makewavelets |

Save wavelet decomposition results to the workfile.

Syntax

Series View: series_name.makewaveobj(options)

Options

Basic Options

proc=arg (default=“decomp”) | Wavelet analysis type: “decomp” (transform), “anova” (variance decomposition), “outlier” (outlier detection), “threshold” (threshold - denoising). |

Wavelet Transform Options

transform=arg (default=“dwt”) | Wavelet transform type: “dwt” (discrete wavelet transform – DWT), “modwt” (maximum overlap DWT – MODWT), “mra” (DWT multiresolution analysis – DWT MRA), or “momra” (MODWT MRA). Note that when performing DWT or MRA, 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 and MRA transforms: “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). |

basename=arg (default is series name) | Basename for output: 1. When “transform=dwt” or “transform=modwt”: Wavelet coefficient output will be saved in vectors with names given by basename followed by “_w#” where “#” is the scale level. Scaling coefficient output will be saved in vectors with names given by basename followed by “_v#” where “#” is the scale level. 2. When “transform=mra” or “transform=momra”: Detail output will be saved in vectors with names given by basename followed by “_d#” where “#” is the scale level. Smooth output will be saved in vectors with names given by basename followed by “_s#” where “#” is the scale level. |

Wavelet Variance Decomposition Options

variance=arg (default = “nobias”) | Wavelet variance type: “nobias” (unbiased variance), “bias” (biased variance). |

ci=arg (default = “none”) | Confidence interval type: “none” (no CIs computed), “gauss” (asymptotic normal), “chisq” (asymptotic chi-square), “blimit” (band-limited). |

cilevel=arg (default = 0.95) | Confidence interval coverage as a number between 0 and 1. |

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 and MRA transforms: “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). |

basename=arg (default is series name) | Basename for variance output. Variance output will be saved in vector with name given by basename followed by “_var”. Confidence interval output will be saved in matrix with name given by basename followed by “_varci”. |

Wavelet Threshold and Outlier 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. |

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 and MRA transforms: “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). |

Outlier Output Options

basename=arg (default is series name) | Basename for outlier output (when “proc=outlier”). Output will be saved in vectors with name given by basename followed by “_olr#” where “#” is the scale level. |

Threshold Output Options

basename=arg (default is series name) | Basename for threshold output (when “proc = threshold”): Fit (signal) output will be saved in vector with name given by basename followed by “_sig_th”. Noise output will be saved in vector with name given by basename followed by “_res_th”. Threshold coefficient output will be saved in vectors with names given by basename followed by “_w#_th” (threshold coefficients), and “_v#” (scaling coefficients) where “#” is the scale level. |

Examples

srs.makewaveobj(base=out)

creates vectors OUT_W1, OUT_W2, etc., and OUT_V1, OUT_V2, etc., associated with the wavelet coefficients and scaling coefficients from the DWT using a Haar filter.

srs.makewaveobj(transform=modwt, filter=d, flen=6, base=out)

creates vectors OUT_V1, OUT_V2, etc., associated with the scaling coefficients from the MODWT using a Daubechies filter of length 6.

srs.makewaveobj(proc=anova, maxscale=2, fixlen=median, base=out)

creates the vector OUT_VAR with containing variance decomposition per scale using a DWT with maximum scale 2, and a series length adjustment by padding with median values of the series SRS.

srs.makewaveobj(proc=outlier, base=out)

creates vectors OUT_OLR1, OUT_OLR1, etc. with outlier identifiers using a DWT, Haar filter, soft threshold, universal threshold limit, and Gaussian median computation for the wavelet coefficient variance.

srs.makewaveobj(proc=threshold, transform=modwt, threshtype=hard, threshlim=sureshrink, base=OUT)

creates a vector OUT_SIG_TH containing values for the thresholded series, a vector OUT_RES_TH containing noise values from the thresholding procedure, and vectors OUT_W1_TH, OUT_W2_TH, etc. and OUT_W1_TH, CVEC_W2_TH associated with the thresholded wavelet coefficients and the original scaling coefficient for the series SRS. The underlying computation uses a MODWT with a Haar filter, a hard threshold with a SureShrink threshold limit.Cross-references

Examples

See
“Wavelet Analysis” and
“Wavelet Variance Decomposition” for discussion. See also
“Wavelet Objects”.