fts.dpca.var: Proportion of variance explained by dynamic principal...

In kidzik/fda.ts: Functional Time Series: Dynamic Functional Principal Components

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 [-π,π].

Details

Consider a spectral density operator \mathcal{F}_ω and let λ_\ell(ω) by the \ell-th dynamic eigenvalue. The proportion of variance described by the \ell-th dynamic principal component is given as v_\ell:=\int_{-π}^π λ_\ell(ω)dω/\int_{-π}^π \mathrm{tr}(\mathcal{F}_ω)dω. 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

kidzik/fda.ts documentation built on April 19, 2022, 5:34 a.m.