View source: R/fts.dpca.KLexpansion.R
fts.dpca.KLexpansion | R Documentation |
Computes the dynamic KL expansion up to a given order.
fts.dpca.KLexpansion(X, dpcs = fts.dpca.filters(fts.spectral.density(X)))
X |
a functional time series given as an object of class |
dpcs |
an object of class |
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).
An object of class fd
.
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.KLexpansion
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