fts.dpca.scores: Functional dynamic principal component scores

View source: R/fts.dpca.scores.R

fts.dpca.scoresR Documentation

Functional dynamic principal component scores


Computes the dynamic principal component scores of a functional time series.


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



a functional time series given as an object of class fd.


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.


The \ell-th dynamic principal components score sequence is defined by

Y_{\ell t}:=∑_{k\in\mathbf{Z}} \int_0^1 φ_{\ell k}(v) X_{t-k}(v)dv,\quad 1≤q \ell≤q d,

where φ_{\ell k}(v) and d are explained in fts.dpca.filters. (The integral is not necessarily restricted to the interval [0,1], this depends on the data.) 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).


A (T\times \code{Ndpc})-matix with Ndpc = dim(dpcs$operators)[1]. The \ell-th column contains the \ell-th dynamic principal component score sequence.


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.scores

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