed.

smooth.cvtol

If cross-validated wavelet shrinkage (smooth.policy="cv") is used then this argument supplies the cross-validation tolerance.

smooth.cvnorm

no description for object

smooth.transform

The transform function to use to transform the wavelet periodogram estimate. The wavelet periodogram coefficients are typically chi-squared in nature, a log transform can pull the coefficients towards normality so that a smooth.policy

smooth.inverse

the inverse transform of smooth.transform.

`Value`

A list with the following components:
SThe evolutionary wavelet spectral estimate of the input x. This object is of class wd and so can be plotted, printed in the usual way.
WavPerThe raw wavelet periodogram of the input x. The EWS estimate (above) is the smoothed corrected version of the wavelet periodgram. The wavelet periodogram is of class wd and so can be plotted, printed in the usual way.
rmThis is the matrix A from the paper by Nason, von Sachs and Kroisandt. Its inverse is used to correct the raw wavelet periodogram. This matrix is computed using the ipndacw function.
irmThe inverse of the matrix A from the paper by Nason, von Sachs and Kroisandt. It is used to correct the raw wavelet periodogram.

`RELEASE`

`Details`

This function computes an estimate of the evolutionary wavelet spectrum of a time series according to the paper by Nason, von Sachs and Kroisandt. The function works as follows: 
[object Object],[object Object],[object Object],[object Object]
To display the EWS use the plotfunction on the S component, see the examples below. 
It is possible to supply the non-decimated wavelet transform of the time series and set DoSWT=F or to supply the squared modulus of the non-decimated wavelet transform using LocalSpec and setting UseLocalSpec=F. This facility saves time because the function is then only used for smoothing and correction.

`References`

Nason, G.P., von Sachs, R. and Kroisandt, G. (1998). Wavelet processes and adaptive estimation of the evolutionary wavelet spectrum. Technical Report, Department of Mathematics University of Bristol/ Fachbereich Mathematik, Kaiserslautern.

`See Also`

Baby Data, filter.select, ipndacw, LocalSpec, threshold wd wd.object

`Examples`

Run this code#
# Apply the EWS estimate function to the baby data
#
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