Skip to contents

SAZED: Spectral-ACF Zero-crossing Ensemble Detection

Source: R/seasonal.R
sazed.Rd

A parameter-free ensemble method for robust period detection that combines five different detection approaches and uses majority voting to determine the consensus period.

Usage

sazed(fdataobj, tolerance = 0.1, detrend_method = c("none", "linear", "auto"))

Arguments

fdataobj

An fdata object.

tolerance

Relative tolerance for considering periods equal when voting. Default: 0.1 (10% relative difference). Use smaller values for stricter matching, larger values for more lenient matching.

detrend_method

Detrending method to apply before period estimation:

"none"

No detrending (default)

"linear"

Remove linear trend

"auto"

Automatic AIC-based selection of detrending method

Value

A list of class "sazed_result" with components:

period

Consensus period (average of agreeing components)

confidence

Confidence score (0-1, proportion of agreeing components)

agreeing_components

Number of components that agreed on the period

components

List of individual component estimates:

Details

SAZED combines five detection methods:

  1. Spectral: Finds peaks in the FFT periodogram above the noise floor

  2. ACF Peak: Identifies the first significant peak in the autocorrelation function

  3. ACF Average: Computes a weighted mean of ACF peak locations

  4. Zero-crossing: Estimates period from ACF zero-crossing intervals

  5. Spectral Diff: Applies FFT to first-differenced signal (trend removal)

The final period is chosen by majority voting: periods within the tolerance are grouped together, and the group with the most members determines the consensus. The returned period is the average of the agreeing estimates.

This method is particularly robust because:

  • It requires no tuning parameters (tolerance has sensible defaults)

  • Multiple methods must agree for high confidence

  • Differencing component handles trends automatically

  • Works well across different signal types

See also

estimate.period for single-method estimation, detect.periods for detecting multiple concurrent periods

Examples

# Generate seasonal data with period = 2
t <- seq(0, 20, length.out = 400)
X <- matrix(sin(2 * pi * t / 2) + 0.1 * rnorm(400), nrow = 1)
fd <- fdata(X, argvals = t)

# Detect period using SAZED
result <- sazed(fd)
print(result)  # Shows consensus period and component details
#> SAZED Period Detection
#> ----------------------
#> Period:     2.0029
#> Confidence: 1.00 (5/5 components agree)
#> 
#> Component estimates:
#>   Spectral:      2.0050
#>   ACF Peak:      2.0050
#>   ACF Average:   2.0036
#>   Zero-crossing: 2.0010
#>   Spectral Diff: 2.0000

# With trend - SAZED's spectral_diff component handles this
X_trend <- matrix(0.3 * t + sin(2 * pi * t / 2), nrow = 1)
fd_trend <- fdata(X_trend, argvals = t)
result <- sazed(fd_trend)