fda.preprocess: Natural Spline Preprocessing of Funtional Data

In ottosven/dffm: Approximate Functional Factor Model

Natural Spline Preprocessing of Funtional Data

Description

The fda.preprocess function transforms discrete point observations of functional data (functional time series) into functional data evaluated on a dense equidistant grid. This function uses a direct interpolation approach, using natural splines to interpolate missing values. In addition, it performs the eigendecomposition of the sample covariance operator and computes the empirical Karhunen-Loève expansion (empirical functional principal components). Missing values at the beginning or end are reconstructed using the Kneip and Liebl (2020) optimal reconstruction operator.

Usage

fda.preprocess(data, observationgrid = NULL, workinggrid = NULL)

Arguments

data	A multivariate time series or data in 'ts' or 'data.frame' format. The function expects data to represent discrete observations of functional data (functional time series) that may contain missing values.
observationgrid	An optional numeric vector specifying the observation grid of the input data. If NULL (default), the function attempts to infer the grid from column names of 'data'.
workinggrid	An optional numeric vector defining an equidistant grid for the analysis. If NULL (default), the function generates an equidistant grid based on the minimum difference in 'observationgrid'

Value

Returns an object of class 'fdaobj', which includes the following components:

densedata	The data interpolated onto the dense working grid.
workinggrid	The generated or specified dense equidistant working grid.
operator	The operator for which the eigenelements are computed. Here: "sample_covariance(FPC)".
scores	The coefficients representing the projections of 'densedata' onto each eigenfunction.
eigenfunctions	A matrix of orthonormal eigenfunctions derived from the sample covariance operator, representing the functional principal components.
eigenvalues	The eigenvalues associated with each eigenfunction, indicating the variance explained by each principal component.
scores.centered	The projection coefficients after demeaning 'densedata'.
meanfunction	The sample mean function calculated across the dense data.
raw.data	The original input data.
observationgrid	The observation grid used or inferred from the input data.

References

• Hsing, T., & Eubank, R. (2015). Theoretical foundations of functional data analysis, with an introduction to linear operators. John Wiley & Sons.

• Kneip, A., & Liebl, D. (2020). On the optimal reconstruction of partially observed functional data. The Annals of Statistics, 48, 1692-1717.

• Otto, S., & Salish, N. (2024). Approximate Factor Models For Functional Time Series. arXiv:2201.02532.

Examples

# Example with standard working grid
fed = load.fed()
fda.preprocess(data = fed)

# Example with a customized tighter working grid
wg = seq(1,360, by=0.5)
fda.preprocess(fed, workinggrid = wg)

ottosven/dffm documentation built on Feb. 23, 2025, 1:15 p.m.