  Many studies record replicated time series epochs from different groups with
the goal of using frequency domain properties to discriminate between the
groups. In many applications, there exists variation in cyclical patterns from
time series in the same group. Although a number of frequency domain methods
for the discriminant analysis of time series have been explored, there is a
dearth of models and methods that account for within-group spectral
variability. This article proposes a model for groups of time series in which
transfer functions are modeled as stochastic variables that can account for
both between-group and within-group differences in spectra that are identified
from individual replicates. An ensuing discriminant analysis of stochastic
cepstra under this model is developed to obtain parsimonious measures of
relative power that optimally separate groups in the presence of within-group
spectral variability. The approach possess favorable properties in classifying
new observations and can be consistently estimated through a simple
discriminant analysis of a finite number of estimated cepstral coefficients.
Benefits in accounting for within-group spectral variability are empirically
illustrated in a simulation study and through an analysis of gait variability.
