select.basis.auto: Automatic Per-Curve Basis Type and Number Selection

Description

Selects the optimal basis type (Fourier or P-spline) and number of basis functions for each curve individually using model selection criteria. This is useful when working with mixed datasets containing both seasonal and non-seasonal curves.

Usage

select.basis.auto(
  fdataobj,
  criterion = c("GCV", "AIC", "BIC"),
  nbasis.range = NULL,
  lambda.pspline = NULL,
  use.seasonal.hint = TRUE
)

Value

A list of class "basis.auto" with:

basis.type: Character vector ("pspline" or "fourier") for each curve
nbasis: Integer vector of selected nbasis per curve
score: Numeric vector of best criterion scores
coefficients: List of coefficient vectors for each curve
fitted: fdata object with fitted values
edf: Numeric vector of effective degrees of freedom
seasonal.detected: Logical vector indicating detected seasonality
lambda: Numeric vector of lambda values (NA for Fourier curves)
criterion: Character string of criterion used
original: Original fdata object

Arguments

fdataobj: An fdata object.
criterion: Model selection criterion: "GCV" (default), "AIC", or "BIC".
nbasis.range: Optional numeric vector of length 2 specifying c(min, max) for nbasis search range. If NULL, automatic ranges are used: Fourier 3-25, P-spline 6-40 (or limited by data length).
lambda.pspline: Smoothing parameter for P-splines. If NULL (default), lambda is automatically selected from a grid for each curve.
use.seasonal.hint: Logical. If TRUE (default), uses FFT-based seasonality detection to inform basis preference. Seasonal curves start Fourier search from 5 basis functions.

Details

For each curve, the function searches over:

Fourier basis: odd nbasis values from 3 (or 5 if seasonal) to min(m/3, 25)
P-spline basis: nbasis from 6 to min(m/2, 40), with lambda from grid {0.001, 0.01, 0.1, 1, 10, 100} if lambda.pspline is NULL

The function uses parallel processing (via Rust/rayon) for efficiency when processing multiple curves.

Examples

Run this code

# Generate mixed data: some seasonal, some polynomial
set.seed(42)
t <- seq(0, 10, length.out = 100)

# 3 seasonal curves
X_seasonal <- matrix(0, 3, 100)
for (i in 1:3) {
  X_seasonal[i, ] <- sin(2 * pi * t / 2.5) + rnorm(100, sd = 0.2)
}

# 3 polynomial curves
X_poly <- matrix(0, 3, 100)
for (i in 1:3) {
  X_poly[i, ] <- 0.1 * t^2 - t + rnorm(100, sd = 0.5)
}

fd <- fdata(rbind(X_seasonal, X_poly), argvals = t)

# Auto-select optimal basis for each curve
result <- select.basis.auto(fd)
print(result)

# Should detect: first 3 as Fourier, last 3 as P-spline
table(result$basis.type)