Estimate Seasonal Period using FFT

Estimates the dominant period in functional data using Fast Fourier Transform and periodogram analysis.

Usage

estimate.period(
  fdataobj,
  method = c("fft", "acf"),
  max_lag = NULL,
  detrend_method = c("none", "linear", "auto")
)

Arguments

fdataobj

An fdata object.

method

Method for period estimation: "fft" (Fast Fourier Transform, default) or "acf" (autocorrelation function).

max_lag

Maximum lag for ACF method. Default: half the series length.

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 with components:

period

Estimated period

frequency

Dominant frequency (1/period)

power

Power at the dominant frequency

confidence

Confidence measure (ratio of peak power to mean power)

Details

The function computes the periodogram of the mean curve and finds the frequency with maximum power. The confidence measure indicates how pronounced the dominant frequency is relative to the background.

For data with trends, the detrend_method parameter can significantly improve period estimation accuracy. Strong trends can mask the true seasonal period.

Examples

# Generate seasonal data with period = 2
t <- seq(0, 10, length.out = 200)
X <- matrix(sin(2 * pi * t / 2) + rnorm(200, sd = 0.1), nrow = 1)
fd <- fdata(X, argvals = t)

# Estimate period
result <- estimate.period(fd, method = "fft")
print(result$period)  # Should be close to 2
#> [1] 2.01005

# With trend - detrending improves estimation
X_trend <- matrix(2 + 0.5 * t + sin(2 * pi * t / 2), nrow = 1)
fd_trend <- fdata(X_trend, argvals = t)
result <- estimate.period(fd_trend, detrend_method = "linear")