Sparse Dynamic Principal Components Analysis in the Frequency Domain

Matt Attard, University of Malta

Co-authors: David Paul Suda, University of Malta; Fiona Sammut, University of Malta

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 variance-covariance 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 l0-penalty. Some preliminary results based on simulated data will be presented, and future research considerations set out.