Detect Amplitude Modulation in Seasonal Time Series

Detects whether the amplitude of a seasonal pattern changes over time (amplitude modulation). Uses either Hilbert transform or wavelet analysis to extract the time-varying amplitude envelope.

Usage

detect_amplitude_modulation(
  fdataobj,
  period,
  method = c("hilbert", "wavelet"),
  modulation_threshold = 0.15,
  seasonality_threshold = 0.3
)

Arguments

fdataobj

An fdata object.

period

Seasonal period in argvals units.

method

Method for amplitude extraction: "hilbert" (default) or "wavelet".

modulation_threshold

Coefficient of variation threshold for detecting modulation. Default: 0.15 (i.e., CV > 15% indicates modulation).

seasonality_threshold

Strength threshold for seasonality detection. Default: 0.3.

Value

A list with components:

is_seasonal

Logical, whether seasonality is detected

seasonal_strength

Overall seasonal strength (spectral method)

has_modulation

Logical, whether amplitude modulation is detected

modulation_type

Character: "stable", "emerging", "fading", "oscillating", or "non_seasonal"

modulation_score

Coefficient of variation of amplitude (0 = stable)

amplitude_trend

Trend in amplitude (-1 to 1): negative = fading, positive = emerging

amplitude_curve

Time-varying amplitude (fdata object)

time_points

Time points for the amplitude curve

Details

The function first checks if seasonality is present using the spectral method (which is robust to amplitude modulation). If seasonality is detected, it extracts the amplitude envelope and analyzes its variation.

Hilbert method: Uses Hilbert transform to compute the analytic signal and extract instantaneous amplitude. Fast but assumes narrowband signals.

Wavelet method: Uses Morlet wavelet transform at the target period. More robust to noise and non-stationarity.

Modulation types:

• stable: Constant amplitude (modulation_score < threshold)

• emerging: Amplitude increases over time (amplitude_trend > 0.3)

• fading: Amplitude decreases over time (amplitude_trend < -0.3)

• oscillating: Amplitude varies but no clear trend

• non_seasonal: No seasonality detected

Examples

# Generate data with emerging seasonality
t <- seq(0, 1, length.out = 200)
amplitude <- 0.2 + 0.8 * t  # Amplitude grows over time
X <- matrix(amplitude * sin(2 * pi * t / 0.2), nrow = 1)
fd <- fdata(X, argvals = t)

result <- detect_amplitude_modulation(fd, period = 0.2)
print(result$modulation_type)  # "emerging"
#> [1] "emerging"
print(result$amplitude_trend)  # Positive value
#> [1] 1

# Compare Hilbert vs Wavelet methods
result_hilbert <- detect_amplitude_modulation(fd, period = 0.2, method = "hilbert")
result_wavelet <- detect_amplitude_modulation(fd, period = 0.2, method = "wavelet")