wavethresh |

Perform wavelet thresholding (denoising) of the series.

Syntax

Series View: series_name.wavethresh(options)

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. |

prompt | Force the dialog to appear from within a program. |

p | 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 . MODWT: . |

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 |

flen=integer | 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). |

Examples

dgp.wavethresh(maxscale=3)

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.

Cross-references

See
“Wavelet Analysis” and
“Wavelet Threshold (Denoising)” for discussion. See also
“Wavelet Objects”.