This package provides a fast and reliable implementation of Brillinger's dynamic principal component analysis. The main use case is estimation of Generalized Dynamic Factor Models (Forni & Lippi, 2001, Forni, Hallin, Lippi and Reichlin, 2000).

At its core, this package features multivariate spectral density estimation based on the lag-window estimator. Based on an estimated spectrum, dynamic principal components are computed using an efficient numerical procedure for eigenvalue/eigenvector decomposition (Implicitly Restarted Arnoldi Method).

Moreover, dpca implements the method to select the number of dynamic principal components of Hallin & Liska (2007). Also the information criteria by Bai & Ng, 2003 are implemented, with the additional feature that the constant multplier in the penalty term is chosen in a data-driven way analogously to Hallin & Liska (2007).

• Estimation of multivariate spectral density using lag-window technique.
• Fast computation of dynamic eigenvalues/eigenvectors of spectrum using ARPACK.
• Discrete fourier transformation to obtain filters/transfer functions.
• The selection criterion of Hallin & Liska (2007) to determine the number of dynamic factors.
• Ship ARPACK.
• Interface to common time series data formats (zoo, ts).
• One-Sided representation of the the dynamic common component using the approach of Forni, Hallin, Lippi, Zaffaroni (2015).
• Forecasting methods.
• Model assessment.

We are aware of the R package freqdom, developed by Siegfried Hörmann and Lukas Kidzinsiki which is a pure R implementation. dpca is written mainly in C. Although providing a similiar interface to that of freqdom, dpca has some unique features apart from being much faster.

For instance, the convoluted filter which computes the dynamic common component from the output in freqdom is obtained by filtering the output twice: first to get the inputs (what in freqdom is called "scores" in analogy to their FDA context) and, second these inputs are filtered again to get the dynamic common component ("KLexpansion"). dpca computes the convolution in the frequency domain. The advantage of this approach is that this filter is invariant with respect to multiplications of dynamic eigenvectors by a unit-length complex number.

dpca depends on ARPACK to compute dynamic eigenvalues/eigenvectors using the Implicitly Restarted Arnoldi Method which is much faster than R's base::eigen() whenever a truncated instead of the full spectral decomposition is required. ARPACK is shipped with dpca.

To install dpca using devtools:

devtools::install_github("https://github.com/christophrust/dpca.git")

set.seed(123456)

## simulate some data
nrx <- 100L
ncx <- 1000L
q <- 4L

epsilon <- matrix(rnorm((ncx + 10) * q), nrow = q)

filter_coefs <- vapply(1:10, function(l) {
  matrix(rnorm(q * nrx, sd = 1/l), nrx, q)
}, matrix(0, nrx, q))

chi1 <- multivariate_filter(epsilon, filter_coefs, 1:10)

x <- chi + rnorm(nrx * ncx, sd = 0.1 * sd(chi))
bw <- floor(ncol(x)^(1/3))

dpc <- dpca(x, q = q, bandwidth = bw)
str(dpc)