dpca.scores: Obtain dynamic principal components scores

In freqdom: Frequency Domain Based Analysis: Dynamic PCA

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}:=∑_{k\in\mathbf{Z}} φ_{\ell k}^\prime X_{t-k},\quad 1≤q \ell≤q d,

where φ_{\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 φ_{\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

freqdom documentation built on Oct. 4, 2022, 5:05 p.m.