Principal components in time-series modelling

This paper describes Principal Component Analysis (PCA) used for pre-processing data before training artificial neural networks. Interpretation of the pre-processed data is attempted for time-series data and it is argued that the principal components extracted by linear PCA have an interpretation in the frequency domain. Results are cited showing that a frequency domain interpretation of the eigenvalues and eigenvectors of the autocorrelation matrix is possible for processes with discrete spectral representations. It is argued that it is reasonable to extend this interpretation to broad spectrum processes. Nonlinear methods for PCA are briefly mentioned and there is an introduction to some recent work on kernel PCA, and the relations between PCA, sparsity and smoothing.