fts.cumAC: Cumulative Outer Product Autocovariance Eigendecomposition...

In ottosven/dffm: Approximate Functional Factor Model

Cumulative Outer Product Autocovariance Eigendecomposition for Functional Time Series

Description

This function performs the eigendecomposition of the cumulative outer product autocovariance operator, denoted D, for functional time series. It is used to estimate factors and loadings in the context of the Otto and Salish (2024) approximate factor model.

Usage

fts.cumAC(fdaobj, q0 = 1, start = NULL, end = NULL)

Arguments

fdaobj	An object of class 'fdaobj', typically the output from fda.preprocess, representing preprocessed functional time series data.
q0	The number of cumulative lags to consider in the autocovariance computation. Default is 1.
start	An optional integer specifying the start index for the period over which the eigendecomposition is calculated. If not provided, analysis starts from the beginning of the data series.
end	An optional integer specifying the end index for the period over which the eigendecomposition is calculated. If not provided, analysis goes until the end of the data series.

Value

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

densedata	The dense data from the input object.
workinggrid	The wirkinggrod from the input object.
operator	The operator for which the eigenelements are computed. Here: "cumAC_operator".
scores	The coefficients representing the projections of 'densedata' onto each eigenfunction.
eigenfunctions	A matrix of orthonormal eigenfunctions derived from the cumulative outer product autocovariance operator.
eigenvalues	The eigenvalues associated with each eigenfunction, indicating the autocovariance explained by each eigenfunction.
scores.centered	The projection coefficients after demeaning 'densedata'.
meanfunction	The sample mean function from the input object.
raw.data	The raw data from the input object.
observationgrid	The observation grid from the input object.

Examples

# Example with default settings on a standard working grid
fed = load.fed()
fdaobj = fda.preprocess(data = fed)
fts.cumAC(fdaobj)

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