R/dpca.scores.R

In freqdom: Frequency Domain Based Analysis: Dynamic PCA

#' Computes dynamic principal component score vectors of a vector time series.
#'
#' The \eqn{\ell}-th dynamic principal components score sequence is defined by
#' \deqn{
#'   Y_{\ell t}:=\sum_{k\in\mathbf{Z}}  \phi_{\ell k}^\prime X_{t-k},\quad 1\leq \ell\leq d,
#' }
#' where \eqn{\phi_{\ell k}} are the dynamic PC filters as explained in  \code{\link{dpca.filters}}. For the sample version the sum extends
#' over the range of lags for which the \eqn{\phi_{\ell k}} are defined. The actual operation carried out is \code{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).
#'
#' @title Obtain dynamic principal components scores
#' @param X a vector time series given as a \eqn{(T\times d)}-matix. Each row corresponds to a timepoint.
#' @param dpcs an object of class \code{timedom}, representing the dpca filters obtained from the sample X. If \code{dpsc = NULL}, then \code{dpcs =
#' dpca.filter(spectral.density(X))} is used.
#' @return A \eqn{T\times} \code{Ndpc}-matix with \code{Ndpc = dim(dpcs$operators)[1]}. The \eqn{\ell}-th column contains the
#' \eqn{\ell}-th dynamic principal component score sequence.
#' @seealso \code{\link{dpca.filters}}, \code{\link{dpca.KLexpansion}}, \code{\link{dpca.var}}
#' @references Hormann, S., Kidzinski, L., and Hallin, M.
#' \emph{Dynamic functional principal components.} Journal of the Royal
#' Statistical Society: Series B (Statistical Methodology) 77.2 (2015): 319-348.
#' @references Brillinger, D.
#' \emph{Time Series} (2001), SIAM, San Francisco.
#' @references Shumway, R.H., and Stoffer, D.S.
#' \emph{Time Series Analysis and Its Applications} (2006), Springer, New York.
#' @keywords DPCA
#' @export
dpca.scores = function(X,dpcs = dpca.filters(spectral.density(X))){
  X %c% dpcs
}