Modeling Evolution of Spectral Properties in Stationary Processes of Varying Dimensions

• Activity Number: 457 - Novel Statistical Approaches to Time Series of Networks
• Type: Topic Contributed
• Date/Time: Wednesday, July 31, 2019 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Raanju Sundararajan* and Hernando Ombao
• Companies: King Abdullah University of Science and Technology and King Abdullah University of Science and Technology (KAUST)
• Keywords: multivariate time series; spectral domain; nonstationarity; local field potential

Abstract

Analysis of multivariate time series, stationary and nonstationary, often involves a linear decomposition of the observed series into latent sources. Methods like PCA, ICA and Stationary Subspace Analysis (SSA) assume the observed multivariate process is linearly generated by latent sources that can be stationary or nonstationary. Neuroscience experiements typically involve multivariate time series data from several epochs, with the assumption that in each epoch there exists a certain number of latent stationary sources. Realistically, the dimension of these latent stationary sources should be allowed to change across epochs thereby making the overall analysis challenging. Motivated by such experiments, we develop a method to compare the spread of spectral information in several multivariate stationary processes with different dimensions. A statistic, blind to the dimension of the stationary process, is proposed to capture the spread of spectral information in various frequency ranges and its asymptotic properties are derived. We discuss an application of the proposed method in discriminating local field potential of rats recorded before and after the occurrence of induced stroke.