Modeling Spectral Properties in Stationary Processes of Varying Dimensions with Applications to Brain Local Field Potential Signals

TL;DR

This paper introduces a spectral ratio method to analyze changes in the complexity of multivariate stationary processes, exemplified by brain signals from rats before and after stroke, capturing spectral information across frequencies.

Contribution

The paper develops a dimension-blind spectral ratio statistic for analyzing spectral information in multivariate stationary processes, with applications to brain signals and complexity tracking.

Findings

Spectral information in the beta band changed significantly post-stroke.

The FS-ratio effectively captures spectral complexity independent of process dimension.

Application to rat LFP signals demonstrated the method's utility in neurological studies.

Abstract

A common class of methods for analyzing of multivariate time series, stationary and nonstationary, decomposes the observed series into latent sources. Methods such as principal compoment analysis (PCA), independent component analysis (ICA) and Stationary Subspace Analysis (SSA) assume the observed multivariate process is generated by latent sources that are stationary or nonstationary. We develop a method that tracks changes in the complexity of a 32-channel local field potential (LFP) signal from a rat following an experimentally induced stroke. We study complexity through the latent sources and their dimensions that can change across epochs due to an induced shock to the cortical system. Our method compares the spread of spectral information in several multivariate stationary processes with different dimensions. A frequency specific spectral ratio (FS-ratio) statistic is proposed and its asymptotic properties are derived. The FS-ratio is blind to the dimension of the stationary process and captures the proportion of spectral information in various (user-specified) frequency bands. We apply our method to study differences in complexity and structure of the LFP before and after system shock. The analysis indicates that spectral information in the beta frequency band (12-30 Hertz) demonstrated the greatest change in structure and complexity due to the stroke.