Object Reference : Object View and Procedure Reference : Series
Perform wavelet thresholding (denoising) of the series.
Series View: series_name.wavethresh(options)
Basic Options
threshtype=arg (default = “soft”)
Wavelet threshold type: “hard” (hard thresholding), “soft” (soft thresholding).
threshlim=arg (default = “universal”)
Wavelet threshold limit type: “universal” (universal), “adaptive” (universal adaptive), “minimax” (minimax), “sureshrink” (SureShrink), “fdr” (false discovery rate).
If “threshlim=sureshrink”, the grid length may be specified using “ssglen=”.
If “threshlim=fdr”, the significance level may be specified using “fdrsig=”
wavevar=arg (default = “gauss”)
Wavelet coefficient variance method: “mean” (mean absolute deviation), “gauss” (median absolute deviation with Gaussian adjustment), “median” (median absolute deviation), “meanmedian” (mean median absolute deviation).
sslen=arg (default = 10)
Grid length used in determining the SureShrink limit.
fdrsig=arg (default = .05)
Significance level as a number between 0 and 1 for false discovery rate limit determination.
Force the dialog to appear from within a program.
Print results.
Wavelet Transform Options
transform=arg (default=“dwt”)
Wavelet transform type: “dwt” (discrete wavelet transform – DWT), “modwt” (maximum overlap DWT – MODWT). Note that when performing DWT, if the series length is not dyadic, a dyadic fix may be set with the “fixlen=” option
fixlen=arg (default=“mean”)
Fix dyadic lengths in DWT: “zeros” (pad remainder with zeros), “mean” (pad remainder with mean of series), “median” (pad remainder with median of series), “shorten” (cut series length to dyadic length preceding series length).
maxscale=integer (default = max possible)
Maximum scale for wavelet transform.
The max possible is obtained as follows. Let denote the series length and decompose into its dyadic component and a remainder: , . The default maxscale is then set with the following rules:
DWT: (1) if then , otherwise (2) if expanding the series, and (3) if contracting the series .
filter=arg (default=“h”)
Wavelet filter class: “h” (Haar), “d” (Daubechies), “la” (least asymmetric).
If “filter=h” or “filter=la”, the filter length may be specified using “flen=”.
Wavelet filter boundary conditions are specified using the “bound=” option
Wavelet filter excess length as an even number between 2 and 20.
For use when “filter=d” (default= 4) or “filter=la” (default=8).
bound=arg (default = “p”)
Filter boundary handling: “p” (periodic), “r” (reflective).
The line above will perform wavelet thresholding on a series called DGP, using a soft threshold and the universal threshold limit. This procedure is also known as VisuShrink. It will do so up to the third wavelet scale and will use the MAD with a Gaussian correction for the measure of loss.
dgp.wavethresh(filter=d, flen=4, maxscale=1, threshtype=hard, threshlim=fdr)
The line above will perform wavelet thresholding using a Daubechies wavelet filter of length 4, up to the first wavelet scale. Furthermore, it will use a hard threshold and the false discovery rate limit with significance level 0.05.
See “Wavelet Analysis” and “Wavelet Threshold (Denoising)” for discussion. See also “Wavelet Objects”.
See also Series::wavedecomp, Series::waveanova, Series::waveoutlier, and Series::makewavelets.