Additive wavelet analysis with CWT diagnostics — analyze_wavelet

Combines CWT analysis (visualization and significance testing) with MODWT MRA (additive components). CWT is used for diagnostics only; MODWT MRA provides the additive component extraction used downstream.

This function expects analyze_wavelet_spectrum() to be available elsewhere in the package.

Usage

analyze_wavelet_additive(
  series,
  signif = 0.9,
  noise = "red",
  min_period = 2,
  detrend = FALSE,
  filter = c("la8", "haar", "d4", "d6", "d8", "la16"),
  n_levels = NULL,
  boundary = "periodic",
  include_smooth = TRUE,
  max_period_frac = 1/3,
  cwt_mode = c("fast", "complete"),
  diagnostics = FALSE
)

Arguments

series: Numeric vector. Input series (regularly spaced, no missing values).
signif: Numeric scalar in (0, 1). Significance level for CWT.
noise: Character. Background noise model for CWT significance testing. Typically "white" or "red".
min_period: Numeric scalar. Minimum Fourier period for CWT.
detrend: Logical. If TRUE, removes a linear trend before CWT.
filter: Character. MODWT filter name. One of "la8" (default), "haar", "d4", "d6", "d8", "la16".
n_levels: Integer scalar or NULL. MODWT levels. If NULL, chosen from CWT significance (when available) and constrained by stability and max-period caps.
boundary: Character. Boundary handling method. Only "periodic" is supported.
include_smooth: Logical. If TRUE, includes the smooth component SJ.
max_period_frac: Numeric scalar in (0, 1]. No structure beyond this fraction of n. Default is 1/3.
cwt_mode: Character. CWT routine mode. One of "fast" or "complete".
diagnostics: Logical. If TRUE, attaches additional diagnostics (caps and covariance).

Value

A list with class "wavelet_additive". The object contains: - cwt: output from analyze_wavelet_spectrum() - components: additive MODWT MRA components (matrix) - component_names: component column names - periods: representative MODWT periods per component - variance, variance_fraction: component variance and fraction of total - n_levels, filter, filter_length, boundary, include_smooth, max_period_frac - has_significance, cwt_signif_periods: CWT significance flags and periods - cwt_to_modwt_map: MODWT levels implied by significant CWT periods (under caps) - variance-accounting fields copied from modwt_mra() - optional diagnostics list when requested