View source: R/fts.dpca.scores.R
fts.dpca.scores | R Documentation |
Computes the dynamic principal component scores of a functional time series.
fts.dpca.scores(X, dpcs = fts.dpca.filters(spectral.density(X)))
X |
a functional time series given as an object of class |
dpcs |
an object of class |
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.
The multivariate equivalent in the freqdom
package: dpca.scores
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