A0484
Title: Adaptive wavelet domain principal component analysis for nonstationary time series
Authors: Marina Knight - University of York (United Kingdom) [presenting]
Matthew Nunes - University of Bath (United Kingdom)
Jessica Hargreaves - University of York (United Kingdom)
Abstract: High-dimensional multivariate nonstationary time series, i.e. data whose second-order properties vary over time, are common in many scientific and industrial applications. A novel wavelet domain dimension reduction technique for nonstationary time series is proposed. By constructing a time-scale adaptive principal component analysis of the data, the proposed method is able to capture the salient dynamic features of the multivariate time series. A new time and scale-dependent cross-coherence measure are also introduced, and it is shown to successfully quantify the extent of association between a multivariate nonstationary time series and its proposed wavelet domain principal component representation. Theoretical results establish that the associated estimation scheme enjoys good bias and consistency properties when determining wavelet domain principal components of input data. The proposed method is illustrated using extensive simulations, and its applicability on a real-world dataset arising in a neuroscience study is demonstrated.
