Dependence Among Spectral-Based Measures Through Copulas: Theoretical Framework and Research on Change-Points

• Activity Number: 173 - Recent Advances on Neuroimaging Analysis
• Type: Contributed
• Date/Time: Monday, July 30, 2018 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics in Imaging
• Author(s): Charles Fontaine* and Hernando Ombao and Yongxin Zhu
• Companies: King Abdullah University of Science and Technology and King Abdullah University of Science and Technology and King Abdullah University of Science and Technology
• Keywords: Parametric copulas; Fourier transforms; Permutation tests; Neuroimaging

Abstract

Analysis of multiple time series is a common task in brain sciences and finance. The key point is to assess the dependence between these time series and to detect any change in such dependencies. The first objective here is to consider an approach to express standard copulas when time series are expressed using spectral-based quantities under stationarity. We express the dependence with a function of the coherence measure between signals for elliptic models and with a rank-based coherence measure for the Archimedean ones. We present the necessary theoretical background and our detailed methodology for a goodness-of-fit of rank-based coherence measure. The second objective is to present a theoretical framework for two main applications. The first is detecting any breakpoint in the spectra across the epochs in the trend of a specific frequency band using a permutation test. The second is to detect the change in the dependence between two brain channels, at specific frequencies, as a result of introducing a shock to the time series. This work is illustrated to local field potentials in rats to study the impact of stroke on dependence between different neuronal sub-populations.