Sparse dynamic principal components analysis in the frequency domain

Abstract

The main focus of this paper will be the sparsity treatment of dynamic principal components analysis (DPCA), which is an extension of principal components analysis (PCA) in a time series setting. Several sparse extensions for the high-dimensional data setting have been introduced in the past two decades. However, peer-reviewed literature addressing high-dimensionality in the DPCA setting remains scarce. This study addresses the high-dimensionality problem on the frequency-domain variant of DPCA, which replicates the classical dynamic approach on cross-spectra, the frequency domain analogue of the variancecovariance matrix. Taking cue from literature in sparse PCA, this research seeks to extend these methods on the frequency-domain DPCA via the cross-spectrum. The method being proposed is based on sparse eigenvector extraction from cross-spectral matrices with the la-penalty. Some preliminary results based on simulated data will be presented, and future research considerations set out.