decompose: Seasonal-Trend Decomposition

Description

Decomposes functional data into trend, seasonal, and remainder components. Similar to STL (Seasonal-Trend decomposition using LOESS).

Usage

decompose(
  fdataobj,
  period = NULL,
  method = c("additive", "multiplicative"),
  trend_method = c("loess", "spline"),
  bandwidth = 0.3,
  n_harmonics = 3
)

Value

A list with components:

trend: fdata object with trend component
seasonal: fdata object with seasonal component
remainder: fdata object with remainder/residual
period: Period used for decomposition
method: Decomposition method ("additive" or "multiplicative")

Arguments

fdataobj

An fdata object.

period

Seasonal period. If NULL, estimated automatically using FFT.

method

Decomposition method:

"additive": data = trend + seasonal + remainder (default)

"multiplicative"

data = trend * seasonal * remainder

trend_method

Method for trend extraction: "loess" or "spline". Default: "loess".

bandwidth

Bandwidth for trend extraction (fraction of range). Default: 0.3.

n_harmonics

Number of Fourier harmonics for seasonal component. Default: 3.

Details

For additive decomposition: data = trend + seasonal + remainder. The trend is extracted using LOESS or spline smoothing, then the seasonal component is estimated by fitting Fourier harmonics to the detrended data.

For multiplicative decomposition: data = trend * seasonal * remainder. This is achieved by log-transforming the data, applying additive decomposition, and back-transforming. Use this when the seasonal amplitude grows with the trend level.

Examples

Run this code

# Additive seasonal pattern
t <- seq(0, 20, length.out = 400)
X <- matrix(2 + 0.3 * t + sin(2 * pi * t / 2.5), nrow = 1)
fd <- fdata(X, argvals = t)

result <- decompose(fd, period = 2.5, method = "additive")
# plot(result$trend)      # Linear trend
# plot(result$seasonal)   # Sinusoidal seasonal
# plot(result$remainder)  # Residual noise

# Multiplicative pattern (amplitude grows with level)
X_mult <- matrix((2 + 0.3 * t) * (1 + 0.3 * sin(2 * pi * t / 2.5)), nrow = 1)
fd_mult <- fdata(X_mult, argvals = t)

result_mult <- decompose(fd_mult, period = 2.5, method = "multiplicative")