# fts.dpca.scores: Functional dynamic principal component scores In freqdom.fda: Functional Time Series: Dynamic Functional Principal Components

 fts.dpca.scores R Documentation

## Functional dynamic principal component scores

### Description

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

### Usage

fts.dpca.scores(X, dpcs = fts.dpca.filters(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

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).

### Value

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.

### 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.

The multivariate equivalent in the freqdom package: dpca.scores