fdars (version 0.3.3)

detect.periods: Detect Multiple Concurrent Periods

Description

Detects multiple periodicities in functional data using iterative residual subtraction. At each iteration, the dominant period is detected using FFT, its sinusoidal component is subtracted, and the process repeats on the residual until stopping criteria are met.

Usage

detect.periods(
  fdataobj,
  max_periods = 3,
  min_confidence = 0.5,
  min_strength = 0.2,
  detrend_method = c("auto", "none", "linear")
)

Value

A list with components:

periods

Numeric vector of detected periods

confidence

FFT confidence for each period

strength

Seasonal strength for each period

amplitude

Amplitude of the sinusoidal component

phase

Phase of the sinusoidal component (radians)

n_periods

Number of periods detected

Arguments

fdataobj

An fdata object.

max_periods

Maximum number of periods to detect. Default: 3.

min_confidence

Minimum FFT confidence to continue detection. Default: 0.5.

min_strength

Minimum seasonal strength to continue detection. Default: 0.2.

detrend_method

Detrending method to apply before period detection:

"auto"

Automatic AIC-based selection of detrending method (default)

"none"

No detrending

"linear"

Remove linear trend

Details

The function uses two stopping criteria:

• FFT confidence: How prominent the dominant frequency is

• Seasonal strength: How much variance is explained by the periodicity

Both must exceed their thresholds for detection to continue. Higher thresholds result in fewer (but more reliable) detected periods.

Periods are detected in order of amplitude (FFT power), not period length. A weak yearly cycle will be detected after a strong weekly cycle.

Trends can interfere with period detection. The default "auto" detrending automatically selects an appropriate method to remove trends.

See Also

estimate.period for single period estimation, detrend for standalone detrending

Examples

# Signal with two periods: 2 and 7
t <- seq(0, 20, length.out = 400)
X <- sin(2 * pi * t / 2) + 0.6 * sin(2 * pi * t / 7)
fd <- fdata(matrix(X, nrow = 1), argvals = t)

# Detect multiple periods
result <- detect.periods(fd, max_periods = 3)
print(result$periods)  # Should find approximately 2 and 7
print(result$n_periods)  # Should be 2