Generalized Spectral Measures of Cross-Dependence

• Activity Number: 285
• Type: Topic Contributed
• Date/Time: Tuesday, August 2, 2011 : 8:30 AM to 10:20 AM
• Sponsor: ENAR
• Author(s): Hernando Ombao*+
• Companies: Brown University
• Keywords: Multivariate time series ; Electroencephalograms ; Coherence ; Spectral Analysis ; Fourier analysis

Abstract

Coherence is one common measure of cross-dependence between components in multivariate time series. Under the classical Cram\'er representation of stochastic processes, cross-coherence at a single frequency $\omega$ is the squared magnitude of the cross-correlation between the random increments at frequency $\omega$ of two time series.It identifies frequency bands that drive linear association between signals. However, classical coherence may not fully capture the dependence in complex signals such as electroencephalograms (EEGs). In this talk, we extend the concept of coherence at a single frequency to coherence at dual frequency (a pair of frequencies) at both contemporaneous and lagged time blocks. Under this novel concept, one may investigate how oscillatory activity at frequency $\omega$ at the (b-1)-th time block predict activity at frequency $\lambda$ at the b-th time block. We develop simple estimators for dual coherence based on replicated trials and derive their asymptotic distributions. Our results generalize the classical results on coherence analysis. These novel measures will be utilized to analyze EEG data recorded during a visual-motor experiment.