fts.dpca.KLexpansion {freqdom.fda}

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):=\sum_{\ell=1}^L\sum_{k\in\mathbf{Z}} Y_{\ell,t+k} \phi_{\ell k}(u),\quad 1\leq L\leq d,

where \phi_{\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 \phi_{\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