Title: Addressing high-dimensionality for dynamic principal components analysis in the frequency domain Authors:  David Paul Suda - University of Malta (Malta) [presenting]
Matthew Attard - University of Malta (Malta)
Fiona Sammut - University of Malta (Malta)
Dan Vilenchik - Ben-Gurion University (Israel)
Abstract: Dynamic principal components analysis refers to a class of dimension reduction methods of multivariate data in a time series setting. These methods are important as they address the handling of time-dependence and/or short-term correlation, which classical principal components analysis does not cater for. Brillinger's frequency domain approach is the earliest of such approaches and is aimed at a single realisation setting. In the last decade, time-domain approaches have also evolved, addressing both the single realisation and multiple realisation settings. Authors of the latter two approaches have also introduced a sparsity extension, which allows one to generalise these approaches to the high-dimensional data setting. Peer-reviewed literature addressing high-dimensionality in the frequency domain setting remains missing. The frequency domain approach to principal components essentially replicates the classical approach but on cross-spectra instead of the covariance matrix, ultimately recuperating the loadings through the Fourier inverse and the principal components through the dynamic Karhunen-Loeve expansion. The aim is to address the void concerning high-dimensionality in academic literature when it comes to frequency-domain principal components. This can be done by applying techniques for addressing sparsity in the static case, which can be readily adapted to the frequency-domain approach. Some preliminary results on real or simulated data are expected to be presented.