detrend: Remove Trend from Functional Data

Description

Removes trend from functional data using various methods. This is useful for preprocessing data before seasonal analysis when the data has a significant trend component.

Usage

detrend(
  fdataobj,
  method = c("linear", "polynomial", "diff1", "diff2", "loess", "auto"),
  degree = 2,
  bandwidth = 0.3,
  return_trend = FALSE
)

Value

If return_trend = FALSE, an fdata object with detrended data. If return_trend = TRUE, a list with components:

detrended: fdata object with detrended data
trend: fdata object with estimated trend
method: Method used for detrending
rss: Residual sum of squares per curve

Arguments

fdataobj

An fdata object.

method

Detrending method:

"linear": Least squares linear fit (default)

"polynomial"

Polynomial regression of specified degree

"diff1"

First-order differencing

"diff2"

Second-order differencing

"loess"

Local polynomial regression (LOESS)

"auto"

Automatic selection via AIC

degree

Polynomial degree for "polynomial" method. Default: 2.

bandwidth

Bandwidth as fraction of data range for "loess" method. Default: 0.3.

return_trend

Logical. If TRUE, return both trend and detrended data. Default: FALSE.

Details

For series with polynomial trends, "linear" or "polynomial" methods are appropriate. For more complex trends, "loess" provides flexibility. The "auto" method compares linear, polynomial (degree 2 and 3), and LOESS, selecting the method with lowest AIC.

Differencing methods ("diff1", "diff2") reduce the series length by 1 or 2 points respectively. The resulting fdata has correspondingly shorter argvals.

Examples

Run this code

# Generate data with linear trend and seasonal component
t <- seq(0, 10, length.out = 200)
X <- matrix(2 + 0.5 * t + sin(2 * pi * t / 2), nrow = 1)
fd <- fdata(X, argvals = t)

# Detrend with linear method
fd_detrended <- detrend(fd, method = "linear")

# Now estimate period on detrended data
period <- estimate.period(fd_detrended)
print(period$period)  # Should be close to 2

# Get both trend and detrended data
result <- detrend(fd, method = "linear", return_trend = TRUE)
# plot(result$trend)  # Shows the linear trend