Dynamic principal component analysis (DPCA) decomposes multivariate time series into uncorrelated components. Compared to classical principal components, DPCA decomposition outputs components which are uncorrelated in time, allowing simpler modeling of the processes and maximizing long run variance of the projection.
a vector time series given as a (T\times d)-matix. Each row corresponds to a timepoint.
window size for the kernel estimator, i.e. a positive integer.
a vector containing frequencies in [-π, π] on which the spectral density should be evaluated.
is the number of principal component filters to compute as in
This convenience function applies the DPCA methodology and returns filters (
dpca.scores), the spectral density (
spectral.density), variances (
Karhunen-Leove expansion (
See the example for understanding usage, and help pages for details on individual functions.
A list containing
scores \quad DPCA scores (
filters \quad DPCA filters (
spec.density \quad spectral density of
var \quad amount of variance explained by dynamic principal components (
Xhat \quad Karhunen-Loeve expansion using
Ndpc dynamic principal components (
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., and Stoffer, D. Time series analysis and its applications: with R examples (2010), Springer Science & Business Media
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X = rar(100,3) # Compute DPCA with only one component res.dpca = dpca(X, q = 5, Ndpc = 1) # Compute PCA with only one component res.pca = prcomp(X, center = TRUE) res.pca$x[,-1] = 0 # Reconstruct the data var.dpca = (1 - sum( (res.dpca$Xhat - X)**2 ) / sum(X**2))*100 var.pca = (1 - sum( (res.pca$x %*% t(res.pca$rotation) - X)**2 ) / sum(X**2))*100 cat("Variance explained by DPCA:\t",var.dpca,"%\n") cat("Variance explained by PCA:\t",var.pca,"%\n")
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