  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.
