dpca.scores {freqdom}

Obtain dynamic principal components scores

Description

Computes dynamic principal component score vectors of a vector time series.

Usage

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

Arguments

X

a vector time series given as a (T\times d)-matix. Each row corresponds to a timepoint.

dpcs

an object of class timedom, representing the dpca filters obtained from the sample X. If dpsc = NULL, then dpcs = dpca.filter(spectral.density(X)) is used.

Details

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

Y_{\ell t}:=\sum_{k\in\mathbf{Z}} \phi_{\ell k}^\prime X_{t-k},\quad 1\leq \ell\leq d,

where \phi_{\ell k} are the dynamic PC filters as explained in dpca.filters. For the sample version the sum extends over the range of lags for which the \phi_{\ell k} are defined. The actual operation carried out is filter.process(X, A = dpcs).

We for more details we refer to Chapter 9 in Brillinger (2001), Chapter 7.8 in Shumway and Stoffer (2006) and to Hormann et al. (2015).

Value

A T\times 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.

Brillinger, D. Time Series (2001), SIAM, San Francisco.

Shumway, R.H., and Stoffer, D.S. Time Series Analysis and Its Applications (2006), Springer, New York.

See Also

dpca.filters, dpca.KLexpansion, dpca.var