Measure Seasonal Strength

Computes the strength of seasonality in functional data. Values range from 0 (no seasonality) to 1 (pure seasonal signal).

Usage

seasonal.strength(
  fdataobj,
  period = NULL,
  method = c("variance", "spectral", "wavelet"),
  n_harmonics = 3,
  detrend_method = c("none", "linear", "auto")
)

Arguments

fdataobj

An fdata object.

period

Known or estimated period. If NULL, period is estimated automatically using FFT.

method

Method for computing strength:

"variance"

Variance decomposition: Var(seasonal) / Var(total)

"spectral"

Spectral: power at seasonal frequencies / total power

"wavelet"

Wavelet: Morlet wavelet power at seasonal period / total variance

n_harmonics

Number of Fourier harmonics to use (for variance method). Default: 3.

detrend_method

Detrending method to apply before computing strength:

"none"

No detrending (default)

"linear"

Remove linear trend

"auto"

Automatic AIC-based selection of detrending method

Value

A numeric value between 0 and 1 representing seasonal strength.

Details

The variance method decomposes the signal into a seasonal component (using Fourier basis with the specified period) and computes the proportion of variance explained by the seasonal component.

The spectral method computes the proportion of total spectral power that falls at the seasonal frequency and its harmonics.

The wavelet method uses a Morlet wavelet to measure power at the target period. It provides time-localized frequency information and is robust to non-stationary signals.

Trends can artificially lower the seasonal strength measure by contributing non-seasonal variance. Use detrend_method to remove trends before computing strength.

Examples

# Pure seasonal signal
t <- seq(0, 10, length.out = 200)
X <- matrix(sin(2 * pi * t / 2), nrow = 1)
fd_seasonal <- fdata(X, argvals = t)
seasonal.strength(fd_seasonal, period = 2)  # Should be close to 1
#> [1] 1

# Pure noise
X_noise <- matrix(rnorm(200), nrow = 1)
fd_noise <- fdata(X_noise, argvals = t)
seasonal.strength(fd_noise, period = 2)  # Should be close to 0
#> [1] 0.02096016

# Trending data - detrending improves strength estimate
X_trend <- matrix(2 + 0.5 * t + sin(2 * pi * t / 2), nrow = 1)
fd_trend <- fdata(X_trend, argvals = t)
seasonal.strength(fd_trend, period = 2, detrend_method = "linear")
#> [1] 0.9763512