Matthew Nunes (University of Bath) – Adaptive Principal Component Analysis for Multivariate Nonstationary Time Series

Abstract: High-dimensional multivariate nonstationary time series are commonly observed in many scientific and industrial applications. In this work, we introduce a novel wavelet-domain dimension reduction technique that constructs time-scale adaptive principal components, as well as a new between-domain cross-coherence measure. The new tools are shown to successfully capture the salient dynamic features of the data as well as quantify the extent of its association with the new representation. We establish theoretical and numerical results on the technique, and demonstrate the tools on a dataset arising in a neuroscience study. This is joint work with Marina Knight and Jessica Hargreaves (University of York).