fts.dpca.var {freqdom.fda}R Documentation

Proportion of variance explained by dynamic principal components

Description

Computes the proportion and cumulative proportion of variance explained by dynamic principal components.

Usage

fts.dpca.var(F)

Arguments

F

spectral density operator, provided as an object of class fts.freqdom. To guarantee accuracy of numerical integration it is important that F$freq is a dense grid of frequencies in [-\pi,\pi].

Details

Consider a spectral density operator \mathcal{F}_\omega and let \lambda_\ell(\omega) by the \ell-th dynamic eigenvalue. The proportion of variance described by the \ell-th dynamic principal component is given as v_\ell:=\int_{-\pi}^\pi \lambda_\ell(\omega)d\omega/\int_{-\pi}^\pi \mathrm{tr}(\mathcal{F}_\omega)d\omega. This function numerically computes the vectors (v_\ell).

For more details we refer to Hormann et al. (2015).

Value

A vector containing the v_\ell.

References

Hormann, S., Kidzinski, L., and Hallin, M. Dynamic functional principal components. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 77.2 (2015): 319-348.

See Also

The multivariate equivalent in the freqdom package: dpca.var


[Package freqdom.fda version 1.0.1 Index]