fts.dpca.KLexpansion: Dynamic KL expansion

In freqdom.fda: Functional Time Series: Dynamic Functional Principal Components

Dynamic KL expansion

Description

Computes the dynamic KL expansion up to a given order.

Usage

fts.dpca.KLexpansion(X, dpcs = fts.dpca.filters(fts.spectral.density(X)))

Arguments

X	a functional time series given as an object of class fd.
dpcs	an object of class fts.timedom, representing the dpca filters obtained from the sample X. If dpsc = NULL, then dpcs = fts.dpca.filter(fts.spectral.density(X)) is used.

Details

This function computes the L-order dynamic functional principal components expansion, defined by

\hat{X}_{t}^L(u):=∑_{\ell=1}^L∑_{k\in\mathbf{Z}} Y_{\ell,t+k} φ_{\ell k}(u),\quad 1≤q L≤q d,

where φ_{\ell k}(v) and d are explained in fts.dpca.filters and Y_{\ell k} are the dynamic functional PC scores as in fts.dpca.scores. For the sample version the sum extends over the range of lags for which the φ_{\ell k} are defined.

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

Value

An object of class fd.

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.KLexpansion

freqdom.fda documentation built on April 19, 2022, 1:06 a.m.