fdars (version 0.3.3)

stl.fd: STL Decomposition: Seasonal and Trend decomposition using LOESS

Description

Performs STL (Seasonal and Trend decomposition using LOESS) on functional data following Cleveland et al. (1990). This is a robust iterative procedure that separates a time series into trend, seasonal, and remainder components.

Usage

stl.fd(fdataobj, period, s.window = NULL, t.window = NULL, robust = TRUE)

Value

A list of class "stl_result" with components:

trend

fdata object containing trend components

seasonal

fdata object containing seasonal components

remainder

fdata object containing remainder (residual) components

weights

Matrix of robustness weights (1 = full weight, 0 = outlier)

period

The period used

s.window

Seasonal smoothing window used

t.window

Trend smoothing window used

inner.iterations

Number of inner loop iterations

outer.iterations

Number of outer (robustness) iterations

call

The function call

Arguments

fdataobj

An fdata object.

period

Integer. The seasonal period (number of observations per cycle).

s.window

Seasonal smoothing window. Must be odd. If NULL, defaults to 7. Larger values produce smoother seasonal components.

t.window

Trend smoothing window. Must be odd. If NULL, automatically calculated based on period and s.window.

robust

Logical. If TRUE, performs robustness iterations to downweight outliers using bisquare weighting. Default: TRUE.

Details

The STL algorithm proceeds as follows:

Inner Loop (repeated n.inner times):

1. Detrending: Subtract current trend estimate

2. Cycle-subseries smoothing: Smooth values at each seasonal position across cycles

3. Low-pass filtering: Remove high-frequency noise

4. Detrending the smoothed cycle-subseries

5. Deseasonalizing: Subtract seasonal from original data

6. Trend smoothing: Apply LOESS to deseasonalized data

Outer Loop (for robustness):

1. Compute residuals from current decomposition

2. Calculate robustness weights using bisquare function

3. Re-run inner loop with weighted smoothing

STL is particularly effective for:

• Long time series with many cycles

• Data with outliers (when robust=TRUE)

• Slowly changing seasonal patterns

References

Cleveland, R. B., Cleveland, W. S., McRae, J. E., & Terpenning, I. (1990). STL: A Seasonal-Trend Decomposition Procedure Based on Loess. Journal of Official Statistics, 6(1), 3-73.

See Also

decompose, detrend, seasonal.strength

Examples

# Create seasonal data with trend
t <- seq(0, 20, length.out = 400)
period <- 2  # corresponds to 40 observations
period_obs <- 40
X <- matrix(0.05 * t + sin(2 * pi * t / period) + rnorm(length(t), sd = 0.2), nrow = 1)
fd <- fdata(X, argvals = t)

# Perform STL decomposition
result <- stl.fd(fd, period = period_obs)
print(result)

# Plot the decomposition
plot(result)

# Non-robust version (faster but sensitive to outliers)
result_fast <- stl.fd(fd, period = period_obs, robust = FALSE)